# Thermodynamic dislocation theory: Finite deformations

## TL;DR

This paper extends the thermodynamic dislocation theory to account for non-uniform finite plastic deformations, deriving new equations of motion and applying them to finite strain shear in single crystals.

## Contribution

It introduces a generalized theory for finite deformations in dislocation mechanics, including simplified models and specific application to shear problems.

## Key findings

- Derived equations of motion from variational principles.
- Applied theory to finite strain constrained shear of single crystals.
- Demonstrated the theory's capability to model complex deformation behaviors.

## Abstract

The present paper extends the thermodynamic dislocation theory initiated by Langer, Bouchbinder and Lookman [2010] to non-uniform finite plastic deformations. The equations of motion are derived from the variational equation involving the free energy density and the positive definite dissipation function. We also consider the simplified theory by neglecting the excess dislocations. For illustration, the problem of finite strain constrained shear of single crystals with one active slip system is solved within the proposed theory.