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, Available online , doi: 10.11883/bzycj-2025-0288
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Strut-based lattice metamaterials are a category of ultra-lightweight, load-bearing, and energy-absorbing materials with broad application prospects in fields such as impact protection, aerospace engineering, and lightweight structural design. Benefiting from their unique periodic architectures and adjustable meso-structural parameters, these materials exhibit exceptional mechanical tunability and multifunctional potential. However, due to the extensive parameter space of mesoscopic configurations and the highly nonlinear correlation between the structural geometry and the mechanical response, the optimization of mechanical performance for lattice metamaterials remains a formidable challenge. Based on the meso-structural characteristics of strut-based lattice metamaterials, an efficient rapid digital modeling method was proposed. A Python script coupled with Abaqus software was utilized for the rapid modeling of truss lattice metamaterials and fast calculations about the mechanical properties of the metamaterials. Based on the calculation results, a machine learning dataset was constructed. Three types of truss lattice structures were randomly selected and additively manufactured. Quasi-static compression tests on these three lattice structures were conducted using a universal testing machine to verify the reliability of the dataset. Subsequently, an artificial neural network (ANN) was trained to rapidly predict the mechanical properties of the truss lattice metamaterials. Focusing on the load-bearing capacity, energy absorption capability, and the concurrent optimization of both, a non-dominated sorting genetic algorithm II (NSGA-Ⅱ) was employed. The well-trained ANN served as a surrogate model embedded within NSGA-II. Lattice configurations that exhibited high load-bearing capacity and superior energy absorption characteristics were generated by the optimization process. These configurations also achieved a balance between load-bearing and energy-absorption performance, facilitating the optimization design of truss lattice metamaterials. Additionally, simulation validations confirmed the reliability of the optimization outcomes, demonstrating the effectiveness of integrating ANN with evolutionary algorithms for the advanced design of metamaterials. By integrating machine learning with numerical simulations, the computational cost of optimization design was effectively reduced, offering support for the rapid performance optimization and customized design of complex lattice metamaterials.
Strut-based lattice metamaterials are a category of ultra-lightweight, load-bearing, and energy-absorbing materials with broad application prospects in fields such as impact protection, aerospace engineering, and lightweight structural design. Benefiting from their unique periodic architectures and adjustable meso-structural parameters, these materials exhibit exceptional mechanical tunability and multifunctional potential. However, due to the extensive parameter space of mesoscopic configurations and the highly nonlinear correlation between the structural geometry and the mechanical response, the optimization of mechanical performance for lattice metamaterials remains a formidable challenge. Based on the meso-structural characteristics of strut-based lattice metamaterials, an efficient rapid digital modeling method was proposed. A Python script coupled with Abaqus software was utilized for the rapid modeling of truss lattice metamaterials and fast calculations about the mechanical properties of the metamaterials. Based on the calculation results, a machine learning dataset was constructed. Three types of truss lattice structures were randomly selected and additively manufactured. Quasi-static compression tests on these three lattice structures were conducted using a universal testing machine to verify the reliability of the dataset. Subsequently, an artificial neural network (ANN) was trained to rapidly predict the mechanical properties of the truss lattice metamaterials. Focusing on the load-bearing capacity, energy absorption capability, and the concurrent optimization of both, a non-dominated sorting genetic algorithm II (NSGA-Ⅱ) was employed. The well-trained ANN served as a surrogate model embedded within NSGA-II. Lattice configurations that exhibited high load-bearing capacity and superior energy absorption characteristics were generated by the optimization process. These configurations also achieved a balance between load-bearing and energy-absorption performance, facilitating the optimization design of truss lattice metamaterials. Additionally, simulation validations confirmed the reliability of the optimization outcomes, demonstrating the effectiveness of integrating ANN with evolutionary algorithms for the advanced design of metamaterials. By integrating machine learning with numerical simulations, the computational cost of optimization design was effectively reduced, offering support for the rapid performance optimization and customized design of complex lattice metamaterials.
, Available online , doi: 10.11883/bzycj-2025-0103
Abstract:
To accurately characterize the stress-strain constitutive relationship of metal materials under high strain-rate conditions, a novel, high-precision constitutive-relationship-prediction model based on Graph Neural Networks (GNNs) and Kolmogorov-Arnold Networks (KANs) was developed. Traditional Johnson-Cook (JC) models often fail to account for the coupling effects among temperature, strain rate, and strain, all of which are crucial for describing the dynamic behavior of materials under extreme conditions. This limitation was addressed by constructing graph-structured data in the GNN model to capture the nonlinear correlations of multidimensional parameters and by leveraging the Kolmogorov-Arnold theorem in the KAN model to achieve precise mapping of high-dimensional input spaces. The research methodology involved several key steps. Experimental data from ODS copper subjected to high-strain-rate compression were collected using a split Hopkinson pressure bar (SHPB) system and subsequently preprocessed. The dataset included temperature, strain rate, strain, and stress. In the GNN model, when temperature and strain rate were held constant, nodes were connected sequentially based on strain values to form edges. When temperature was held constant, a reasonable threshold was established between nodes with adjacent strain rates, and nodes within this threshold were connected to form edges. The GNN employed a Message Passing Neural Network (MPNN) architecture to learn and predict material properties. Model parameters were optimized using the Adam optimizer, with the Root Mean Squared Error (RMSE) serving as the loss function. The KAN model was constructed based on the Kolmogorov-Arnold representation theorem and consisted of multiple KAN-Linear layers. Each KAN-Linear unit included base weights and spline weights. Base weights handled linear relationships through traditional linear transformations, while spline weights managed nonlinear mappings via B-spline interpolation. Both models were trained on the preprocessed dataset, and their performance was evaluated using metrics such as the Mean Relative Error (MRE), Root Mean Squared Error (RMSE), and the coefficient of determination (R2). The GNN model achieved an average MRE of 9.2% with an R2 value exceeding 0.95, while the KAN model recorded an MRE of 9.1% with a similar R2 value. Both models significantly outperformed the JC model, which had an MRE of 38% and an R2 value of 0.75. Furthermore, the predictive capabilities of the GNN and KAN models were validated through finite element simulations. The simulation results demonstrated that the stress-strain distributions predicted by the GNN and KAN models were more consistent with theoretical expectations compared to those predicted by the JC model, particularly in capturing the material's softening phase. The findings highlight the potential of integrating advanced machine - learning techniques, such as GNNs and KANs, into the field of materials science to enhance the accuracy and efficiency of constitutive modeling. These models offer a promising alternative to traditional empirical models and hold significant implications for engineering applications in aerospace, automotive, and other industries where materials are subjected to high strain rates.
To accurately characterize the stress-strain constitutive relationship of metal materials under high strain-rate conditions, a novel, high-precision constitutive-relationship-prediction model based on Graph Neural Networks (GNNs) and Kolmogorov-Arnold Networks (KANs) was developed. Traditional Johnson-Cook (JC) models often fail to account for the coupling effects among temperature, strain rate, and strain, all of which are crucial for describing the dynamic behavior of materials under extreme conditions. This limitation was addressed by constructing graph-structured data in the GNN model to capture the nonlinear correlations of multidimensional parameters and by leveraging the Kolmogorov-Arnold theorem in the KAN model to achieve precise mapping of high-dimensional input spaces. The research methodology involved several key steps. Experimental data from ODS copper subjected to high-strain-rate compression were collected using a split Hopkinson pressure bar (SHPB) system and subsequently preprocessed. The dataset included temperature, strain rate, strain, and stress. In the GNN model, when temperature and strain rate were held constant, nodes were connected sequentially based on strain values to form edges. When temperature was held constant, a reasonable threshold was established between nodes with adjacent strain rates, and nodes within this threshold were connected to form edges. The GNN employed a Message Passing Neural Network (MPNN) architecture to learn and predict material properties. Model parameters were optimized using the Adam optimizer, with the Root Mean Squared Error (RMSE) serving as the loss function. The KAN model was constructed based on the Kolmogorov-Arnold representation theorem and consisted of multiple KAN-Linear layers. Each KAN-Linear unit included base weights and spline weights. Base weights handled linear relationships through traditional linear transformations, while spline weights managed nonlinear mappings via B-spline interpolation. Both models were trained on the preprocessed dataset, and their performance was evaluated using metrics such as the Mean Relative Error (MRE), Root Mean Squared Error (RMSE), and the coefficient of determination (R2). The GNN model achieved an average MRE of 9.2% with an R2 value exceeding 0.95, while the KAN model recorded an MRE of 9.1% with a similar R2 value. Both models significantly outperformed the JC model, which had an MRE of 38% and an R2 value of 0.75. Furthermore, the predictive capabilities of the GNN and KAN models were validated through finite element simulations. The simulation results demonstrated that the stress-strain distributions predicted by the GNN and KAN models were more consistent with theoretical expectations compared to those predicted by the JC model, particularly in capturing the material's softening phase. The findings highlight the potential of integrating advanced machine - learning techniques, such as GNNs and KANs, into the field of materials science to enhance the accuracy and efficiency of constitutive modeling. These models offer a promising alternative to traditional empirical models and hold significant implications for engineering applications in aerospace, automotive, and other industries where materials are subjected to high strain rates.
, Available online , doi: 10.11883/bzycj-2024-0488
Abstract:
Regarding the displacement response of clamped circular plates under multiple far-field blast loads, we proposes a novel theoretical modeling approach based on membrane theory energy equations, by simplifying multiple blast loads into linearly decaying pulse sequences, a theoretical displacement response model for clamped circular plates is established for the first time, considering both strain rate strengthening effects and cumulative hardening effects. The linear displacement field approximation is adopted for the initial loading phase, while a quadratic function displacement field assumption is introduced for subsequent loading phases, deriving recursive formulas for midpoint displacements under multiple blasts. Numerical validations were conducted using LS-DYNA for both double and triple blast scenarios. For double blast cases, theoretical predictions exhibited errors of 20%–30% compared to simulation results, while errors reduced to below 20% for triple blast conditions. The ASTM A415 steel circular plate model was used for the simulations, and the strain rate strengthening effect was described by the Cowper-Symonds model. Finite element models with quadrilateral shell elements demonstrated strong agreement with experimental data (errors <10%), confirming model reliability. The assumption of quadratic function displacement field for subsequent loading phases was verified by numerical displacement curves of the middle profiles of the plates. Further parametric analysis proved that the theoretical model is effective for different tangent modulus, which represents the strength of the strain strengthening effect. The model reveals that midpoint displacement can be characterized as a weighted square root function combining the final explosion’s individual displacement and prior cumulative displacement, with displacement increments from subsequent explosions decreasing as prior cumulative displacement increases. This study provides the first closed-form solution for multi-blast displacement prediction, addressing a critical gap in theoretical blast dynamics. This theoretical framework provides fundamental support for multiple blast damage assessments, unveils nonlinear cumulative damage growth characteristics, and offers guidance for optimizing explosive attack strategies.
Regarding the displacement response of clamped circular plates under multiple far-field blast loads, we proposes a novel theoretical modeling approach based on membrane theory energy equations, by simplifying multiple blast loads into linearly decaying pulse sequences, a theoretical displacement response model for clamped circular plates is established for the first time, considering both strain rate strengthening effects and cumulative hardening effects. The linear displacement field approximation is adopted for the initial loading phase, while a quadratic function displacement field assumption is introduced for subsequent loading phases, deriving recursive formulas for midpoint displacements under multiple blasts. Numerical validations were conducted using LS-DYNA for both double and triple blast scenarios. For double blast cases, theoretical predictions exhibited errors of 20%–30% compared to simulation results, while errors reduced to below 20% for triple blast conditions. The ASTM A415 steel circular plate model was used for the simulations, and the strain rate strengthening effect was described by the Cowper-Symonds model. Finite element models with quadrilateral shell elements demonstrated strong agreement with experimental data (errors <10%), confirming model reliability. The assumption of quadratic function displacement field for subsequent loading phases was verified by numerical displacement curves of the middle profiles of the plates. Further parametric analysis proved that the theoretical model is effective for different tangent modulus, which represents the strength of the strain strengthening effect. The model reveals that midpoint displacement can be characterized as a weighted square root function combining the final explosion’s individual displacement and prior cumulative displacement, with displacement increments from subsequent explosions decreasing as prior cumulative displacement increases. This study provides the first closed-form solution for multi-blast displacement prediction, addressing a critical gap in theoretical blast dynamics. This theoretical framework provides fundamental support for multiple blast damage assessments, unveils nonlinear cumulative damage growth characteristics, and offers guidance for optimizing explosive attack strategies.
, Available online , doi: 10.11883/bzycj-2025-0243
Abstract:
In the field of material dynamic mechanical properties research, it is significant to obtain reliable data of materials under complex stress states. To address the challenge of achieving a stable stress ratio during combined loading, this work developed a novel device based on the electromagnetic Hopkinson bar (ESHB) platform. This device uniquely enables unilateral synchronous tension/compression-torsion combined dynamic loading. The paper detailed the device’s configuration and loading principles. The core innovation of this device is the independent generation of trapezoidal tensile/compressive and torsional stress waves. A multi-circuit pulse shaper produced tensile/compressive waves, while shear waves were generated using an electromagnetic clamp with torque storage. Crucially, a high-precision digital delay generator (DDG) ensured wave synchronization. With triggering accuracy within 0.1 μs, it controlled the arrival time difference of these distinct waves at the specimen to within 5 μs. This overcame the challenge posed by their different propagation velocities. Additionally, it described the synchronization control methodology and the wave propagation analysis essential for timing calculations. To validate the apparatus, dynamic tension-torsion experiments were conducted on CoCrFeMnNi high-entropy alloy specimens. The results show that the device is highly reliable and effective. It successfully achieved a stable stress ratio of approximately 1.7 throughout the loading duration. Furthermore, the experiments conclusively showed a key finding. Trapezoidal wave loading significantly enhances stress-ratio stability during combined dynamic loading. This improvement contrasts with the effect of traditional sinusoidal wave loading. This advancement offers a robust and controllable experimental method. It enables the study of materials’ dynamic mechanical responses under complex stress states. These states involve high-strain rates and multiaxial loading. This capability is especially valuable for aerospace, impact engineering, and materials science applications. The successful implementation of constant stress-ratio loading opens avenues for more accurate characterization of material yield criteria and failure mechanisms under dynamic multiaxial conditions.
In the field of material dynamic mechanical properties research, it is significant to obtain reliable data of materials under complex stress states. To address the challenge of achieving a stable stress ratio during combined loading, this work developed a novel device based on the electromagnetic Hopkinson bar (ESHB) platform. This device uniquely enables unilateral synchronous tension/compression-torsion combined dynamic loading. The paper detailed the device’s configuration and loading principles. The core innovation of this device is the independent generation of trapezoidal tensile/compressive and torsional stress waves. A multi-circuit pulse shaper produced tensile/compressive waves, while shear waves were generated using an electromagnetic clamp with torque storage. Crucially, a high-precision digital delay generator (DDG) ensured wave synchronization. With triggering accuracy within 0.1 μs, it controlled the arrival time difference of these distinct waves at the specimen to within 5 μs. This overcame the challenge posed by their different propagation velocities. Additionally, it described the synchronization control methodology and the wave propagation analysis essential for timing calculations. To validate the apparatus, dynamic tension-torsion experiments were conducted on CoCrFeMnNi high-entropy alloy specimens. The results show that the device is highly reliable and effective. It successfully achieved a stable stress ratio of approximately 1.7 throughout the loading duration. Furthermore, the experiments conclusively showed a key finding. Trapezoidal wave loading significantly enhances stress-ratio stability during combined dynamic loading. This improvement contrasts with the effect of traditional sinusoidal wave loading. This advancement offers a robust and controllable experimental method. It enables the study of materials’ dynamic mechanical responses under complex stress states. These states involve high-strain rates and multiaxial loading. This capability is especially valuable for aerospace, impact engineering, and materials science applications. The successful implementation of constant stress-ratio loading opens avenues for more accurate characterization of material yield criteria and failure mechanisms under dynamic multiaxial conditions.
, Available online , doi: 10.11883/bzycj-2025-0040
Abstract:
Against the backdrop of rising global terrorism and industrial accidents, research on infrastructure safety under blast impact has become critically urgent. As a pivotal approach for investigating dynamic responses and damage characteristics of materials and structures subjected to explosive loading, the equivalent blast-loading techniques, which show safe, efficient, and accurate, have emerged as both a research frontier and challenge. This review synthesizes advancements in equivalent blast-loading techniques for far-field explosion simulation, encompassing explosive-driven shock tubes, high-pressure gas-driven shock tubes, drop-weight impact testing machines, and hydraulically-actuated simulators. While each technique exhibits distinct advantages and limitations in simulating blast shockwaves, all strive to establish controlled and secure experimental environments that reproduce high-velocity air flow fields and pressure waves generated by explosions. Through comparative assessment, their performance in load replication fidelity, applicability, and operational efficiency are elucidated, alongside discussions on implementation challenges and potential. Finally, a novel blast simulation technique leveraging liquid-gas phase-transition-driven expansion is introduced and the follow-up research directions are prospected.
Against the backdrop of rising global terrorism and industrial accidents, research on infrastructure safety under blast impact has become critically urgent. As a pivotal approach for investigating dynamic responses and damage characteristics of materials and structures subjected to explosive loading, the equivalent blast-loading techniques, which show safe, efficient, and accurate, have emerged as both a research frontier and challenge. This review synthesizes advancements in equivalent blast-loading techniques for far-field explosion simulation, encompassing explosive-driven shock tubes, high-pressure gas-driven shock tubes, drop-weight impact testing machines, and hydraulically-actuated simulators. While each technique exhibits distinct advantages and limitations in simulating blast shockwaves, all strive to establish controlled and secure experimental environments that reproduce high-velocity air flow fields and pressure waves generated by explosions. Through comparative assessment, their performance in load replication fidelity, applicability, and operational efficiency are elucidated, alongside discussions on implementation challenges and potential. Finally, a novel blast simulation technique leveraging liquid-gas phase-transition-driven expansion is introduced and the follow-up research directions are prospected.
, Available online , doi: 10.11883/bzycj-2025-0041
Abstract:
With the rapid development of hypervelocity weapons, analyzing the penetration effectiveness of hypervelocity weapon warheads on concrete shields is significant for the design of newly-built protective structures and the safety evaluation of as-built protective structures. Focusing on the penetration performance of AGM-183A hypervelocity weapon warhead against three typical shields: normal strength concrete (NSC), ultra-high performance concrete (UHPC), and corundum rubble concrete (CRC), firstly, the reliability of the numerical algorithms, mesh size, and material model parameters used in the finite element analysis method was fully validated by comparing the experimental and simulation results of three types of target subjected to penetration of steel/tungsten alloy projectiles. Subsequently, a numerical analysis method for the prototype scenario was established based on a mesh transition strategy equivalent to penetration depth and recovered projectile length. Finally, a series of simulations were conducted for the AGM-183A hypervelocity weapon warhead penetrating the aforementioned three shields at Ma ranging from 3 to 8. The results indicate that: (1) the AGM-183A hypervelocity weapon warhead reaches maximum penetration depth when NSC, UHPC, and CRC shields subjected to penetration at Ma=4, Ma=4, and Ma=3, respectively, with depths of 4.26, 3.74, and 1.00 m. Due to instability phenomena of projectiles, such as fractures at the junction between the head and body caused by local stress concentration, further increases in penetration velocity lead to a decrease in penetration effectiveness; (2) compared with the combined penetration and explosion damage depths of conventional sound speed penetrating warheads SDB, WDU-43/B, and BLU-109/B, the penetration depths induced by AGM-183A into NSC, UHPC, and CRC shields are 3.2, 1.6, and 1.8 times, 4.7, 2.1, and 2.2 times, and 3.4, 1.3, and 1.5 times higher, respectively; (3) the recommended design thicknesses of the three shields against the AGM-183A hypervelocity weapon warhead are 8.01, 7.03, and 1.88 m, respectively. The UHPC shield shows no significant improvement subjected to hypervelocity penetration compared with the NSC shield. Comparatively, the CRC shield is recommended for shield design, which can be effectively subjected to both conventional subsonic and hypervelocity impacts.
With the rapid development of hypervelocity weapons, analyzing the penetration effectiveness of hypervelocity weapon warheads on concrete shields is significant for the design of newly-built protective structures and the safety evaluation of as-built protective structures. Focusing on the penetration performance of AGM-183A hypervelocity weapon warhead against three typical shields: normal strength concrete (NSC), ultra-high performance concrete (UHPC), and corundum rubble concrete (CRC), firstly, the reliability of the numerical algorithms, mesh size, and material model parameters used in the finite element analysis method was fully validated by comparing the experimental and simulation results of three types of target subjected to penetration of steel/tungsten alloy projectiles. Subsequently, a numerical analysis method for the prototype scenario was established based on a mesh transition strategy equivalent to penetration depth and recovered projectile length. Finally, a series of simulations were conducted for the AGM-183A hypervelocity weapon warhead penetrating the aforementioned three shields at Ma ranging from 3 to 8. The results indicate that: (1) the AGM-183A hypervelocity weapon warhead reaches maximum penetration depth when NSC, UHPC, and CRC shields subjected to penetration at Ma=4, Ma=4, and Ma=3, respectively, with depths of 4.26, 3.74, and 1.00 m. Due to instability phenomena of projectiles, such as fractures at the junction between the head and body caused by local stress concentration, further increases in penetration velocity lead to a decrease in penetration effectiveness; (2) compared with the combined penetration and explosion damage depths of conventional sound speed penetrating warheads SDB, WDU-43/B, and BLU-109/B, the penetration depths induced by AGM-183A into NSC, UHPC, and CRC shields are 3.2, 1.6, and 1.8 times, 4.7, 2.1, and 2.2 times, and 3.4, 1.3, and 1.5 times higher, respectively; (3) the recommended design thicknesses of the three shields against the AGM-183A hypervelocity weapon warhead are 8.01, 7.03, and 1.88 m, respectively. The UHPC shield shows no significant improvement subjected to hypervelocity penetration compared with the NSC shield. Comparatively, the CRC shield is recommended for shield design, which can be effectively subjected to both conventional subsonic and hypervelocity impacts.
, Available online , doi: 10.11883/bzycj-2024-0324
Abstract:
To address the longstanding challenge of accurately evaluating the dynamic fracture toughness of ceramic materials, a new mode I dynamic fracture testing method was developed based on the conventional split-Hopkinson pressure bar (SHPB) technique. This approach introduced a miniature fracture specimen specifically designed to ensure pure mode I loading, along with a custom fixture system that enabled stable and repeatable dynamic fracture experiments on alumina ceramics with varying loading rates. The combined experimental-numerical method was used to obtain the variation of the mode I dynamic stress intensity factor at the crack tip under different loading rates. Fracture initiation time was obtained with high precision using the strain gauge method, allowing for the determination of mode I dynamic fracture toughness. To further validate the accuracy of the measured fracture initiation time, high-speed photography was employed to capture the entire failure process in real time and corroborate the onset of fracture of the tested specimens. The results show that as the applied loading rate increases from 0.45 TPa·m1/2·s−1 to 1.83 TPa·m1/2·s−1, the dynamic fracture toughness of alumina ceramics rises significantly from 8.39 MPa·m1/2 to 15.76 MPa·m1/2, indicating a pronounced strengthening effect induced by higher loading rates. Meanwhile, the crack initiation time decreases notably with increasing loading rate. Fractographic analysis using scanning electron microscopy reveals a clear fracture mode transition behavior. Under lower loading rates, the fracture of alumina ceramics predominantly exhibits intergranular fracture features. Under higher loading rates, the fracture shows a mixed-mode fracture involving both intergranular and transgranular features. This transition is attributed to the activation and propagation of more micro-defects under higher rates, resulting in increased microcracking. The emergence of this mixed fracture mode is associated with greater energy dissipation, which fundamentally contributes to the increase in mode I dynamic fracture toughness. The proposed method offers a robust framework for accurately assessing the mode I dynamic fracture properties of ceramic materials.
To address the longstanding challenge of accurately evaluating the dynamic fracture toughness of ceramic materials, a new mode I dynamic fracture testing method was developed based on the conventional split-Hopkinson pressure bar (SHPB) technique. This approach introduced a miniature fracture specimen specifically designed to ensure pure mode I loading, along with a custom fixture system that enabled stable and repeatable dynamic fracture experiments on alumina ceramics with varying loading rates. The combined experimental-numerical method was used to obtain the variation of the mode I dynamic stress intensity factor at the crack tip under different loading rates. Fracture initiation time was obtained with high precision using the strain gauge method, allowing for the determination of mode I dynamic fracture toughness. To further validate the accuracy of the measured fracture initiation time, high-speed photography was employed to capture the entire failure process in real time and corroborate the onset of fracture of the tested specimens. The results show that as the applied loading rate increases from 0.45 TPa·m1/2·s−1 to 1.83 TPa·m1/2·s−1, the dynamic fracture toughness of alumina ceramics rises significantly from 8.39 MPa·m1/2 to 15.76 MPa·m1/2, indicating a pronounced strengthening effect induced by higher loading rates. Meanwhile, the crack initiation time decreases notably with increasing loading rate. Fractographic analysis using scanning electron microscopy reveals a clear fracture mode transition behavior. Under lower loading rates, the fracture of alumina ceramics predominantly exhibits intergranular fracture features. Under higher loading rates, the fracture shows a mixed-mode fracture involving both intergranular and transgranular features. This transition is attributed to the activation and propagation of more micro-defects under higher rates, resulting in increased microcracking. The emergence of this mixed fracture mode is associated with greater energy dissipation, which fundamentally contributes to the increase in mode I dynamic fracture toughness. The proposed method offers a robust framework for accurately assessing the mode I dynamic fracture properties of ceramic materials.
, Available online , doi: 10.11883/bzycj-2025-0282
Abstract:
Inspired by the hybrid topology design that integrates Miura origami and star-shaped honeycomb, this study proposes a novel origami metamaterial sandwich and employs machine learning to predict low-velocity impact response and perform multi-objective optimization. Through drop-weight impact experiments and finite element simulations, the dynamic mechanical response and deformation failure modes of the sandwich under low-velocity impact are systematically investigated. The results demonstrate that the origami-inspired topologies effectively transform the instantaneous complete fracture of traditional honeycombs into progressive crushing failure, thereby significantly enhancing impact resistance. Subsequently, a residual connection-enhanced deep learning model is developed, enabling rapid and precise end-to-end prediction of the complete low-velocity impact response, with computational efficiency substantially surpassing that of finite element simulations. Parameterized analysis based on this model reveals the regulatory mechanisms of key angle parameters on impact response and effective density. Particularly, angle variations induce a load redistribution phenomenon between panel tension-compression deformation and crease bending deformation, allowing the metamaterial to switch between bearing and buffering protective functions. This provides a mechanism basis for actively controlling impact response and failure modes. Furthermore, by integrating reinforcement learning and Pareto front analysis, the trained deep learning model served as a surrogate model to achieve lightweight multi-objective optimization tailored for load-bearing and impact-mitigation protection requirements. At similar effective densities, the metamaterial enables broad-range tuning of peak force, offering significant advantages for developing customized protective structures for diverse scenarios. This research not only establishes a solid foundation for creating customizable high-performance impact protection structures but also advances the field toward a new paradigm of intelligent, on-demand design.
Inspired by the hybrid topology design that integrates Miura origami and star-shaped honeycomb, this study proposes a novel origami metamaterial sandwich and employs machine learning to predict low-velocity impact response and perform multi-objective optimization. Through drop-weight impact experiments and finite element simulations, the dynamic mechanical response and deformation failure modes of the sandwich under low-velocity impact are systematically investigated. The results demonstrate that the origami-inspired topologies effectively transform the instantaneous complete fracture of traditional honeycombs into progressive crushing failure, thereby significantly enhancing impact resistance. Subsequently, a residual connection-enhanced deep learning model is developed, enabling rapid and precise end-to-end prediction of the complete low-velocity impact response, with computational efficiency substantially surpassing that of finite element simulations. Parameterized analysis based on this model reveals the regulatory mechanisms of key angle parameters on impact response and effective density. Particularly, angle variations induce a load redistribution phenomenon between panel tension-compression deformation and crease bending deformation, allowing the metamaterial to switch between bearing and buffering protective functions. This provides a mechanism basis for actively controlling impact response and failure modes. Furthermore, by integrating reinforcement learning and Pareto front analysis, the trained deep learning model served as a surrogate model to achieve lightweight multi-objective optimization tailored for load-bearing and impact-mitigation protection requirements. At similar effective densities, the metamaterial enables broad-range tuning of peak force, offering significant advantages for developing customized protective structures for diverse scenarios. This research not only establishes a solid foundation for creating customizable high-performance impact protection structures but also advances the field toward a new paradigm of intelligent, on-demand design.
, Available online , doi: 10.11883/bzycj-2024-0404
Abstract:
To develop an engineering model based on the physical mechanism of the non-shock initiation reaction of structural charge, which can be used to describe the reaction evolution process and quantify the reaction intensity for evaluating weapons and ammunition safety. Considering the cavity expansion volume, a constrained charge combustion reaction evolution model was established in this paper, with fracture toughness and reaction pressure as the main parameters based on the main control mechanism of charge reaction crack propagation, which can describe the combustion gaseous product pressurization and shell constraint strength during combustion evolution. Relevant details for the control model establishment process were given. The model reliability of confined charge reaction combustion evolution was verified via the experiments of PBX-3 (87% HMX) explosive combustion reaction evolution under mass inertial confinement. The mass velocity time was recorded by PDV (photonic Doppler velocimetry) transducers, the pressure-time profiles were recorded via pressure transducers, and the experimental process was captured via a high-speed camera. The experimental results were compared with calculated results from the control model proposed in this work. The results show that the reaction pressurization process calculated via the model is roughly consistent with the pressure-increasing trend in the experiment (calculated by the mass velocity). The control model considering the structural venting effect can reflect the competition mechanism between combustion gas pressurization and venting in the pressure-increasing process, and the relationship between the pressure-increasing trend and the vent coefficient is in line with the mechanism analysis expectation. The results can support deepening the understanding of the accidental explosive combustion reaction evolution mechanism.
To develop an engineering model based on the physical mechanism of the non-shock initiation reaction of structural charge, which can be used to describe the reaction evolution process and quantify the reaction intensity for evaluating weapons and ammunition safety. Considering the cavity expansion volume, a constrained charge combustion reaction evolution model was established in this paper, with fracture toughness and reaction pressure as the main parameters based on the main control mechanism of charge reaction crack propagation, which can describe the combustion gaseous product pressurization and shell constraint strength during combustion evolution. Relevant details for the control model establishment process were given. The model reliability of confined charge reaction combustion evolution was verified via the experiments of PBX-3 (87% HMX) explosive combustion reaction evolution under mass inertial confinement. The mass velocity time was recorded by PDV (photonic Doppler velocimetry) transducers, the pressure-time profiles were recorded via pressure transducers, and the experimental process was captured via a high-speed camera. The experimental results were compared with calculated results from the control model proposed in this work. The results show that the reaction pressurization process calculated via the model is roughly consistent with the pressure-increasing trend in the experiment (calculated by the mass velocity). The control model considering the structural venting effect can reflect the competition mechanism between combustion gas pressurization and venting in the pressure-increasing process, and the relationship between the pressure-increasing trend and the vent coefficient is in line with the mechanism analysis expectation. The results can support deepening the understanding of the accidental explosive combustion reaction evolution mechanism.
, Available online , doi: 10.11883/bzycj-2025-0100
Abstract:
When a high-velocity fragment impacted the fuel tank, hydrodynamic ram occurred. The fuel spurt caused by hydrodynamic ram may result in the ignition or even explosion of the fuel tank, thus threatening the survivability of the high-value target. To study the characteristics of fuel spurt caused by the hydrodynamic ram event, an experiment of a high-velocity fragment impacting a simulated fuel tank was conducted, and the characteristics of velocity and spatial distribution of the fuel spurt were tested and analyzed. In order to quantitatively describe the initial motion velocity of the fuel spurt and the attenuation process of its movement in the air, the specific volume unit within the fuel was defined as fuel mass. The concepts of initial motion velocity v0 and dispersion velocity of the fuel mass were proposed. The process of fuel mass spurting from the penetration orifices was simplified into three stages: (1) the fuel mass was about to spurt out, (2) the fuel mass spurted from the penetration orifices; (3) the fuel mass was moving in the air and gradually became atomized. On this basis, the theoretical model of the distribution of fuel spurt was established. According to the cracks at the penetration orifices and the shape change of the material at the edge of the orifices, the value of the coefficient of discharge was classified, and the influence of the distribution of pressure in the fuel was also taken into account during the calculation. When v0≤737 m/s, the range of Cv is from 0.60 to 0.70. When 737 m/s<v0<906 m/s, Cv ranges from 0.25 to 0.55. When v0≥906 m/s, Cv ranges from 0.75 to 0.95. The research showed that the average error between the calculation results of the fuel spurt axial distance and the experimental results was less than 15%. The error between the calculation results of the corrected theoretical model of radial distance and the experimental results was about 5%. The calculated results of the theoretical model were in good agreement with the experimental results.
When a high-velocity fragment impacted the fuel tank, hydrodynamic ram occurred. The fuel spurt caused by hydrodynamic ram may result in the ignition or even explosion of the fuel tank, thus threatening the survivability of the high-value target. To study the characteristics of fuel spurt caused by the hydrodynamic ram event, an experiment of a high-velocity fragment impacting a simulated fuel tank was conducted, and the characteristics of velocity and spatial distribution of the fuel spurt were tested and analyzed. In order to quantitatively describe the initial motion velocity of the fuel spurt and the attenuation process of its movement in the air, the specific volume unit within the fuel was defined as fuel mass. The concepts of initial motion velocity v0 and dispersion velocity of the fuel mass were proposed. The process of fuel mass spurting from the penetration orifices was simplified into three stages: (1) the fuel mass was about to spurt out, (2) the fuel mass spurted from the penetration orifices; (3) the fuel mass was moving in the air and gradually became atomized. On this basis, the theoretical model of the distribution of fuel spurt was established. According to the cracks at the penetration orifices and the shape change of the material at the edge of the orifices, the value of the coefficient of discharge was classified, and the influence of the distribution of pressure in the fuel was also taken into account during the calculation. When v0≤737 m/s, the range of Cv is from 0.60 to 0.70. When 737 m/s<v0<906 m/s, Cv ranges from 0.25 to 0.55. When v0≥906 m/s, Cv ranges from 0.75 to 0.95. The research showed that the average error between the calculation results of the fuel spurt axial distance and the experimental results was less than 15%. The error between the calculation results of the corrected theoretical model of radial distance and the experimental results was about 5%. The calculated results of the theoretical model were in good agreement with the experimental results.
, Available online , doi: 10.11883/bzycj-2024-0505
Abstract:
In response to the research demand for the impact resistance of carbon fiber-reinforced polymer (CFRP) laminates commonly used in aircraft, spherical fragment penetration and static blast tests were conducted on T800/3200 CFRP laminates, with CT scanning technology and damage assessment theories employed for further analysis. The damage characteristics and performance of T800/3200 CFRP laminates under two typical loads-fragment penetration and explosive shock waves-were investigated and compared with 2024-T3 aluminum, a material widely used in the aviation manufacturing industry. Two control groups were established: tungsten fragments impacting aerospace aluminum plates and tungsten steel fragments striking CFRP laminates. Impact velocities and residual velocities were precisely measured using high-speed photography. During fragment penetration tests, relationships among incident velocity, residual velocity, and energy absorption were analyzed based on the Recht–Ipson ballistic limit model. The internal damage morphology of CFRP targets was examined in detail using high-resolution CT scanning technology to characterize delamination patterns and progressive failure across different depths and plies. In blast tests, the damage morphology and maximum deflection of target plates were systematically observed and recorded. The blast resistance of CFRP laminates and aluminum plates was quantitatively compared using advanced mathematical methods incorporating boundary condition equivalence and overpressure equivalence principles to ensure a fair and accurate comparison. The results show that, after spherical fragment penetration, the T800/3200 CFRP laminate generates a delamination damage zone resembling a truncated cone, with the volume of the cone decreasing as the penetration velocity of fragments increases. The T800/3200 CFRP laminate exhibits inferior performance against fragment penetration compared with aerospace aluminum but offers significantly enhanced blast resistance. This characteristic makes it more effective in maintaining structural safety and aerodynamic stability during flight missions under explosive threats. The findings provide theoretical and empirical support for improving the safety and reliability of aerospace vehicles through optimized material selection and structural design.
In response to the research demand for the impact resistance of carbon fiber-reinforced polymer (CFRP) laminates commonly used in aircraft, spherical fragment penetration and static blast tests were conducted on T800/3200 CFRP laminates, with CT scanning technology and damage assessment theories employed for further analysis. The damage characteristics and performance of T800/3200 CFRP laminates under two typical loads-fragment penetration and explosive shock waves-were investigated and compared with 2024-T3 aluminum, a material widely used in the aviation manufacturing industry. Two control groups were established: tungsten fragments impacting aerospace aluminum plates and tungsten steel fragments striking CFRP laminates. Impact velocities and residual velocities were precisely measured using high-speed photography. During fragment penetration tests, relationships among incident velocity, residual velocity, and energy absorption were analyzed based on the Recht–Ipson ballistic limit model. The internal damage morphology of CFRP targets was examined in detail using high-resolution CT scanning technology to characterize delamination patterns and progressive failure across different depths and plies. In blast tests, the damage morphology and maximum deflection of target plates were systematically observed and recorded. The blast resistance of CFRP laminates and aluminum plates was quantitatively compared using advanced mathematical methods incorporating boundary condition equivalence and overpressure equivalence principles to ensure a fair and accurate comparison. The results show that, after spherical fragment penetration, the T800/3200 CFRP laminate generates a delamination damage zone resembling a truncated cone, with the volume of the cone decreasing as the penetration velocity of fragments increases. The T800/3200 CFRP laminate exhibits inferior performance against fragment penetration compared with aerospace aluminum but offers significantly enhanced blast resistance. This characteristic makes it more effective in maintaining structural safety and aerodynamic stability during flight missions under explosive threats. The findings provide theoretical and empirical support for improving the safety and reliability of aerospace vehicles through optimized material selection and structural design.
, Available online , doi: 10.11883/bzycj-2024-0470
Abstract:
In physics, a “source” denotes the origin of matter or energy, while a “sink” refers to the terminal point of matter or energy. By analogizing with the energy source problem in underground explosions, this study proposes an energy sink problem for ideal fluid cavity annihilation. A detailed analysis is conducted on the energy balance and adjustment mechanisms in the ideal fluid cavity annihilation problem, establishing the relationships among fluid pressure work, energy convergence, transmission and transformation. A characteristic energy factor is introduced to describe the “centripetal convergence” behavior of energy sinks. The characteristic energy factor for energy sinks incorporates the information on converged energy, geometric dimensions of cavities and physical properties of fluids, effectively characterizing the “convergence” behavior of energy sink problems and laying a theoretical foundation for the subsequent research on “energy sink” problems in solids. The physical mechanisms and mathematical foundations of the characteristic energy factor are analyzed, and its characteristics and advantages are expounded. Specifically, the introduction of the characteristic energy factor circumvents the need for complex stress-strain relationships, boundary conditions, and unknown internal material structures in traditional continuum mechanics, significantly simplifying the complexity of the problem. The characteristic energy factor is primarily applicable to the predictions of engineering disasters with large scales or well-defined failure zones (e.g., underground explosions, large-scale surrounding rock deformation, zonal disintegration or pendulum waves, and shear-slip rock bursts in ore pillars), whereas its applicability to highly localized engineering disasters with unknown failure zones (e.g., strain-type rock bursts) requires further investigation.
In physics, a “source” denotes the origin of matter or energy, while a “sink” refers to the terminal point of matter or energy. By analogizing with the energy source problem in underground explosions, this study proposes an energy sink problem for ideal fluid cavity annihilation. A detailed analysis is conducted on the energy balance and adjustment mechanisms in the ideal fluid cavity annihilation problem, establishing the relationships among fluid pressure work, energy convergence, transmission and transformation. A characteristic energy factor is introduced to describe the “centripetal convergence” behavior of energy sinks. The characteristic energy factor for energy sinks incorporates the information on converged energy, geometric dimensions of cavities and physical properties of fluids, effectively characterizing the “convergence” behavior of energy sink problems and laying a theoretical foundation for the subsequent research on “energy sink” problems in solids. The physical mechanisms and mathematical foundations of the characteristic energy factor are analyzed, and its characteristics and advantages are expounded. Specifically, the introduction of the characteristic energy factor circumvents the need for complex stress-strain relationships, boundary conditions, and unknown internal material structures in traditional continuum mechanics, significantly simplifying the complexity of the problem. The characteristic energy factor is primarily applicable to the predictions of engineering disasters with large scales or well-defined failure zones (e.g., underground explosions, large-scale surrounding rock deformation, zonal disintegration or pendulum waves, and shear-slip rock bursts in ore pillars), whereas its applicability to highly localized engineering disasters with unknown failure zones (e.g., strain-type rock bursts) requires further investigation.
, Available online , doi: 10.11883/bzycj-2025-0171
Abstract:
In order to investigate the dynamic mechanical properties of ultra-high performance concrete (UHPC) under coupled high-temperature and explosive impact effects, a 75 mm-diameter high-temperature split Hopkinson pressure bar (SHPB) apparatus was employed. Uniaxial compression tests were conducted on C140 UHPC specimens in the temperatures ranging from 25 ℃ to 600 ℃ and the strain rate ranging from 90 s−1 to 200 s−1. A systematic analysis was performed on the strength, strain, toughness, stress-strain relationship, and failure modes of the material under the combined condition of high temperature and impact loading. The influence of temperature and strain rate on the dynamic mechanical properties was revealed, and the yield surface of the Holmquist-Johnson-Cook (HJC) constitutive model was modified by incorporating thermal effects. The results indicate that UHPC exhibits a significant strain rate strengthening effect under high-temperature dynamic compression, while elevated temperatures simultaneously degrade its mechanical properties. The evolution of material strain capacity and toughness stems from the synergistic interaction between thermal and strain rate effects. At identical temperatures, increased strain rates exacerbate the damage of UHPC. When temperatures exceed 400 ℃, matrix degradation and steel fiber oxidation cause the material to exhibit overall brittle failure characteristics; however, its local core region remains integrity and retains notable residual load-bearing capacity. The modified HJC yield surface is suitable for describing the dynamic mechanical behavior of this material under coupled high-temperature and impact conditions. These findings provide theoretical foundations and data support for the safety design and evaluation of military and civil protective engineering.
In order to investigate the dynamic mechanical properties of ultra-high performance concrete (UHPC) under coupled high-temperature and explosive impact effects, a 75 mm-diameter high-temperature split Hopkinson pressure bar (SHPB) apparatus was employed. Uniaxial compression tests were conducted on C140 UHPC specimens in the temperatures ranging from 25 ℃ to 600 ℃ and the strain rate ranging from 90 s−1 to 200 s−1. A systematic analysis was performed on the strength, strain, toughness, stress-strain relationship, and failure modes of the material under the combined condition of high temperature and impact loading. The influence of temperature and strain rate on the dynamic mechanical properties was revealed, and the yield surface of the Holmquist-Johnson-Cook (HJC) constitutive model was modified by incorporating thermal effects. The results indicate that UHPC exhibits a significant strain rate strengthening effect under high-temperature dynamic compression, while elevated temperatures simultaneously degrade its mechanical properties. The evolution of material strain capacity and toughness stems from the synergistic interaction between thermal and strain rate effects. At identical temperatures, increased strain rates exacerbate the damage of UHPC. When temperatures exceed 400 ℃, matrix degradation and steel fiber oxidation cause the material to exhibit overall brittle failure characteristics; however, its local core region remains integrity and retains notable residual load-bearing capacity. The modified HJC yield surface is suitable for describing the dynamic mechanical behavior of this material under coupled high-temperature and impact conditions. These findings provide theoretical foundations and data support for the safety design and evaluation of military and civil protective engineering.
, Available online , doi: 10.11883/bzycj-2025-0178
Abstract:
With the development of modern weapon systems, the requirements for the survivability of ammunition in various complex environments have been continuously increasing. During the processes of storage, flight, and combat, ammunition may be subjected to extreme impact loads such as high-speed impacts, shock waves, bullet and fragment impacts. The external impacts can induce plastic deformation and fracture of the ammunition casing, and even detonate the internal explosives. These responses involve complex phenomena including impact loading, thermo-mechanical coupling of materials, chemical reactions of explosives, and blast effects, representing a typical dynamic response problem of reactive materials under extreme thermo-mechanical coupling conditions. Accurately predicting the responses of ammunition under impact loading is critical for its design optimization and safety assessment. Based on the Hot Optimal Transportation Meshfree (HOTM) method, a meshfree numerical approach was proposed to accurately predict the ammunition responses under different impact loadings. Meanwhile, a thermo-mechanical-chemical coupling constitutive model of explosives was established, which took the effects of temperature and pressure on the explosive’s chemical reaction and detonation into account. The Arrhenius thermal-chemical reaction coupling model for explosive initiation and the Lee-Tarver three-term pressure ignition model induced by local high pressure were integrated to accurately simulate the different initiation mechanisms of explosives under varying impact velocities, thereby predict complex physical phenomena during the impact loading of ammunition. These phenomena include high-speed contact, large plastic deformation of the metal casing, material fracture, heat conduction, explosive initiation, and the expansion work performed by chemical reaction products. Taking the numerical simulations of two typical impact scenarios—bullet impact on ammunition at 850 m/s and fragment impact at1850 m/s—as examples, the influence of impact velocity on the initiation mechanisms of explosives and the overall response of ammunition was analyzed, with comparisons made against relevant experimental results. The proposed approach and findings provide reliable technical support for the optimization of impact-resistant design and safety assessment of ammunition.
With the development of modern weapon systems, the requirements for the survivability of ammunition in various complex environments have been continuously increasing. During the processes of storage, flight, and combat, ammunition may be subjected to extreme impact loads such as high-speed impacts, shock waves, bullet and fragment impacts. The external impacts can induce plastic deformation and fracture of the ammunition casing, and even detonate the internal explosives. These responses involve complex phenomena including impact loading, thermo-mechanical coupling of materials, chemical reactions of explosives, and blast effects, representing a typical dynamic response problem of reactive materials under extreme thermo-mechanical coupling conditions. Accurately predicting the responses of ammunition under impact loading is critical for its design optimization and safety assessment. Based on the Hot Optimal Transportation Meshfree (HOTM) method, a meshfree numerical approach was proposed to accurately predict the ammunition responses under different impact loadings. Meanwhile, a thermo-mechanical-chemical coupling constitutive model of explosives was established, which took the effects of temperature and pressure on the explosive’s chemical reaction and detonation into account. The Arrhenius thermal-chemical reaction coupling model for explosive initiation and the Lee-Tarver three-term pressure ignition model induced by local high pressure were integrated to accurately simulate the different initiation mechanisms of explosives under varying impact velocities, thereby predict complex physical phenomena during the impact loading of ammunition. These phenomena include high-speed contact, large plastic deformation of the metal casing, material fracture, heat conduction, explosive initiation, and the expansion work performed by chemical reaction products. Taking the numerical simulations of two typical impact scenarios—bullet impact on ammunition at 850 m/s and fragment impact at
, Available online , doi: 10.11883/bzycj-2024-0511
Abstract:
A compressible multiphase flow numerical scheme, induced from the multi- component diffuse interface model with arbitrary number of materials, is established to simulate the interaction between distinct materials under extreme conditions. A robust, low dissipation and high efficiency reconstruction method, the MTBVD (muscl thinc boundary variation diminishing), is proposed with the aid of artificial intelligence technology, which can adaptively select the most suitable reconstruction method in the essential regions such as shock wave, contact discontinuity and material interface, and can achieve the minimum global numerical dissipation. Furthermore, it has a higher computational efficiency than the traditional BVD (boundary variation diminishing) scheme. The automatic geometric modeling and grid meshing based on global geographic information system, adaptive mesh refinement and large-scale parallel computing method are established to realize the whole numerical simulation of shock wave propagation in complex terrain and real urban environments. Our schemes allows for the effective simulation of intense blast wave scenarios on a large scale within intricate urban settings, employing billions of meshes, a pressure spectrum ranging from 103 Pa to 1015 Pa, and a minimum spacing size of 10 km. We have conducted multiple numerical simulations that demonstrate the propagation of blast waves through complex landscapes and urban areas, which corroborate our methodologies.
A compressible multiphase flow numerical scheme, induced from the multi- component diffuse interface model with arbitrary number of materials, is established to simulate the interaction between distinct materials under extreme conditions. A robust, low dissipation and high efficiency reconstruction method, the MTBVD (muscl thinc boundary variation diminishing), is proposed with the aid of artificial intelligence technology, which can adaptively select the most suitable reconstruction method in the essential regions such as shock wave, contact discontinuity and material interface, and can achieve the minimum global numerical dissipation. Furthermore, it has a higher computational efficiency than the traditional BVD (boundary variation diminishing) scheme. The automatic geometric modeling and grid meshing based on global geographic information system, adaptive mesh refinement and large-scale parallel computing method are established to realize the whole numerical simulation of shock wave propagation in complex terrain and real urban environments. Our schemes allows for the effective simulation of intense blast wave scenarios on a large scale within intricate urban settings, employing billions of meshes, a pressure spectrum ranging from 103 Pa to 1015 Pa, and a minimum spacing size of 10 km. We have conducted multiple numerical simulations that demonstrate the propagation of blast waves through complex landscapes and urban areas, which corroborate our methodologies.
, Available online , doi: 10.11883/bzycj-2025-0290
Abstract:
Hypergravity centrifuge model testing serves as an effective method for simulating prototype explosion effects, whose successful application relies on soil simulants capable of replicating the dynamic response of in-situ soil. To address the challenges of particle size effects and material similarity in centrifuge modeling of explosions in sandy gravel, this study aims to establish a systematic methodology for the preparation and validation of such simulants. Through theoretical analysis, the soil key parameters governing ground shock effects under explosions were identified as density and wave velocity (wave impedance), which are fundamentally controlled by the soil's gradation characteristics. Based on this premise, twelve types of simulants with varying maximum particle sizes were systematically prepared using four scaling methods: the removal method, equal quantity replacement method, similar gradation method, and hybrid method. Through void ratio tests and bender element testing under effective confining pressure, quantitative relationships were revealed between the extreme void ratios of sandy gravel and its fines content and mean particle size. Based on this, an empirical predictive model for the small strain elastic modulus was established. Comparison of the model-predicted wave velocities with in-situ measured data indicates that the coefficient of uniformity, fines content, and mean particle size are the key controlling indices for achieving dynamic similarity in sandy gravel under explosion loading. Among these, the simulant prepared by the equal quantity replacement method, with a maximum particle size of 10 mm, demonstrated the closest equivalence to the in-situ soil in terms of the aforementioned indices. Hypergravity centrifuge explosion tests using this equivalent simulant further verified that the attenuation law of normalized peak accelerations within the source plane corresponds highly consistently with the in-situ data. This research confirms that by controlling key gradation indices and employing the equal quantity replacement method, it is possible to successfully prepare simulants that are equivalent to in-situ sandy gravel in their dynamic response to explosions. This provides a practical and effective technical pathway for centrifuge model testing in related fields.
Hypergravity centrifuge model testing serves as an effective method for simulating prototype explosion effects, whose successful application relies on soil simulants capable of replicating the dynamic response of in-situ soil. To address the challenges of particle size effects and material similarity in centrifuge modeling of explosions in sandy gravel, this study aims to establish a systematic methodology for the preparation and validation of such simulants. Through theoretical analysis, the soil key parameters governing ground shock effects under explosions were identified as density and wave velocity (wave impedance), which are fundamentally controlled by the soil's gradation characteristics. Based on this premise, twelve types of simulants with varying maximum particle sizes were systematically prepared using four scaling methods: the removal method, equal quantity replacement method, similar gradation method, and hybrid method. Through void ratio tests and bender element testing under effective confining pressure, quantitative relationships were revealed between the extreme void ratios of sandy gravel and its fines content and mean particle size. Based on this, an empirical predictive model for the small strain elastic modulus was established. Comparison of the model-predicted wave velocities with in-situ measured data indicates that the coefficient of uniformity, fines content, and mean particle size are the key controlling indices for achieving dynamic similarity in sandy gravel under explosion loading. Among these, the simulant prepared by the equal quantity replacement method, with a maximum particle size of 10 mm, demonstrated the closest equivalence to the in-situ soil in terms of the aforementioned indices. Hypergravity centrifuge explosion tests using this equivalent simulant further verified that the attenuation law of normalized peak accelerations within the source plane corresponds highly consistently with the in-situ data. This research confirms that by controlling key gradation indices and employing the equal quantity replacement method, it is possible to successfully prepare simulants that are equivalent to in-situ sandy gravel in their dynamic response to explosions. This provides a practical and effective technical pathway for centrifuge model testing in related fields.
, Available online , doi: 10.11883/bzycj-2025-0175
Abstract:
To investigate the shear-enhanced compaction effect and strain-rate effect on the equation of state (EoS) of concrete-like materials subjected to blast and impact loadings, high-fidelity numerical simulations were performed based on two types of EoS behavior tests for cement mortar, including hydrostatic compression tests and flyer-plate impact tests. These simulations employed the Kong-Fang hydro-elasto-plastic model for concrete-like materials and were implemented using the smoothed particle Galerkin (SPG) algorithm in LS-DYNA, enabling accurate reproduction of complex dynamic mechanical behaviors, including the shear-enhanced compaction effect and strain-rate effect. Based on the high-fidelity numerical simulations described above, a quantitative analysis was conducted to investigate the influence of the shear-enhanced compaction effect and strain-rate effect on EoS behavior of concrete-like materials, and the challenges associated with eliminating the shear-enhanced compaction and strain-rate coupling effects in flyer-plate impact tests were systematically identified. The results demonstrate that the Kong-Fang model, when combined with the SPG algorithm, can accurately simulate the complex dynamic mechanical behaviors of concrete-like materials, including shear-enhanced compaction effect and strain-rate effect. To achieve high-precision simulation of dynamic mechanical behaviors of concrete-like materials subjected to blast and impact loadings across high-medium-low pressure ranges, it is essential to establish an EoS with a wide-range pressure based on experimental data from EoS behavior tests. However, shear-enhanced compaction and strain-rate coupling effects should be eliminated when using flyer-plate impact test data to calibrate the EoS parameters. A paradox arises in the establishment of EoS with wide-range pressure for concrete-like materials, and the application of numerical iteration correction methodology may represent an effective approach to resolving this challenge. These findings provide a theoretical foundation for the future development of a numerical iteration correction methodology to eliminate the shear-enhanced compaction effect and strain-rate effect on the EoS of concrete-like materials, thereby facilitating the establishment of a high-precision EoS with a wide range of pressure for concrete-like materials subjected to impact and blast loadings.
To investigate the shear-enhanced compaction effect and strain-rate effect on the equation of state (EoS) of concrete-like materials subjected to blast and impact loadings, high-fidelity numerical simulations were performed based on two types of EoS behavior tests for cement mortar, including hydrostatic compression tests and flyer-plate impact tests. These simulations employed the Kong-Fang hydro-elasto-plastic model for concrete-like materials and were implemented using the smoothed particle Galerkin (SPG) algorithm in LS-DYNA, enabling accurate reproduction of complex dynamic mechanical behaviors, including the shear-enhanced compaction effect and strain-rate effect. Based on the high-fidelity numerical simulations described above, a quantitative analysis was conducted to investigate the influence of the shear-enhanced compaction effect and strain-rate effect on EoS behavior of concrete-like materials, and the challenges associated with eliminating the shear-enhanced compaction and strain-rate coupling effects in flyer-plate impact tests were systematically identified. The results demonstrate that the Kong-Fang model, when combined with the SPG algorithm, can accurately simulate the complex dynamic mechanical behaviors of concrete-like materials, including shear-enhanced compaction effect and strain-rate effect. To achieve high-precision simulation of dynamic mechanical behaviors of concrete-like materials subjected to blast and impact loadings across high-medium-low pressure ranges, it is essential to establish an EoS with a wide-range pressure based on experimental data from EoS behavior tests. However, shear-enhanced compaction and strain-rate coupling effects should be eliminated when using flyer-plate impact test data to calibrate the EoS parameters. A paradox arises in the establishment of EoS with wide-range pressure for concrete-like materials, and the application of numerical iteration correction methodology may represent an effective approach to resolving this challenge. These findings provide a theoretical foundation for the future development of a numerical iteration correction methodology to eliminate the shear-enhanced compaction effect and strain-rate effect on the EoS of concrete-like materials, thereby facilitating the establishment of a high-precision EoS with a wide range of pressure for concrete-like materials subjected to impact and blast loadings.
, Available online , doi: 10.11883/bzycj-2025-0123
Abstract:
Renewable energy is addressing some of the key challenges facing global society today, and zero-carbon energy systems are the fundamental way to achieve carbon neutrality. Therefore, hydrogen and ammonia have gained great attention as zero-carbon energy sources. To further study the combustion characteristics of ammonia-hydrogen-air premixed gas flame inside and outside the duct, the influence of ammonia doped amount (φ) on the flame morphology and the evolution of pressure inside and outside the duct under stoichiometric ratio was explored with the help of high-speed photography and pressure sensor in a2000 mm stainless steel duct with a 400-mm-long and 70-mm-wide observation window. The results show that φ significantly affects the pressure inside and outside the duct, and the time to reach the reverse flow phenomenon caused by the secondary explosion also increases. The pressure measuring point PS1 is set at 400 mm away from the explosion vent in the duct to collect data. The pressure curves in the duct under each working condition are presented as a three-peak structure, named p1, p2, and p3. The three pressure peaks are caused by the rupture of the explosion vent film, the gas venting in the duct, and the gas reverse generated by the secondary explosion outside the duct. The size of p1 depends on the tensile strength of the explosion venting membrane, and its amplitude is almost independent of the φ. p2 and p3 both increase with the increase of φ, and the p3 increase rate is the largest when φ is in 50%-65%. p2 changes from a single peak to a fluctuating pressure platform in the pressure curve diagram, and the time of the platform extends with the increase of φ. The pressure measurement point PS2 is set at the horizontal central axis, 500mm away from the explosion vent outside the duct, to collect data. And the peak pressure of the secondary explosion outside the duct (pout) decreases with the increase of the φ, and the time to reach pout increases. This study provides a theoretical basis for the utilization of ammonia and hydrogen energy.
Renewable energy is addressing some of the key challenges facing global society today, and zero-carbon energy systems are the fundamental way to achieve carbon neutrality. Therefore, hydrogen and ammonia have gained great attention as zero-carbon energy sources. To further study the combustion characteristics of ammonia-hydrogen-air premixed gas flame inside and outside the duct, the influence of ammonia doped amount (φ) on the flame morphology and the evolution of pressure inside and outside the duct under stoichiometric ratio was explored with the help of high-speed photography and pressure sensor in a
, Available online , doi: 10.11883/bzycj-2025-0145
Abstract:
Hydrogen is a renewable, carbon-free energy carrier and an important chemical feedstock. However, its high burning velocity and low ignition energy render it more hazardous than conventional fuels. To effectively control the explosion intensity of hydrogen-air mixtures in confined spaces and elucidate the suppression mechanism of micron-sized water mist containing dimethyl methylphosphonate (O=P(CH3)(OCH3)2), a rectangular constant-volume combustion chamber was first constructed, and a schlieren optical system was employed to capture fine flame structures under the addition of the suppressant. Secondly, based on the kinetic models proposed by Jayaweera et al. and Jing et al., a coupled chemical kinetic mechanism for O=P(CH3)(OCH3)2 was developed and validated for accuracy. Lastly, the influence of O=P(CH3)(OCH3)2-containing fine water mist on flame instability structures, mean flame speed, explosion overpressure, and mean pressure rise rate was then investigated under different equivalence ratios, together with the chemical kinetic mechanism and pathways governing hydrogen-air deflagration suppression. Results indicate that water mist containing O=P(CH3)(OCH3)2 promotes the formation of cellular structures on the flame front, thereby inducing flame instability. At equivalence ratios of 0.8, 1.0, and 1.5, the O=P(CH3)(OCH3)2-laden water mist effectively reduces the average flame speed (with reductions ranging from 24.2% to 47.2%) and suppresses the formation of tulip flames, which are replaced by wrinkled flame structures. The mist suppresses the pressure rise rate by reducing the laminar flame speed, but simultaneously enhances flame instability, which tends to increase the pressure rise rate. The overall suppression performance (with pressure reduction ranging from 41.0% to 65.8%) results from the coupling of these two opposing effects. Additionally, the O=P(CH3)(OCH3)2-laden mist achieves effective explosion suppression by reducing the concentrations of H∙, O∙, and OH∙ radicals, with reductions exceeding 80%. The physical suppression arises from pre-flame cooling and dilution effects of the water mist, while the chemical suppression is attributed to the decomposition of O=P(CH3)(OCH3)2 into phosphorus-containing radicals such as HOPO∙, HOPO2∙, HPO2∙, PO(OH)2∙, and PO(H)(OH)∙. These species scavenge reactive H∙ and OH∙ radicals, promoting the formation of stable products like H2 and H2O, thereby interrupting the chain reactions in hydrogen-air explosions.
Hydrogen is a renewable, carbon-free energy carrier and an important chemical feedstock. However, its high burning velocity and low ignition energy render it more hazardous than conventional fuels. To effectively control the explosion intensity of hydrogen-air mixtures in confined spaces and elucidate the suppression mechanism of micron-sized water mist containing dimethyl methylphosphonate (O=P(CH3)(OCH3)2), a rectangular constant-volume combustion chamber was first constructed, and a schlieren optical system was employed to capture fine flame structures under the addition of the suppressant. Secondly, based on the kinetic models proposed by Jayaweera et al. and Jing et al., a coupled chemical kinetic mechanism for O=P(CH3)(OCH3)2 was developed and validated for accuracy. Lastly, the influence of O=P(CH3)(OCH3)2-containing fine water mist on flame instability structures, mean flame speed, explosion overpressure, and mean pressure rise rate was then investigated under different equivalence ratios, together with the chemical kinetic mechanism and pathways governing hydrogen-air deflagration suppression. Results indicate that water mist containing O=P(CH3)(OCH3)2 promotes the formation of cellular structures on the flame front, thereby inducing flame instability. At equivalence ratios of 0.8, 1.0, and 1.5, the O=P(CH3)(OCH3)2-laden water mist effectively reduces the average flame speed (with reductions ranging from 24.2% to 47.2%) and suppresses the formation of tulip flames, which are replaced by wrinkled flame structures. The mist suppresses the pressure rise rate by reducing the laminar flame speed, but simultaneously enhances flame instability, which tends to increase the pressure rise rate. The overall suppression performance (with pressure reduction ranging from 41.0% to 65.8%) results from the coupling of these two opposing effects. Additionally, the O=P(CH3)(OCH3)2-laden mist achieves effective explosion suppression by reducing the concentrations of H∙, O∙, and OH∙ radicals, with reductions exceeding 80%. The physical suppression arises from pre-flame cooling and dilution effects of the water mist, while the chemical suppression is attributed to the decomposition of O=P(CH3)(OCH3)2 into phosphorus-containing radicals such as HOPO∙, HOPO2∙, HPO2∙, PO(OH)2∙, and PO(H)(OH)∙. These species scavenge reactive H∙ and OH∙ radicals, promoting the formation of stable products like H2 and H2O, thereby interrupting the chain reactions in hydrogen-air explosions.
, Available online , doi: 10.11883/bzycj-2025-0250
Abstract:
Prefabricated building structures have been widely applied in civil engineering due to their advantages of energy conservation, environmental protection, controllable quality, and efficient construction. As the core load-bearing components of prefabricated building structures, precast reinforced concrete (PC) slabs are vulnerable to threats from gas explosions, industrial explosions, and terrorist attacks. To accurately assess the damage state of PC slabs under explosion, enhance structural blast resistance, and reduce casualties, an explosion response dataset of PC slabs was constructed. Six geometric parameters (slab thickness/length/width, steel reinforcement ratio, compressive strength of concrete, etc.) and two explosion load parameters (explosive weight and explosive distance) were selected as input features. Three machine learning algorithms (GPR, RF, and XGBoost) were used to predict the maximum displacement of PC slabs, and their prediction accuracies are compared by root mean square error, coefficient of determination, mean absolute error, scattering index, and comprehensive performance objective function. Furthermore, a damage classification evaluation model based on the support rotation angle damage criterion is proposed. The performance differences of the model under three criteria are analyzed by confusion matrix and five classification indices (accuracy, precision, recall, F1-score, and Kappa coefficient), and compared with simplified models and empirical prediction methods. The research results indicate that in terms of maximum displacement prediction for PC slabs under explosion loads, the XGBoost model demonstrates the best performance among the three machine learning models (GPR、RF and XGBoost). Specifically, the fitting degree of XGBoost is superior to those of GPR and RF models. Meanwhile, and the XGBoost shows the most outstanding comprehensive performance, with a damage recognition accuracy of 92.5%, which demonstrates its high-efficiency in identifying different damage types. The XGBoost-based damage classification evaluation model for PC slabs under explosion loads exhibits powerful performance, providing important references for structural blast resistance design and rapid post-blast damage assessment.
Prefabricated building structures have been widely applied in civil engineering due to their advantages of energy conservation, environmental protection, controllable quality, and efficient construction. As the core load-bearing components of prefabricated building structures, precast reinforced concrete (PC) slabs are vulnerable to threats from gas explosions, industrial explosions, and terrorist attacks. To accurately assess the damage state of PC slabs under explosion, enhance structural blast resistance, and reduce casualties, an explosion response dataset of PC slabs was constructed. Six geometric parameters (slab thickness/length/width, steel reinforcement ratio, compressive strength of concrete, etc.) and two explosion load parameters (explosive weight and explosive distance) were selected as input features. Three machine learning algorithms (GPR, RF, and XGBoost) were used to predict the maximum displacement of PC slabs, and their prediction accuracies are compared by root mean square error, coefficient of determination, mean absolute error, scattering index, and comprehensive performance objective function. Furthermore, a damage classification evaluation model based on the support rotation angle damage criterion is proposed. The performance differences of the model under three criteria are analyzed by confusion matrix and five classification indices (accuracy, precision, recall, F1-score, and Kappa coefficient), and compared with simplified models and empirical prediction methods. The research results indicate that in terms of maximum displacement prediction for PC slabs under explosion loads, the XGBoost model demonstrates the best performance among the three machine learning models (GPR、RF and XGBoost). Specifically, the fitting degree of XGBoost is superior to those of GPR and RF models. Meanwhile, and the XGBoost shows the most outstanding comprehensive performance, with a damage recognition accuracy of 92.5%, which demonstrates its high-efficiency in identifying different damage types. The XGBoost-based damage classification evaluation model for PC slabs under explosion loads exhibits powerful performance, providing important references for structural blast resistance design and rapid post-blast damage assessment.
, Available online , doi: 10.11883/bzycj-2025-0164
Abstract:
The catenary reinforced method can enhance the crashworthiness of re-entrant honeycomb (RH) by avoiding hollow structural characteristics, strengthening negative Poission’s ratio effect, and utilizing the high load-bearing effectiveness of catenary structures. Based on the above effects the sandwich beam with reinforced RH (RRH) was proposed. The metallic specimens from the proposed structure were fabricated for three-point bending tests. Results show that the introduced catenary structure can limit the rotation deformation of inclined cell walls around vertices, and the drop in load-bearing force after initial plastic deformation is reduced from 29.3% to 6.6%. Compared to classical RH cored beams, the maximum load-bearing force and energy absorption of RRH ones can be improved by 26.7% and 8.9%, respectively. A parametric analysis was conducted to reveal that the thicknesses of front facesheet, back facesheet, and core had a significant effect on deformation behavior and energy absorption of RRH cored sandwich beams. The thickness of front facesheets, cores, and back facesheets was employed as optimization variables, and the mass, maximum load-bearing force, and energy absorption were used as optimization objectives to perform the multi-objective optimization of RRH cored sandwich beams. The optimized sandwich beam exhibits increases of 64.9% in maximum load-bearing capacity and 46.9% in energy absorption. The impact resistance of conventional honeycomb sandwich beams under in-plane and out-of-plane loading was compared at identical wall thickness and mass, respectively. Analysis demonstrated the superior energy-absorbing protective performance of the proposed RRH sandwich beams. The research results can provide useful guidance for the reinforcement design of honeycomb cored sandwich beams.
The catenary reinforced method can enhance the crashworthiness of re-entrant honeycomb (RH) by avoiding hollow structural characteristics, strengthening negative Poission’s ratio effect, and utilizing the high load-bearing effectiveness of catenary structures. Based on the above effects the sandwich beam with reinforced RH (RRH) was proposed. The metallic specimens from the proposed structure were fabricated for three-point bending tests. Results show that the introduced catenary structure can limit the rotation deformation of inclined cell walls around vertices, and the drop in load-bearing force after initial plastic deformation is reduced from 29.3% to 6.6%. Compared to classical RH cored beams, the maximum load-bearing force and energy absorption of RRH ones can be improved by 26.7% and 8.9%, respectively. A parametric analysis was conducted to reveal that the thicknesses of front facesheet, back facesheet, and core had a significant effect on deformation behavior and energy absorption of RRH cored sandwich beams. The thickness of front facesheets, cores, and back facesheets was employed as optimization variables, and the mass, maximum load-bearing force, and energy absorption were used as optimization objectives to perform the multi-objective optimization of RRH cored sandwich beams. The optimized sandwich beam exhibits increases of 64.9% in maximum load-bearing capacity and 46.9% in energy absorption. The impact resistance of conventional honeycomb sandwich beams under in-plane and out-of-plane loading was compared at identical wall thickness and mass, respectively. Analysis demonstrated the superior energy-absorbing protective performance of the proposed RRH sandwich beams. The research results can provide useful guidance for the reinforcement design of honeycomb cored sandwich beams.
, Available online , doi: 10.11883/bzycj-2025-0087
Abstract:
To further explore the influence of interstitial C atom on the strain rate effect and temperature effect of CoCrNi-based medium-entropy alloy, the compression mechanical behavior, microstructure evolution and deformation mechanism of CoCrNiSi0.3C0.048 medium-entropy alloy were systematically studied at a wide temperature and strain rate range. The investigated alloy is composed of face-centered cubic (FCC) matrix and three-level precipitate microstructure, i.e. the primary Cr23C6 carbides (2−10 μm), the secondary SiC precipitates (200−500 nm), and the tertiary SiC precipitates (～50 nm). The results show that the serrated flow phenomenon is observed on the true stress-strain curve of the alloy at 400 ℃, and the amplitude of the serrations decreases gradually with the increase of strain and ultimately vanishes. In addition, the abnormal stress peak (the 3rd-type strain aging phenomenon) appears on the curve of the quasi-static flow stress with temperature, but at high strain rate, the abnormal stress peak disappears. Through the analysis of the characterization of the deformed microstructure, it is speculated that the main reason for the phenomenon of 3rd-type strain aging under quasi-static conditions may be the existence of interstitial C atoms. During the process of continuous plastic deformation and development, a series of mixed structures similar to heterogeneous structures are generated, which are composed of dense dislocation cells, micro bands, stack faults, dislocation clusters and deformation twins. These mixed structures intensify the interaction between interstitial atoms and moving dislocation, and then pin the dislocation, which results in dynamic strain aging phenomenon occurs. The reason why the 3rd-type strain aging does not appear under dynamic conditions may be that the solute atoms move slower than the dislocation. The dislocation cannot be pinned in time. In addition, the precipitation of a large number of nanoscale SiC precipitates weakens the "pinning" effect of interstitial atoms under dynamic loading.
To further explore the influence of interstitial C atom on the strain rate effect and temperature effect of CoCrNi-based medium-entropy alloy, the compression mechanical behavior, microstructure evolution and deformation mechanism of CoCrNiSi0.3C0.048 medium-entropy alloy were systematically studied at a wide temperature and strain rate range. The investigated alloy is composed of face-centered cubic (FCC) matrix and three-level precipitate microstructure, i.e. the primary Cr23C6 carbides (2−10 μm), the secondary SiC precipitates (200−500 nm), and the tertiary SiC precipitates (～50 nm). The results show that the serrated flow phenomenon is observed on the true stress-strain curve of the alloy at 400 ℃, and the amplitude of the serrations decreases gradually with the increase of strain and ultimately vanishes. In addition, the abnormal stress peak (the 3rd-type strain aging phenomenon) appears on the curve of the quasi-static flow stress with temperature, but at high strain rate, the abnormal stress peak disappears. Through the analysis of the characterization of the deformed microstructure, it is speculated that the main reason for the phenomenon of 3rd-type strain aging under quasi-static conditions may be the existence of interstitial C atoms. During the process of continuous plastic deformation and development, a series of mixed structures similar to heterogeneous structures are generated, which are composed of dense dislocation cells, micro bands, stack faults, dislocation clusters and deformation twins. These mixed structures intensify the interaction between interstitial atoms and moving dislocation, and then pin the dislocation, which results in dynamic strain aging phenomenon occurs. The reason why the 3rd-type strain aging does not appear under dynamic conditions may be that the solute atoms move slower than the dislocation. The dislocation cannot be pinned in time. In addition, the precipitation of a large number of nanoscale SiC precipitates weakens the "pinning" effect of interstitial atoms under dynamic loading.
, Available online , doi: 10.11883/bzycj-2025-0027
Abstract:
The quasi-static pressure thermodynamic model for confined explosions provides an effective characterization of pressure evolution with mass-to-volume ratio m/V, and derivation of physical quantities such as gas adiabatic index from products and temperature. However, the thermodynamic model based on detonation and combustion equations that neglects reaction equilibrium demonstrates growing deviations from the quasi-static pressure curve in UFC 3-340-02 blast-resistant design standard after carbon precipitates in detonation products, and existing research inadequately addresses the necessity of incorporating reaction equilibrium for various physical quantities in TNT confined explosion thermodynamic models. In order to investigate the influence of reaction equilibrium on thermodynamic calculation results, the model neglecting reaction equilibrium was modified based on the energy conservation equation of isochoric processes and the solid carbon precipitation phenomenon. The modified model has a consistency with the UFC curve for m/V≥0.371 kg/m3. Then, a comparative analysis was conducted on the results of thermodynamic models considering and not considering the reaction equilibrium based on the unified solution framework. The results indicate that incorporating chemical equilibrium into quasi-static pressure calculation introduces a maximum relative deviation below 20%, and critical thresholds alters, i.e., the m/V for carbon precipitation shifts from 0.371 to 3.850 kg/m3, and peak temperature transitions from 0.371 to 0.680 kg/m3. Significant divergence in mole numbers of product composition emerges progressively when m/V exceeds 0.1 kg/m3. Therefore, the reaction equilibrium-based thermodynamic model is a more rational choice for calculating quantities related to components and temperature in TNT confined explosions with m/V>0.1 kg/m3. Finally, a simplified calculation method for products, temperature, and pressure during the quasi-static phase of TNT confined explosions considering reaction equilibrium is proposed based on symbolic regression algorithm. The research contributes to a theoretical understanding of equilibrium effects on thermodynamic model results and the practical implementation of rapid parameter estimation in TNT confined explosion scenarios.
The quasi-static pressure thermodynamic model for confined explosions provides an effective characterization of pressure evolution with mass-to-volume ratio m/V, and derivation of physical quantities such as gas adiabatic index from products and temperature. However, the thermodynamic model based on detonation and combustion equations that neglects reaction equilibrium demonstrates growing deviations from the quasi-static pressure curve in UFC 3-340-02 blast-resistant design standard after carbon precipitates in detonation products, and existing research inadequately addresses the necessity of incorporating reaction equilibrium for various physical quantities in TNT confined explosion thermodynamic models. In order to investigate the influence of reaction equilibrium on thermodynamic calculation results, the model neglecting reaction equilibrium was modified based on the energy conservation equation of isochoric processes and the solid carbon precipitation phenomenon. The modified model has a consistency with the UFC curve for m/V≥0.371 kg/m3. Then, a comparative analysis was conducted on the results of thermodynamic models considering and not considering the reaction equilibrium based on the unified solution framework. The results indicate that incorporating chemical equilibrium into quasi-static pressure calculation introduces a maximum relative deviation below 20%, and critical thresholds alters, i.e., the m/V for carbon precipitation shifts from 0.371 to 3.850 kg/m3, and peak temperature transitions from 0.371 to 0.680 kg/m3. Significant divergence in mole numbers of product composition emerges progressively when m/V exceeds 0.1 kg/m3. Therefore, the reaction equilibrium-based thermodynamic model is a more rational choice for calculating quantities related to components and temperature in TNT confined explosions with m/V>0.1 kg/m3. Finally, a simplified calculation method for products, temperature, and pressure during the quasi-static phase of TNT confined explosions considering reaction equilibrium is proposed based on symbolic regression algorithm. The research contributes to a theoretical understanding of equilibrium effects on thermodynamic model results and the practical implementation of rapid parameter estimation in TNT confined explosion scenarios.
, Available online , doi: 10.11883/bzycj-2024-0497
Abstract:
Layered composite rock masses are widely found in mining, tunnel excavation, and slope stabilization engineering, representing a common geological structure in nature. Due to their formation conditions, the internal strength of layered composite rock masses often exhibits gradient variations. This study simulates layered composite rock masses using epoxy resin materials and employs a dynamic photoelasticity-digital image correlation integrated experimental system to conduct a visualized, detailed analysis of the propagation process of explosive stress waves in gradient media. to investigate the attenuation patterns and energy flux density evolution of explosive stress waves under both forward and reverse gradient conditions. By comparing the dynamic photoelastic stripe patterns, the study visually analyzes the transmission and reflection characteristics under different propagation paths, and uses digital image correlation to quantitatively assess the differences in the attenuation rates of explosive stress waves. The results indicate that the fringe order of the explosive stress wave remains unchanged in the forward propagation path, with significant reflection at the joint surface. In the reverse propagation path, the fringe order exhibits a decaying pattern, and the dynamic photoelastic fringes maintain good continuity at the joint surface. The explosive stress wave demonstrates better penetration in reverse gradient media. Changes in joints and materials within gradient media alter the rate of horizontal stress attenuation, with faster attenuation observed in positive gradient media. By introducing the Poynting vector to compare energy flux density, it was found that energy flux density decays faster in positive gradient materials at the same measurement points, and the propagation of explosive stress waves in positive gradient materials exhibits an “energy-absorbing” process.
Layered composite rock masses are widely found in mining, tunnel excavation, and slope stabilization engineering, representing a common geological structure in nature. Due to their formation conditions, the internal strength of layered composite rock masses often exhibits gradient variations. This study simulates layered composite rock masses using epoxy resin materials and employs a dynamic photoelasticity-digital image correlation integrated experimental system to conduct a visualized, detailed analysis of the propagation process of explosive stress waves in gradient media. to investigate the attenuation patterns and energy flux density evolution of explosive stress waves under both forward and reverse gradient conditions. By comparing the dynamic photoelastic stripe patterns, the study visually analyzes the transmission and reflection characteristics under different propagation paths, and uses digital image correlation to quantitatively assess the differences in the attenuation rates of explosive stress waves. The results indicate that the fringe order of the explosive stress wave remains unchanged in the forward propagation path, with significant reflection at the joint surface. In the reverse propagation path, the fringe order exhibits a decaying pattern, and the dynamic photoelastic fringes maintain good continuity at the joint surface. The explosive stress wave demonstrates better penetration in reverse gradient media. Changes in joints and materials within gradient media alter the rate of horizontal stress attenuation, with faster attenuation observed in positive gradient media. By introducing the Poynting vector to compare energy flux density, it was found that energy flux density decays faster in positive gradient materials at the same measurement points, and the propagation of explosive stress waves in positive gradient materials exhibits an “energy-absorbing” process.
, Available online , doi: 10.11883/bzycj-2024-0520
Abstract:
Significant structural and layout disparities exist between the blended wing body (BWB) civil aircraft and conventional cylindrical fuselage metal aircraft. These differences render the impact resistance characteristics of the non-circular fuselage structure and the injury mechanisms for occupants unclear. To address this, a 460-seat BWB aircraft model was developed based on the pultruded rod stitched efficient unitized structure (PRSEUS) proposed by the National Aeronautics and Space Administration (NASA). The aircraft features a wingspan of 80 meters, a range of approximately 16,000 km, a cruising Mach number of 0.85, and a cruising altitude of 11 000 m. Three typical loading conditions were employed to evaluate the strength and stiffness of the BWB structure: critical maneuvering loads (2.5g positive overload and −1.0g negative overload) and cabin pressurization loads (double the cabin pressurization load). Through iterative structural design optimization, the model was confirmed to meet these typical loading requirements while demonstrating sufficient safety margins. The model incorporated all major structural components of the BWB configuration, including skin, frames, stringers, cargo floor, cabin floor, support columns, and fuselage ribs. In the finite element modeling process, elements with minimal influence on the crash response were reasonably simplified to reduce computational complexity. For instance, the outer wings and engines were simplified as concentrated mass points, and the cabin seats and passengers were modeled as concentrated masses fixed to the seat rails. The primary structural components, such as the skin, stringers, floor, and floor beams, were constructed from AS4 carbon fiber composite laminates and modeled using shell elements. The pultruded rods were made of AS4 carbon fiber composite and modeled using beam elements. The foam core of the frames and fuselage ribs were made of Rohacell-110-WF foam material and modeled using solid elements. The remaining structures were made of7075 aluminum alloy and modeled using shell elements. The final model had a total mass of 162.87 tons and consisted of 2 679 991 elements. Five vertical impact velocities ranging from 7.92 to 9.14 m/s were selected to analyze the cabin space integrity, acceleration response of the cabin floor, and the impact characteristics of the primary load-bearing structures. The results indicate that the cabin area of the lift-body fuselage remains largely intact under the different impact velocities. The primary damage occurs below the cabin floor, with compressive damage concentrated in the lower structures of the middle and aft fuselage. The survivable space is preserved. Compared to a round-section fuselage, the deformation of the BWB frames is relatively small, and upward bulging is not significant, making it challenging to form effective plastic hinges. During the crash, the acceleration load distribution of the blended wing body-integrated aircraft exhibits a decreasing trend from the central aisle to the sides of the fuselage, with peak acceleration loads being higher at the central aisle. Under all five crash conditions, passenger injury levels at various cabin positions fall within the serious but acceptable and safe regions. Regarding structural energy absorption, the frames are identified as the primary energy-absorbing structures, followed by the fuselage ribs. However, the cargo pillars do not effectively crush and absorb energy. For future crashworthiness design of BWB civil aircraft, the cargo structure should be a key consideration.
Significant structural and layout disparities exist between the blended wing body (BWB) civil aircraft and conventional cylindrical fuselage metal aircraft. These differences render the impact resistance characteristics of the non-circular fuselage structure and the injury mechanisms for occupants unclear. To address this, a 460-seat BWB aircraft model was developed based on the pultruded rod stitched efficient unitized structure (PRSEUS) proposed by the National Aeronautics and Space Administration (NASA). The aircraft features a wingspan of 80 meters, a range of approximately 16,000 km, a cruising Mach number of 0.85, and a cruising altitude of 11 000 m. Three typical loading conditions were employed to evaluate the strength and stiffness of the BWB structure: critical maneuvering loads (2.5g positive overload and −1.0g negative overload) and cabin pressurization loads (double the cabin pressurization load). Through iterative structural design optimization, the model was confirmed to meet these typical loading requirements while demonstrating sufficient safety margins. The model incorporated all major structural components of the BWB configuration, including skin, frames, stringers, cargo floor, cabin floor, support columns, and fuselage ribs. In the finite element modeling process, elements with minimal influence on the crash response were reasonably simplified to reduce computational complexity. For instance, the outer wings and engines were simplified as concentrated mass points, and the cabin seats and passengers were modeled as concentrated masses fixed to the seat rails. The primary structural components, such as the skin, stringers, floor, and floor beams, were constructed from AS4 carbon fiber composite laminates and modeled using shell elements. The pultruded rods were made of AS4 carbon fiber composite and modeled using beam elements. The foam core of the frames and fuselage ribs were made of Rohacell-110-WF foam material and modeled using solid elements. The remaining structures were made of
, Available online , doi: 10.11883/bzycj-2024-0471
Abstract:
To accurately predict the explosion power fields in buildings, solving the failure of traditional empirical formulas often failing to account for complex environmental factor due to their inability to account for complex environmental factors, and that of numerical simulations inefficient for large-scale urban scenarios and do not meet the needs of rapid damage assessment. Addressing this challenge, an innovative prediction model for explosion power fields based on Graph Neural Networks (GNN) was constructed using an end-to-end strategy. This model enabled rapid and precise forecasting of three-dimensional physical fields, including peak overpressure, peak impulse, and shock-wave arrival times on building surfaces. Compared to numerical simulations, the proposed GNN model demonstrated excellent predictive performance: it achieved a mean square error of 0.97% for predicting surface overpressure parameters of single buildings with varying geometries, and an average prediction error of 3.17% for complex geometric buildings and building communities. When applied to real-world urban settings, the model maintains an average prediction error of 1.29%, completing individual physical field predictions in under 0.6 seconds—three to four orders of magnitude faster than numerical simulations. Furthermore, the model's high-precision predictions allow for the reconstruction of overpressure time history curves at any building surface location and the accurate assessment of structural damage. The proposed GNN model offers a novel approach for rapidly and accurately predicting explosion power fields in urban buildings during blast events. This advancement significantly enhances the capabilities for explosion damage assessment and anti-explosion design in ultra-large-scale complex engineering scenarios, providing substantial engineering value.
To accurately predict the explosion power fields in buildings, solving the failure of traditional empirical formulas often failing to account for complex environmental factor due to their inability to account for complex environmental factors, and that of numerical simulations inefficient for large-scale urban scenarios and do not meet the needs of rapid damage assessment. Addressing this challenge, an innovative prediction model for explosion power fields based on Graph Neural Networks (GNN) was constructed using an end-to-end strategy. This model enabled rapid and precise forecasting of three-dimensional physical fields, including peak overpressure, peak impulse, and shock-wave arrival times on building surfaces. Compared to numerical simulations, the proposed GNN model demonstrated excellent predictive performance: it achieved a mean square error of 0.97% for predicting surface overpressure parameters of single buildings with varying geometries, and an average prediction error of 3.17% for complex geometric buildings and building communities. When applied to real-world urban settings, the model maintains an average prediction error of 1.29%, completing individual physical field predictions in under 0.6 seconds—three to four orders of magnitude faster than numerical simulations. Furthermore, the model's high-precision predictions allow for the reconstruction of overpressure time history curves at any building surface location and the accurate assessment of structural damage. The proposed GNN model offers a novel approach for rapidly and accurately predicting explosion power fields in urban buildings during blast events. This advancement significantly enhances the capabilities for explosion damage assessment and anti-explosion design in ultra-large-scale complex engineering scenarios, providing substantial engineering value.
, Available online , doi: 10.11883/bzycj-2024-0443
Abstract:
Supercritical CO2 phase transition rock-breaking is a dynamic destruction process under the combined action of shock waves and high-pressure gas. To deeply investigate the rock-breaking mechanisms of supercritical CO2 phase transition under multi-hole synchronous initiation and in-situ stress coupling conditions, targeting the actual working conditions of CO2 field rock-breaking, the initial rock-breaking pressure of a single hole was analyzed based on the thin-walled cylinder theory. A predictive model for the joint rock-breaking radius of multi-hole shock waves and high-pressure gas under in-situ stress was developed by integrating the one-dimensional detonation gas expansion theory. Field experiments on multi-hole CO2 phase transition rock-breaking were subsequently conducted for comparative validation. The results show that when the fracturing pipe is buried shallowly, the influence of in-situ stress on the stress distribution of the rock mass is relatively weak. When the pressure of a single hole is consistent, the more fracturing holes there are, the greater the superposed peak stress of each hole. In the direction perpendicular to the layout of the test hole, the peak stress of each hole shows a U-shaped parabolic distribution. The superposed stress of the fracturing holes at both ends is the largest. In the direction parallel to the layout of the test hole, the peak stress of each hole shows an inverted U-shaped parabolic distribution, and the superposed stress of the middle fracturing hole is the largest. In addition, the rock mass damage and fracture range under multi-pore impact obtained by acoustic wave testing in the field is in the shape of a three-dimensional funnel. The vertical damage and fracture range is between 5.05 and 5.73 m, and the planar damage and fracture range is between 4.3 and 5.6 m. The error between the measured value of the planar damage and fracture range and the theoretically calculated value is between 5.0% and 18.7%. The calculation error mainly comes from the uneven superposition stress of each fracturing hole. Further analysis shows that the radius of supercritical CO2 phase transition rock-breaking increases semi-parabolically with the superposed stress of the fracturing hole and increases logarithmically with the depth of the fracturing hole. As the compressive strength of the rock mass increases, the rock fracture toughness increases nearly linearly, and the corresponding rock-breaking radius decreases nearly linearly. The research results can provide a quantitative design basis for optimizing engineering parameters in the multi-pore supercritical CO2 phase transition for rock-breaking.
Supercritical CO2 phase transition rock-breaking is a dynamic destruction process under the combined action of shock waves and high-pressure gas. To deeply investigate the rock-breaking mechanisms of supercritical CO2 phase transition under multi-hole synchronous initiation and in-situ stress coupling conditions, targeting the actual working conditions of CO2 field rock-breaking, the initial rock-breaking pressure of a single hole was analyzed based on the thin-walled cylinder theory. A predictive model for the joint rock-breaking radius of multi-hole shock waves and high-pressure gas under in-situ stress was developed by integrating the one-dimensional detonation gas expansion theory. Field experiments on multi-hole CO2 phase transition rock-breaking were subsequently conducted for comparative validation. The results show that when the fracturing pipe is buried shallowly, the influence of in-situ stress on the stress distribution of the rock mass is relatively weak. When the pressure of a single hole is consistent, the more fracturing holes there are, the greater the superposed peak stress of each hole. In the direction perpendicular to the layout of the test hole, the peak stress of each hole shows a U-shaped parabolic distribution. The superposed stress of the fracturing holes at both ends is the largest. In the direction parallel to the layout of the test hole, the peak stress of each hole shows an inverted U-shaped parabolic distribution, and the superposed stress of the middle fracturing hole is the largest. In addition, the rock mass damage and fracture range under multi-pore impact obtained by acoustic wave testing in the field is in the shape of a three-dimensional funnel. The vertical damage and fracture range is between 5.05 and 5.73 m, and the planar damage and fracture range is between 4.3 and 5.6 m. The error between the measured value of the planar damage and fracture range and the theoretically calculated value is between 5.0% and 18.7%. The calculation error mainly comes from the uneven superposition stress of each fracturing hole. Further analysis shows that the radius of supercritical CO2 phase transition rock-breaking increases semi-parabolically with the superposed stress of the fracturing hole and increases logarithmically with the depth of the fracturing hole. As the compressive strength of the rock mass increases, the rock fracture toughness increases nearly linearly, and the corresponding rock-breaking radius decreases nearly linearly. The research results can provide a quantitative design basis for optimizing engineering parameters in the multi-pore supercritical CO2 phase transition for rock-breaking.
, Available online , doi: 10.11883/bzycj-2025-0154
Abstract:
Gas leakage and explosion accidents pose a serious threat to public safety. A critical prerequisite for accurately predicting the explosive effects of combustible gas leakage lies in determining the concentration distribution following the leakage. To develop a real-time, full-field spatiotemporal prediction model for combustible gas leakage and diffusion, and to achieve efficient prediction of the equivalent gas cloud volume, a novel graph neural network model based on a dual-neural-network architecture and a multi-stage training strategy, named multi-stage dual graph neural network (MSDGNN), was proposed. The MSDGNN model consists of two synergistic sub-networks: (1) a concentration network (Ncon), which establishes the mapping relationship between the concentration fields of two consecutive timesteps, and (2) a volume network (Nvol), which generates the equivalent gas cloud volume at each timestep to provide a quantitative metric for explosion risk assessment. To further enhance model performance, a multi-stage progressive training strategy was developed to jointly optimize the dual networks. Experimental results demonstrate that compared with mesh-based graph network (MGN), the dual-network architecture effectively decouples the tasks of concentration field prediction and equivalent gas cloud volume prediction. This approach significantly mitigates the interference of weight factors in single-objective loss functions during the training process. The multi-stage training strategy, through stepwise parameter optimization, addresses the issue of insufficient data fitting encountered in traditional methods, significantly reducing the mean absolute percentage error\begin{document}$ {{ \varepsilon }}_{\rm{MAPE}} $\end{document} ![]()
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Gas leakage and explosion accidents pose a serious threat to public safety. A critical prerequisite for accurately predicting the explosive effects of combustible gas leakage lies in determining the concentration distribution following the leakage. To develop a real-time, full-field spatiotemporal prediction model for combustible gas leakage and diffusion, and to achieve efficient prediction of the equivalent gas cloud volume, a novel graph neural network model based on a dual-neural-network architecture and a multi-stage training strategy, named multi-stage dual graph neural network (MSDGNN), was proposed. The MSDGNN model consists of two synergistic sub-networks: (1) a concentration network (Ncon), which establishes the mapping relationship between the concentration fields of two consecutive timesteps, and (2) a volume network (Nvol), which generates the equivalent gas cloud volume at each timestep to provide a quantitative metric for explosion risk assessment. To further enhance model performance, a multi-stage progressive training strategy was developed to jointly optimize the dual networks. Experimental results demonstrate that compared with mesh-based graph network (MGN), the dual-network architecture effectively decouples the tasks of concentration field prediction and equivalent gas cloud volume prediction. This approach significantly mitigates the interference of weight factors in single-objective loss functions during the training process. The multi-stage training strategy, through stepwise parameter optimization, addresses the issue of insufficient data fitting encountered in traditional methods, significantly reducing the mean absolute percentage error
, Available online , doi: 10.11883/bzycj-2025-0134
Abstract:
To explore the anti-penetration abilities of irregular structures made of high-strength alloy steel, a target enhanced with ultra-high-strength spherical structures (UHS-SS) was manufactured in this work. The UHS-SS is fabricated from ultra-high-strength steel (UHSS) and mechanically anchored to the target via threaded high-tensile rods, ensuring structural integrity under projectile penetration loading. A series of penetration tests at an impact velocity of 400 m/s was performed using a 125 mm diameter cannon. The yaw-induced projectile deflection was recorded at5000 s−1, and the failure mode and penetration depth of the projectile were obtained. Through a comparative analysis of anti-penetration experimental results between semi-infinite concrete targets and UHS-SS-reinforced targets, the influences of ultra-high mechanical performances and the spherical yaw-inducing structure on the deflection and fragmentation of the projectile were disclosed. The test results reveal that at a penetration velocity of 400 m/s, the dimensionless penetration depth of the UHS-SS target is 0.11, and the penetration resistance of the UHS-SS target is about 9 times that of C40 concrete. The anti-penetration performance of UHS-SS is significantly enhanced in comparison to that of the ordinary concrete target. Furthermore, as the projectile penetrates the UHS-SS target, the resultant force on the projectile is in a different direction from that of the projectile velocity, which can deflect and shatter the projectile. The behavior of ricocheting off the surface, deflection-induced secondary impact, and fragmentation of the projectile occurred during the anti-penetration test of the UHS-SS target, and the maximal deflection angle was 83º during the experiment, preventing the projectile from penetrating the interior of the protective structure. The UHS-SS target has a severe erosion effect on the projectile at a lower speed of 400m/s, which resulted in a mass loss rate of 23.66% in the experiment. Therefore, the risk of a ground-penetrating weapon penetrating the protective works and detonating is significantly reduced．
To explore the anti-penetration abilities of irregular structures made of high-strength alloy steel, a target enhanced with ultra-high-strength spherical structures (UHS-SS) was manufactured in this work. The UHS-SS is fabricated from ultra-high-strength steel (UHSS) and mechanically anchored to the target via threaded high-tensile rods, ensuring structural integrity under projectile penetration loading. A series of penetration tests at an impact velocity of 400 m/s was performed using a 125 mm diameter cannon. The yaw-induced projectile deflection was recorded at
, Available online , doi: 10.11883/bzycj-2025-0106
Abstract:
To investigate the evolution of phase structure, dislocation distribution, energy absorption capacity, and impact accumulation effect of high-entropy alloys (HEA) under shock loading, molecular dynamics simulations were employed to systematically analyze the dynamic response behavior of Al0.3CoCrFeNi HEA plate subjected to single and secondary impact load. The results show that under the first impact, the phase structure evolution and energy absorption mode of the plastic region of Al0.3CoCrFeNi HEA plate exhibits significant velocity dependence. As the speed increases, the proportion of face-centered cubic structure shows a three-stage downward trend, while the disorder structure increases accordingly. Under low velocity impact (0.5-1.0 km/s), energy is mainly absorbed by dislocation network; at medium velocity impact (1.0-2.0 km/s), both dislocations and disordered atoms contribute; under high velocity impact (2.0-3.0 km/s), disordered atoms dominate energy absorption. Within the velocity range of 0.5-0.8 km/s of the rigid sphere, the dislocation line length increases linearly with the impact velocity. However, at higher impact velocities, the dislocation line length decreases due to the limitation of the plate thickness. The stress analysis shows that when the impact velocity increases, both the maximum stress and the boundary stress of the plastic zone exhibit nonlinear variations characterized by a quadratic relationship. Under the secondary impact, the Al0.3CoCrFeNi HEA plate forms a damage zone resembling a trapezoidal shape after impact. The radius of the pit within this damage zone exhibits a quadratic relationship with the impact velocity. Additionally, the minimum affected area resulting from the secondary impact also demonstrates a quadratic relationship with the impact velocity. Regarding impact resistance, as the initial impact velocity increases, the residual velocity following the secondary impact also rises, indicating a reduction in the resistance capability of HEA. At a distance of 10 nm from the impact center, the ballistic limit velocity decreases nonlinearly with increasing initial impact velocity. However, an increase in the secondary impact velocity mitigates the effects induced by the initial impact.
To investigate the evolution of phase structure, dislocation distribution, energy absorption capacity, and impact accumulation effect of high-entropy alloys (HEA) under shock loading, molecular dynamics simulations were employed to systematically analyze the dynamic response behavior of Al0.3CoCrFeNi HEA plate subjected to single and secondary impact load. The results show that under the first impact, the phase structure evolution and energy absorption mode of the plastic region of Al0.3CoCrFeNi HEA plate exhibits significant velocity dependence. As the speed increases, the proportion of face-centered cubic structure shows a three-stage downward trend, while the disorder structure increases accordingly. Under low velocity impact (0.5-1.0 km/s), energy is mainly absorbed by dislocation network; at medium velocity impact (1.0-2.0 km/s), both dislocations and disordered atoms contribute; under high velocity impact (2.0-3.0 km/s), disordered atoms dominate energy absorption. Within the velocity range of 0.5-0.8 km/s of the rigid sphere, the dislocation line length increases linearly with the impact velocity. However, at higher impact velocities, the dislocation line length decreases due to the limitation of the plate thickness. The stress analysis shows that when the impact velocity increases, both the maximum stress and the boundary stress of the plastic zone exhibit nonlinear variations characterized by a quadratic relationship. Under the secondary impact, the Al0.3CoCrFeNi HEA plate forms a damage zone resembling a trapezoidal shape after impact. The radius of the pit within this damage zone exhibits a quadratic relationship with the impact velocity. Additionally, the minimum affected area resulting from the secondary impact also demonstrates a quadratic relationship with the impact velocity. Regarding impact resistance, as the initial impact velocity increases, the residual velocity following the secondary impact also rises, indicating a reduction in the resistance capability of HEA. At a distance of 10 nm from the impact center, the ballistic limit velocity decreases nonlinearly with increasing initial impact velocity. However, an increase in the secondary impact velocity mitigates the effects induced by the initial impact.
