Martensitic inclusions in low-hysteresis shape memory alloys

I will report some recent analytical results on microstructures in low-hysteresis shape memory alloys. The modelling assumption is that the width of the thermal hysteresis is closely related to the minimal energy that is necessary to build a martensitic nucleus in an austenitic matrix. This energy barrier is typically modeled by (singularly perturbed) nonconvex elasticity functionals. In this talk, I will discuss recent results on the resulting variational problems, including stress-free inclusions and microstructures in the case of almost compatible phases. This talk is partly based on joint works with S. Conti, J. Diermeier, M. Klar, and D. Melching.