A sharp interface evolutionary model for shape memory alloys

TL;DR

This paper proves the existence of solutions for a quasistatic model of shape memory alloys, incorporating phase boundaries, microstructure evolution, and finite length scales, using polyconvex energy densities.

Contribution

It introduces a new evolutionary model for shape memory alloys with phase boundary energies and proves the existence of energetic solutions.

Findings

Existence of energetic solutions for the model.

Inclusion of interface-polyconvex energy for phase boundaries.

Model allows for microstructure evolution with finite length scales.

Abstract

We show the existence of an energetic solution to a quasistatic evolutionary model of shape memory alloys. Elastic behavior of each material phase/variant is described by polyconvex energy density. Additionally, to every phase boundary, there is an interface-polyconvex energy assigned, introduced by M. \v{S}ilhav\'{y}. The model considers internal variables describing the evolving spatial arrangement of the material phases and a deformation mapping with its first-order gradients. It allows for injectivity and orientation-preservation of deformations. Moreover, the resulting material microstructures have finite length scales.