Volume 26, 2020
|Number of page(s)||64|
|Published online||10 December 2020|
Energy scaling laws for geometrically linear elasticity models for microstructures in shape memory alloys*
Institut für Angewandte Mathematik, Universität Bonn,
2 Fakultät für Mathematik, Universität Wien, 1090 Wien, Austria.
3 Institut für Mathematik, Humboldt-Universität zu Berlin, 10117 Berlin, Germany.
** Corresponding author: firstname.lastname@example.org
Accepted: 16 April 2020
We consider a singularly-perturbed two-well problem in the context of planar geometrically linear elasticity to model a rectangular martensitic nucleus in an austenitic matrix. We derive the scaling regimes for the minimal energy in terms of the problem parameters, which represent the shape of the nucleus, the quotient of the elastic moduli of the two phases, the surface energy constant, and the volume fraction of the two martensitic variants. We identify several different scaling regimes, which are distinguished either by the exponents in the parameters, or by logarithmic corrections, for which we have matching upper and lower bounds.
Mathematics Subject Classification: 49J40 / 74N15 / 74G65
Key words: Microstructure / martensitic phase transformation / energy scaling / vectorial calculus of variations / geometrically linear elasticity
© EDP Sciences, SMAI 2020
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