Title: Microstructure in Shape-Memory Alloys: Rigidity,Flexibility and Some Numerical Simulations
Abstract: In this talk I will discuss a striking dichotomy whichoccurs in the mathematical analysis of microstructures in shape-memory alloys:On the one hand, some models for these materials display a very rigid structurewith only very specific microstructures, if one assumes that surface energiesare penalised. On the other hand, without this penalisation, for the samemodels a plethora of very ``wild'' solutions exists.
Motivated by this observation, we seek to furtherunderstand and analyse the underlying mechanisms. Constructing explicitsolutions for a model problem, we show that adding only little regularity tothe model does not suffice to exclude the wild solutions. We illustrate theseconstructions by presenting numerical simulations of them. The talk is based onjoint work with F. Della Porta, J. M. Taylor, Ch. Zillinger and B. Zwicknagl.