Interfacial polyconvex energy-enhanced evolutionary model for shape memory alloys
For researchers in shape memory alloys, this work provides a computational validation of a previously theoretical model, but it is incremental as it only tests existing theory on standard examples without quantitative benchmarks.
The paper computationally tests a sharp-interface model for shape memory alloys using interfacial polyconvex energy, demonstrating its ability to simulate static equilibrium configurations with two-dimensional examples. The code is made publicly available.
A sharp-interface model describing static equilibrium configurations of shape mory alloys by means of interfacial polyconvex energy density introduced by Šilhavý in 2010 and extended to a quasistatic situation by Knüpfer and Kružík 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.