A gradient-dependent constitutive model to simulate impact damage problem

Conventional continuum mechanics models of inelastic deformation processes are size scale independent since they do not possess intrinsic length scales in their constitutive description. In contrast, there is considerable experimental evidence that inelastic flow in crystalline materials is size-dependent. As soon as material failure dominates a deformation process, the material increasingly displays strain softening (localization) and the finite element computation is considerably affected by the mesh size and alignment and gives non-physical descriptions of the localized regions. Gradient-enhanced constitutive viscoplastic and viscodamage equations that include explicit and implicit micro-structural length scale measures are presented in this work. The governing equations are appropriate for polycrystalline metals. Numerical simulations are performed to study the effect of including these material lengths on the dynamic localization of plastic flow in shear bands for impact-damage related problems. It is shown that the inherent material length scale predictions agree well with the width of the shear bands in ductile metals as compared to the experimental results.