Local Strain and Stress Calculation Methods of Irregular Honeycombs Under Dynamic Compression

Abstract

Several continuum-based shock models have been proposed to understand the dynamic compressive behavior of cellular materials, but they are mainly based on the quasi-static stress–strain relation and thus lack sufficient dynamic stress–strain information. A virtual ‘test’ of irregular honeycombs under constant-velocity compression is carried out using the finite element method. A method based on the optimization of local deformation gradient by using the least square method is employed to calculate the one-dimensional strain distribution in the loading direction of the specimen. Meanwhile, a method based on the cross-sectional engineering stress is developed to obtain the one-dimensional stress distribution in the loading direction. The two typical features of cellular materials under dynamic crushing, namely deformation localization and strength enhancement, can be characterized by the strain and stress distributions, respectively. The results also confirm the existence of plastic shock front propagation in cellular structures under high-velocity impact, from which the shock wave speed can be estimated. The shock wave speed obtained from the local strain field method coincides with that from the cross-sectional stress method. The results of shock wave speed are also compared with those predicted by continuum-based shock models. It is shown that the shock wave speed predicted by the R-PP-L (rate-independent, rigid–perfect plastic–locking) shock model or the R-LHP-L (rate-independent, rigid–linearly hardening plastic–locking) shock model is overestimated, but that predicted by the R-PH (rate-independent, rigid–plastic hardening) shock model is close to those obtained from the local strain and cross-sectional stress calculations using the cell-based finite element model.