A variational multiscale method to incorporate strain gradients in a phenomenological plasticity model

摘要

We treat mathematical and computational issues related to the incorporation of strain gradient terms in a phenomenological plasticity model. The strain gradients are associated with incompatibilities due to geometrically necessary dislocations, and are quantified by the Nye dislocation density tensor. When incorporated within a flow rule for the plastic strain rate, this tensor fundamentally alters the mathematical structure of the theory. Several computational complexities also arise as a result. These problems are posed in the setting of a variationally-based multiscale method. It allows the circumvention of some of the mathematical and computational difficulties associated with this model. The phenomenological plasticity model, its enhancement by strain gradients, formulation within a multiscale context and two numerical examples are presented.