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- Title
Energy scaling laws for geometrically linear elasticity models for microstructures in shape memory alloys.
- Authors
Conti, Sergio; Diermeier, Johannes; Melching, David; Zwicknagl, Barbara
- Abstract
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.
- Subjects
SHAPE memory alloys; ELASTICITY; SURFACE energy; MICROSTRUCTURE; ELASTIC modulus; NICKEL-titanium alloys
- Publication
ESAIM: Control, Optimisation & Calculus of Variations, 2020, Vol 26, p1
- ISSN
1292-8119
- Publication type
Article
- DOI
10.1051/cocv/2020020