Enhanced Approach to Consistency in Gradient-Dependent Plasticity

Abstract

This note proposes a modification of gradient-dependent plasticity to improve convergence. In gradient-dependent plasticity, the consistency condition, which results in a differential equation with respect to the plastic multiplier, is solved simultaneously with the equilibrium equation. In each iteration, the consistency condition is not really satisfied and the stress is generally not on the yield surface; this results in poor convergence. A modification is proposed, in which gradient-dependent plasticity is recast into the classical plasticity framework and a strict stress mapping strategy is established. Instead of solving a differential equation simultaneously with the equilibrium equation, the plastic multiplier is solved by minimizing a functional separately. The consistency condition can be satisfied and the stress is mapped back to the yield surface.