Bridging of length scales through gradient theory and diffusion equations of dislocations

Abstract

In order to predict the observed characteristic width of shear bands in plastic materials, internal length scales have been introduced by the incorporation of higher-order gradients into the constitutive equations. The gradient enhanced constitutive model is derived using consistent thermodynamics for a classical rate-independent J 2 plasticity model with kinematic and isotropic hardening. Second-order gradients are introduced in the plasticity potential function and yield criteria through the use of nonlocal measures, which are introduced for each of the local hardening variables selected to describe the material response. The numerical implementation of the nonlocal continuum plasticity model is also presented. In order to link the gradient approach to the microstructure, a discussion is given in which relations for the gradient theory material parameters are given in terms of the microstructural material parameters.