Dynamic stress-strain states of cellular materials and a uniformly approximated relation
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摘要: 多胞材料在高速冲击下呈现出逐层压溃的变形模式，塑性冲击波模型可以用来表征这种集中变形带的传播行为。本文中采用截面应力计算方法得到了随机蜂窝在恒速冲击下的一维应力分布，进而对冲击波的传播规律进行了分析。比较了高速冲击下由不同方法得到的冲击波速度与冲击速度的关系，结果表明R-PP-L（率无关，刚性-理想塑性-锁定）模型高估了冲击波速度，但R-PH（率无关，刚性-塑性硬化）模型以及一维冲击波理论得到的冲击波速度与有限元结果比较接近。冲击波速度与冲击速度在高速情形下趋于线性关系，但随着冲击速度的减小，冲击波速度不断减少并趋于常数。根据这一特征和塑性冲击波模型，发展了可以表征冲击波速度与冲击速度的关系、动态应力应变关系的一致近似模型。Abstract: Cellular material under high-speed impact is deformed in a mode of layer-wise propagation of crushing bands, which can be characterized by the plastic shock models. In this paper, we obtained the one-dimensional stress distribution of a random honeycomb under constant-velocity compression using the cross-sectional stress calculation method, analyzed the shockwave propagation, and examined the relation between the shockwave velocity and the impact velocity obtained by different methods under high-velocity impact. The results show that the shockwave speed is overestimated by the R-PP-L (rate-independent, rigid-perfect plastic-locking) model, but the shockwave speeds obtained by the R-PH (rate-independent, rigid-plastic hardening) model and the one-dimensional shock theory are close to that of finite element simulation. The relation between the shockwave velocity and the impact velocity tends to be linear at high impact velocities, and the shockwave speed reduces to a constant with the decrease of the impact velocity. In light of these characteristics and based on the plastic shockwave model, we developed a uniformly approximated model is developed to characterize the relation between the shockwave velocity and the impact velocity and the dynamic stress-strain relation of cellular material.
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Key words:
- cellular material /
- stress distribution /
- shock theory /
- shock wave speed /
- constitutive relation
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图 1 Voronoi蜂窝试件细观有限元模型
Figure 1. A cell-based finite element model of a Voronoi honeycomb specimen
图 2 两种冲击速度下的应力分布图
Figure 2. One-dimensional stress distributions at two impact velocities
图 3 一维的应力分布及其应力梯度分布
Figure 3. One-dimensional stress distributions and the corresponding stress gradients
图 4 不同冲击速度下冲击波位置随时间的关系
Figure 4. Variation of shock front position with impact time at different impact velocities
图 5 一维应力和应变分布及其理想化
Figure 5. One-dimensional stress and strain distributions and the idealizations
图 6 不同方法得到的冲击波速度的比较
Figure 6. Comparison of shock wave speeds obtained using different methods
图 7 冲击波速度与冲击速度的关系
Figure 7. Variations of the shock wave speed with the impact velocity
图 8 波后应变和波后应力随冲击速度的变化
Figure 8. Variations of strain and stress behind shock front with impact velocity
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