弹体贯穿混凝土数值模拟的改进材料模型

任会兰; 荣誉; 许香照

doi:10.11883/bzycj-2022-0131

弹体贯穿混凝土数值模拟的改进材料模型

doi: 10.11883/bzycj-2022-0131

北京理工大学爆炸科学与技术国家重点实验室，北京 100081

基金项目: 国家自然科学基金（12032006, 12072028）；北京理工大学青年教师学术启动计划（XSQD-202102011）

详细信息

作者简介:
任会兰（1973－　），女，博士，教授，huilanren@bit.edu.cn

通讯作者:
许香照（1989－　），男，博士，副研究员，xzxu@bit.edu.cn

中图分类号: O385
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- 文章访问数: 603
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- 被引次数: 3
出版历程
- 收稿日期: 2022-03-31
- 修回日期: 2022-06-29
- 网络出版日期: 2022-07-01
- 刊出日期: 2022-11-18

An improved material model for numerical simulation of projectile perforating concrete

State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China

摘要

摘要: 研究混凝土结构在冲击载荷下的力学特性对武器以及防护结构的设计和评估具有重要意义，而合适的材料模型可以更准确地预测混凝土结构的力学行为和破坏模式。因此，本文中提出了一种改进的混凝土塑性损伤材料模型来描述其在冲击载荷下的力学响应。该改进模型考虑了压力-体积应变关系、应变率效应、洛德角效应和塑性损伤累积对混凝土材料力学特性的影响，并引入了一个与损伤相关的硬化/软化函数来描述压缩状态下的应变硬化和软化行为。随后，通过对3个独立的强度面进行线性插值得到了该改进模型的破坏强度面，并采用部分关联流动法则考虑了混凝土材料的体积膨胀特性。最后，开展了单个单元在不同加载条件下和弹体贯穿钢筋混凝土靶的数值模拟，验证了该改进模型的可行性、准确性以及预测性能提升。
- 混凝土 /
- 冲击载荷 /
- 材料模型 /
- 硬化/软化函数 /
- 塑性损伤累积
Abstract: Investigating the mechanical property of concrete structures subjected to impact loading has great significance on the design and evaluation of weapons and protective structures, while appropriate material models can more accurately predict the mechanical behavior and damage mode of concrete structures. In this paper, an improved damage-plasticity material model for concrete was proposed to describe its mechanical response subjected to impact loading. The equation of state, including elastic stage, transition stage and compacted stage, is employed to describe the pressure vs. volume strain relationship. The strain rate effect is considered by combining the radial enhancement method and the semi-empirical equation of dynamic increase factor. A unified hardening/softening function related to the shear damage caused by microcracking and the compacted damage caused by pore collapse are introduced to describe the nonlinear ascend and descend of compressive strain-stress curves in plastic stage, while an exponential function related to the tensile damage is employed to reflect the strain softening behavior under tension. Based on the current extent of damage, the failure strength surface of this improved material model is determined through linearly interpolation between the maximum and yield strength surfaces or the maximum and residual strength surfaces, and the influence of third deviatoric stress invariant on the failure strength surface is considered for describing the reduction of shear strength during the transition from high pressure to low pressure. The fractionally associated flow rule is employed to consider the volumetric dilatancy of concrete materials under confining pressure. Then, the availability and accuracy of this improved material model are verified by the numerical simulations of single element under different loading conditions, and its performance improvement is discussed by comparing with the HJC model, RHT model, Kong-Fang model and empirical equation. Finally, the numerical simulations of projectile perforating reinforced concrete slab are conducted to further validate the feasibility and accuracy of this improved material model under impact loading, from which numerical results indicate that the damage mode and residual velocity predicted by this improved material model are closer to experimental results than HJC model.
- concrete /
- impact loading /
- material model /
- hardening/softening function /
- plastic damage accumulation

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图 1 状态方程示意图

Figure 1. Schematic diagram of equation of state

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图 2 强度面示意图

Figure 2. Schematic diagram of strength surfaces

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图 3 单个单元模型

Figure 3. Single element model

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图 4 单轴压缩应力-应变曲线

Figure 4. Uniaxial compressive stress-strain curves

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图 5 单轴拉伸应力-应变曲线

Figure 5. Uniaxial tensile stress-strain curves

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图 6 三轴压缩应力-应变曲线

Figure 6. Triaxial compressive stress-strain curves

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图 7 钢筋和弹体示意图

Figure 7. Schematic diagram of reinforcement and projectile

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图 8 有限元模型

Figure 8. Finite element model

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图 9 前靶和背靶的破坏模式

Figure 9. Damage mode on the front and back surfaces

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图 10 HJC模型预测的横截面破坏模式

Figure 10. Damage mode on the cross section predicted by HJC model

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表 1 改进混凝土模型材料参数

Table 1. Material parameters of improved concrete model

基本力学参数		强度面		应变率效应		状态方程		损伤累积
参数	数值	参数	数值	参数	数值	参数	数值	参数	数值
ρ/(g·cm⁻³)	2440	f_c/MPa	48	W_x	1.6	p_crush/MPa	16	A₁	5.98
ν	0.2	f_t/MPa	4	W_y	5.5	µ_crush	0.001	A₂	1.0
G/GPa	14.86	B₁	1.59	F_m	10	p_lock/MPa	800	D_m	0.035
		N₁	0.90	S	0.8	µ_lock	0.1	ε_frac	0.01
		B₂	0.96	${\dot \varepsilon _0}$ /s⁻¹	1.0	K₁/GPa	85
		N₂	0.86			K₂/GPa	−171
		B₃	1.94			K₃/GPa	208
		N₃	0.83

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表 2 Kong-Fang模型材料参数

Table 2. Material parameters of Kong-Fang model

f_c/MPa	E/GPa	G/GPa	K/GPa	ν	T/MPa	a₁	a₂/MPa⁻¹	ω	α	d₁	d₂	d₃	ε_frac
48	32.8	13.67	18.22	0.2	4	0.5876	0.025/f_c	0.5	1	0.04	1.5	0.1	0.01

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表 3 弹体和钢筋材料参数

Table 3. Material parameters of projectile and reinforcement

材料	密度/（g·cm⁻³）	杨氏模量/GPa	泊松比	屈服强度/MPa	失效参数
弹体	8.0	200	0.3	−	−
钢筋	7.85	210	0.3	235	0.8

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表 4 弹体剩余速度

Table 4. Residual velocities of projectile

冲击速度/ （m·s⁻¹）	实验/ （m·s⁻¹）	数值模拟/（m·s⁻¹）		误差/%
冲击速度/ （m·s⁻¹）	实验/ （m·s⁻¹）	HJC模型	改进模型	HJC模型	改进模型
1058	947	991.2	961.0	4.7	1.5
749	615	649.4	634.6	5.6	3.2
606	449	490.1	475.2	9.2	5.8
434	214	243.8	235.1	13.9	9.9
381	136	164.3	157.1	20.8	15.5

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