English

Interfacial polyconvex energy-enhanced evolutionary model for shape memory alloys

Numerical Analysis 2019-03-26 v2

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.

Cite

@article{arxiv.1809.06698,
  title  = {Interfacial polyconvex energy-enhanced evolutionary model for shape memory alloys},
  author = {Miroslav Frost and Martin Kružík and Jan Valdman},
  journal= {arXiv preprint arXiv:1809.06698},
  year   = {2019}
}

Comments

23 pages, 6 figures. arXiv admin note: text overlap with arXiv:1508.02990

R2 v1 2026-06-23T04:10:01.959Z