Shape memory alloys as gradient-polyconvex materials

TL;DR

This paper proves the existence of solutions for a shape memory alloy model using gradient-polyconvex energy functionals, ensuring physically realistic deformations that are orientation-preserving and injective.

Contribution

It introduces a gradient-polyconvex framework for modeling shape memory alloys and establishes existence of solutions with physically meaningful deformation properties.

Findings

Existence of energetic solutions for the model.

Deformations are orientation-preserving.

Deformations are injective everywhere.

Abstract

We show existence of an energetic solution to a model of shape memory alloys in which the elastic energy is described by means of a gradient-polyconvex functional. This allows us to show existence of a solution based on weak continuity of nonlinear minors of deformation gradients in Sobolev spaces. Resulting deformations are orientation-preserving and injective everywhere in a domain representing the specimen.