Stress Distribution in Graded Cellular Materials Under Dynamic Compression

Abstract

Dynamic compression behaviors of density-homogeneous and density-graded irregular honeycombs are investigated using cell-based finite element models under a constant-velocity impact scenario. A method based on the cross-sectional engineering stress is developed to obtain the one-dimensional stress distribution along the loading direction in a cellular specimen. The cross-sectional engineering stress is contributed by two parts: the node-transitive stress and the contact-induced stress, which are caused by the nodal force and the contact of cell walls, respectively. It is found that the contactinduced stress is dominant for the significantly enhanced stress behind the shock front. The stress enhancement and the compaction wave propagation can be observed through the stress distributions in honeycombs under high-velocity compression. The single and double compaction wave modes are observed directly from the stress distributions. Theoretical analysis of the compaction wave propagation in the density-graded honeycombs based on the R-PH (rigid-plastic hardening) idealization is carried out and verified by the numerical simulations. It is found that stress distribution in cellular materials and the compaction wave propagation characteristics under dynamic compression can be approximately predicted by the R-PH shock model. dynamic crushing. However, most research work is restricted to the stress at the impact/support end and thus the stress distribution is not well considered. KeywordsSignificant enhancement of crushing stress was observed in the dynamic impact experiments of woods (Reid and Peng, 1997;Harrigan et al., 2005), aluminum honeycombs (Zhao and Gary, 1998;Hou et al., 2012) and foams (Mukai et al., 1999;Deshpand and Fleck, 2000;Tan et al., 2005a;Elnasri et al., 2007). Several shock models and mass-spring models have been proposed to understand the shock wave propagation in cellular materials under dynamic impact, such as the R-PP-L (rate-independent, rigid-perfectly plastic-locking) model (Reid and Peng, 1997), the mass-spring model (Li and Meng, 2002), the E-PP-R (elastic-perfectly plastic-rigid) model (Lopatnikov et al., 2003), the power law densification model and the D-R-PH (dynamic, rigidplastic hardening) shock model . Because the assurance of the repeatability of samples and the measurement of local stress and strain states have not been well solved by experimental techniques, finite element (FE) method has been applied to simulate the dynamic crushing of cellular materials, such as regular/irregular honeycombs (Ruan et al., 2003;Zheng et al., 2005;Liu et al., 2009;Zou et al., 2009;Hu and Yu, 2013) and open-/closed-cell foams Zheng et al., 2014;Sun et al., 2016). The typical features of stress enhancement and deformation localization can be appropriately represented.The introduction of gradient to cellular structures may influence the macroscopic mechanical properties, and thus graded cellular materials have become popular in energy absorption and impact resistance. The compressive mechanical ...

Density‐Graded Cellular Solids: Mechanics, Fabrication, and Applications

“…Similar theoretical studies were conducted by Shen et al, [46,47] wherein the compaction wave propagation patterns in density-graded foams were also analyzed using shock wave theory. Results obtained from these studies as well as those of Karagioza and Alves, [48] Liu et al, [49] Wang et al, [50] Zheng et al, [51] and Chang et al [52] suggest that the shock wave propagation patterns in density-graded foams are highly sensitive to density distribution, also referred to as the gradient. It has been shown that the shock wave response in densitygraded foams with a negative gradient (i.e., the higher-density layers are positioned toward the impact side), a double shock wave propagation mode, can develop.…”

Dynamic compressive behaviour of cellular materials: A review of phenomenon, mechanism and modelling

“…Honeycombs resemble parallelly arrayed tubes, for which the dynamic load transmission during axial high-speed impact is controlled by the stress wave propagation in the tube walls [50,51] rather than cell-wall interaction (e.g. contact and compaction) in foams [52,53]. The mesoscopic mechanism of load transmission in cellular materials during high speed impact is still an open topic.…”

Shock wave speed and stress-strain relation of aluminium honeycombs under dynamic compression

“…The method is detailed in Ref. [15]. The stress distribution at the impact velocity of 200 m/s is shown in Fig.…”