Dynamic crushing of cellular materials: A unified framework of plastic shock wave models

Strength enhancement and deformation localisation are typical features of the dynamic response of cellular materials. Several one-dimensional shock models have been developed to explain these features. A unified framework of one-dimensional plastic shock wave models was established in this paper. Based on an arbitrary plastic hardening constitutive model for cellular materials, general solutions, although implicit, have been derived for two impact scenarios. For a rigid–power-law hardening (R-PLH) idealisation involved in three material parameters, namely the yield stress, the strength index and the strain-hardening index, closed-form/semi-closed-form solutions of the physical quantities across the shock front have been derived. The linearly hardening and locking idealisations are found to correspond to the two opposite limit cases with the strain-hardening index of one and infinity, respectively. The shock models based on three different idealisations are verified with cell-based finite element models including an irregular honeycomb and a closed-cell foam. It is found that the force responses predicted by the shock models are not very sensitive to the choice of the idealisations and they are in good agreement with the cell-based finite element results. Deformation features predicted by the shock models are compared well with the cell-based results when the impact velocity is not very low. The comparisons show that using more realistic constitutive models such as the R-PLH idealisation may present more accurate predictions.