Existence result for a dislocation based model of single crystal gradient plasticity with isotropic or linear kinematic hardening

TL;DR

This paper establishes the existence and uniqueness of solutions for a dislocation-based gradient plasticity model in single crystals, incorporating isotropic or linear kinematic hardening, using a variational inequality framework.

Contribution

It introduces a rigorous existence and uniqueness proof for a dislocation-based gradient plasticity model with hardening effects, expanding the mathematical understanding of such models.

Findings

Proved existence and uniqueness of solutions.

Validated the model's mathematical consistency.

Applied variational inequality framework to plasticity modeling.

Abstract

We consider a dislocation-based rate-independent model of single crystal gradient plasticity with isotropic or linear kinematic hardening. The model is weakly formulated through the so-called primal form of the flow rule as a variational inequality for which a result of existence and uniqueness is obtained using the functional analytical framework developed by Han-Reddy.