Elastoplasticity of gradient-polyconvex materials

TL;DR

This paper introduces a new elastoplasticity model for large strain gradient-polyconvex materials, proving the existence of solutions and applicable to shape-memory materials with complex energy dependencies.

Contribution

It develops a rate-independent evolution model for gradient-polyconvex materials with large strains, including existence proofs for energetic solutions.

Findings

Existence of energetic solutions for the proposed model

Applicability to shape-memory materials

Model accommodates large strains and gradient effects

Abstract

We propose a model for rate-independent evolution in elastoplastic materials under external loading, which allows large strains. In the setting of strain-gradient plasticity with multiplicative decomposition of the deformation gradient, we prove the existence of the so-called energetic solution. The stored energy density function is assumed to depend on gradients of minors of the deformation gradient which makes our results applicable to shape-memory materials, for instance.