A gradient plasticity model for the simulation of shear localization

Abstract

The numerical simulation of shear localization under high strain rates can be modeled by a system of four partial differential equations including conservation of momentum, conservation of energy, elastic, and inelastic constitutive relations. This article introduces the gradient terms of the equivalent plastic strain to the inelastic equation based on the implicit gradient theory of plasticity to preserve the ellipticity for the shear band modeling. The model is constructed by the mixed finite element formulation with B-bar to reduce shear locking effects considering displacement, stress, equivalent plastic strain, and temperature as the solution field and thereafter solving the entire nonlinear governing system simultaneously. The performance of the gradient plasticity model is verified by two benchmark shear band problems, and the obtained numerical results are tested with the high-rate experimental results.