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Microstructures in SMA: Rigidity, Non-Rigidity and Simulations

Presented by: 
Angkana Ruland Max-Planck-Institut für Mathematik, Leipzig
Tuesday 15th January 2019 - 14:30 to 15:15
INI Seminar Room 1
Co-authors: Jamie M Taylor (BCAM), Christian Zillinger (USC), Barbara Zwicknagl (TU Berlin)In this talk I will discuss a striking dichotomy which occurs in the mathematical analysis of microstructures in shape-memory alloys: On the one hand, some models for these materials display a very rigid structure with only very specific microstructures, if one assumes that surface energies are penalised. On the other hand, without this penalisation, for the same models a plethora of very wild solutions exists. Motivated by this observation, we seek to further understand and analyse the underlying mechanisms. By discussing a two-dimensional toy model and by constructing explicit solutions, we show that adding only little regularity to the model does not suffice to exclude the wild solutions. We illustrate these constructions by presenting numerical simulations of them. The talk is based on joint work with J. M. Taylor, Ch. Zillinger and B. Zwicknagl.
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons