Finite element analysis of transient strain localization phenomena in frictional solids

Abstract

Finite elements with embedded shocks are used to investigate transient strain localization phenomena in frictional solids. In particular, we seek to elucidate the effect of rate sensitivity and inertia on the development of shear bands in solids subjected to impulsive loading. As in the static case, our results show that shear banding may induce severe softening of the specimen even as the material steadily hardens. As expected, rate sensitivity retards the onset of structural softening and tends to stabilize the post-peak response. It is verified that the static solution is indeed recovered in the inviscid limit. Under dynamic conditions, shear bands are observed to propagate discontinuously, arresting and resuming propagation repeatedly before linking up with the boundary of the specimen. The direction of the band is equally unsteady. In addition, multiple shear banding, with the development of secondary and even tertiary bands, appears to be a prevalent mechanism at sufficiently high impact velocities.