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arXiv · 1809.06698

Interfacial polyconvex energy-enhanced evolutionary model for shape memory alloys

Miroslav Frost·Martin Kružík·Jan Valdman
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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.

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Miroslav Frost, Martin Kružík, Jan Valdman. 2018-09-15. Interfacial polyconvex energy-enhanced evolutionary model for shape memory alloys. https://arxiv.org/abs/1809.06698

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