Singular perturbation of an elastic energy with a singular weight

PHYSICA D-NONLINEAR PHENOMENA

卷:406

Article

Misiats, Oleksandr¹  Topaloglu, Ihsan¹  Vasiliu, Daniel² 

[1] Virginia Commonwealth Univ, Dept Math & Appl Math, Richmond, VA 23284 USA

[2] Coll William & Mary, Dept Math, Williamsburg, VA 23185 USA

关键词: Solid-to-solid phase transitions;    Elastic energy;    Singular perturbation;    Microstructure;    Young measure;    Scaling law;   

DOI  :  10.1016/j.physd.2020.132422

来源: Elsevier

【 摘 要 】

We study the singular perturbation of an elastic energy with a singular weight. The minimization of this energy results in a multi-scale pattern formation. We derive an energy scaling law in terms of the perturbation parameter and prove that, although one cannot expect periodicity of minimizers, the energy of a minimizer is uniformly distributed across the sample. Finally, following the approach developed by Alberti and Muller (2001) we prove that a sequence of minimizers of the perturbed energies converges to a Young measure supported on piecewise-linear periodic functions of slope +/- 1 whose period depends on the location in the domain and the weights in the energy. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free