Interfacial polyconvex energy-enhanced evolutionary model for shape memory alloys

TL;DR

This paper presents a computational study of a sharp-interface model for shape memory alloys, incorporating interfacial polyconvex energy densities and energy dissipation, with applications demonstrated through 2D examples.

Contribution

It extends interfacial polyconvex energy models to a quasistatic setting for shape memory alloys, including energy dissipation and providing computational implementations.

Findings

Validated the model with 2D computational examples

Demonstrated the role of interfacial energies in shape memory behavior

Provided accessible computer code for further research

Abstract

A sharp-interface model describing static equilibrium configurations of shape mory alloys by means of interfacial polyconvex energy density introduced by \v{S}ilhav\'y in 2010 and extended to a quasistatic situation by Kn\"upfer and Kru\v{z}\'ik in 2016 is computationally tested. Elastic properties of variants of martensite and the austenite are described by polyconvex energy density functions. Volume fractions of particular variants are modeled by a map of bounded variation. Additionally, energy stored in martensite-martensite and austenite-martensite interfaces is measured by an interface-polyconvex function. It is assumed that transformations between material variants are accompanied by energy dissipation which, in our case, is positively and one-homogeneous giving rise to a rate-independent model. Various two-dimensional computational examples are presented and the used computer code is made available for downloads.