Dynamic crushingof cellular materials: a particle velocity-based analytical method and its application

Cellular material under high-velocity impacthas a typical feature oflayer-wise collapse.A cell-based finite element model is employed to simulate the direct impact of closed-cell foam, and one-dimensional velocity field distributionsareobtained to characterize thecrushing bandpropagating through a cellular material. An explicit expression of continuous velocity distribution is derivedbased on the features of velocity gradient distribution. The velocity distribution function is adopted to determine the dynamic stress-strain statesof cellular materials under dynamic loading.The local stress-strain history distribution reveals that sectional cells experience a process from the precursor of elastic behavior to the shock stress state, through the dynamic initial crushing state. A power-law relation between the dynamic initial crushing stress andthe strainrate isestablished, which confirms the strain-rate effect of cellular materials. By extracting the critical points immediately before the unloading stage on the local dynamic stress-strain history curves, the dynamic stress-strain statesof cellular materials are determined. They exhibit loading rate-dependence but are independent of the initial impact velocity.Furthermore, with the increase of relative density, the dynamic hardening behaviorof cellular specimen is enhanced and the crushing process event is advanced. The particle velocity-based analytical method is appliedto analyze the dynamic responses of cellular materials.This method is better than continuum-based shock models, since itdoes not require a pre-assumed constitutive relation.Therefore,the particle velocity-based analytical method proposed in this study may provide new ideas to carry out dynamic experimental measurement, which is especially applicable toinhomogeneous materials.