A theoretical study of shock front propagation in the density graded cellular rods

Abstract

The present theoretical study focuses on the shock front propagation in a density graded cellular rod. It aims at the determination of the shock front velocity evolution as well as the stress evolution during the impact. The density gradient leads necessarily to the property gradient, which is taken into account in this analysis. The locking strain in classical shock front theory is replaced by the notion of the locking density to adapt to the studied case. Analytical solutions of linear, quadratic and square root density profiles are obtained. They are compared to the FEM solution with a good agreement. This study reveals a possibility to reduce the maximum impact stress for the impacted structures (same impacting mass, same energy absorption) using a proper density gradient.

Propagation of compaction waves in cellular materials with continuously varying density

“…In the numerical simulations, the authors used an aluminium based foam material with notable strain hardening for which the RPPL material approximation is not accurate. Another model for compaction of graded cellular material using also the RPPL material approximation was proposed by Liu et al (2015) where a predefined locking density was defined from which the densification strains ware obtained. Several functions for the density gradient ware analysed in this study however, the gradient always increased in the direction of the propagation of the compaction wave, which limited the observed phenomena types.…”

Mesoscopic investigation of layered graded metallic foams under dynamic compaction

“…The dynamic response of the metallic foam is critical for the design of foam-filled sandwich structures. Researches (Ajdari et al, 2009; Goetz and Matous, 2013; Hou et al, 2014; Karagiozova and Alves, 2014, 2015; Liu et al, 2015; Shen et al, 2013, 2014) have shown that the mechanical response of graded metallic foam core is superior to the uniform density core. There are two types of density-graded structure.…”

“…Results show that the gradient significantly influences the energy absorption capability. Shen et al (2014) and Liu et al (2015) proposed improved models based on the R-P-P-L model. Goetzet and Matous (2013) proposed an elastic-plastic-densifying (EPD) model to obtain the nonlinear wave equation in the two layer cellular materials.…”

A simplified model and its asymptotic solution for the crashworthiness design of graded cellular material

“…Wang等人 [4,8] 通过变胞元技术构 建了连续密度梯度蜂窝结构的数值计算模型, Yang等 人 [14] 将其进一步拓展到了三维情形. 多种密度分布的梯度多胞材料的冲击响应和吸能 特性已经得到研究 [24,25] . 近来, Yang等人 [14] 提出了反向 设计的思想, 即在给定的冲击力下, 基于冲击波模型对 梯度多胞结构的相对密度分布进行设计, 并利用细观 有限元模型证实了有效性.…”