# Strain gradient visco-plasticity with dislocation densities contributing to the energy

## TL;DR

This paper develops a mathematical model for strain gradient visco-plasticity incorporating dislocation densities, proving existence of solutions using advanced analytical techniques.

## Contribution

It introduces a convex, non-quadratic energy model with curl-dependent plastic strains and establishes existence results via time-discretization and compactness methods.

## Key findings

- Existence of solutions for the proposed model
- Inclusion of dislocation densities in energy formulation
- Use of Helmholtz decompositions and compensated compactness

## Abstract

We consider the energetic description of a visco-plastic evolution and derive an existence result. The energies are convex, but not necessarily quadratic. Our model is a strain gradient model in which the curl of the plastic strain contributes to the energy. Our existence results are based on a time-discretization, the limit procedure relies on Helmholtz decompositions and compensated compactness.