Dynamic crushing of 2D cellular structures: Local strain field and shock wave velocity

Continuum-based shock models have been proposed by different authors to understand the strength enhancement and deformation localization phenomena observed in the dynamic response of cellular materials, but their applicability is still debatable due to continuum-based stress wave theory being used to cellular materials with finite cell sizes. A method based on the optimal local deformation gradient is developed to calculate the local strain field of a deformed cellular structure using a cell-based finite element model. The strain field provides evidences of the existence of a plastic shock front in cellular materials under a high or moderate velocity impact. Due to the feature of shock front propagation, the 2D strain fields are simplified to one-dimensional distributions of strain in the loading direction. Shock wave velocity is measured by an approach that gives the location of the shock front varying with the impact time. A comparison of the cell-based finite element model with continuum-based shock models indicates that the shock model based on a material accounting for the post-locking behaviour is more accurate in predicting the shock wave velocity. Finally, stress–strain states ahead of and behind the shock front are obtained. These results provide an explanation in terms of deformation mechanism for the stress reduction at the support end with increasing impact velocity, which was previously observed in experimental and numerical studies.