Gradient-enhanced continuum plasticity-damage theory for finite deformations under high velocity impact loading

Abstract The thermodynamically consistent formulation of geometrically nonlinear gradient-enhanced viscoinelasticity and the corresponding finite element solution are presented. The proposed integration algorithms are extensions of the classical rate-independent return mapping algorithms to the rate-dependent problems. The proposed finite deformation scheme is based on hypoelastic stress–strain representations and the proposed elastic predictor and coupled viscoplastic–viscodamage corrector algorithm allows for the total uncoupling of geometrical and material nonlinearities. A simple and direct computational algorithm is also used for calculation of the higher-order gradients. Model capabilities are preliminarily illustrated for the dynamic localization of inelastic flow in adiabatic shear bands and the perforation of a 12 mm thick Weldox 460E steel plates by deformable blunt projectiles at various impact speeds. Consequently, the introduced implicit and explicit length-scale measures are able to predict size effects in localization failures.