Energy scaling laws for geometrically linear elasticity models for microstructures in shape memory alloys

被引：18

作者：

Conti, Sergio ^{[1
]}

Diermeier, Johannes ^{[1
]}

Melching, David ^{[2
]}

Zwicknagl, Barbara ^{[3
]}

机构：

[1] Univ Bonn, Inst Angew Math, D-53115 Bonn, Germany

[2] Univ Wien, Fak Math, A-1090 Vienna, Austria

[3] Humboldt Univ, Inst Math, D-10117 Berlin, Germany

来源：

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2020年 / 26卷

关键词：

Microstructure; martensitic phase transformation; energy scaling; vectorial calculus of variations; geometrically linear elasticity; ORTHORHOMBIC PHASE-TRANSITION; RIGIDITY RESULT; BRANCHED MICROSTRUCTURES; NUCLEATION BARRIERS; SURFACE-ENERGY; HYSTERESIS;

D O I：

10.1051/cocv/2020020

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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.

引用

页数：64

共 55 条

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