# Thermodynamic dislocation theory for non-uniform plastic deformations

## TL;DR

This paper extends thermodynamic dislocation theory to non-uniform plastic deformations, deriving new governing equations and demonstrating their application to plane strain shear in single crystals.

## Contribution

It introduces a generalized thermodynamic dislocation framework for non-uniform deformations, including new free energy and dissipation functions, with derivation from variational principles.

## Key findings

- Derived governing equations for non-uniform plasticity
- Applied theory to plane strain shear of single crystals
- Validated the extended model through a specific deformation problem

## Abstract

The present paper extends the thermodynamic dislocation theory developed by Langer, Bouchbinder, and Lookmann to non-uniform plastic deformations. The free energy density as well as the positive definite dissipation function are proposed. The governing equations are derived from the variational equation. As illustration, the problem of plane strain constrained shear of single crystal deforming in single slip is solved within the proposed theory.