Linear Elastic Models of Shape Memory Alloys: Variational Perspective

by Prof. Oleksandr Mitsiats (Virginia Commonwealth University)

Thursday May 8, 2025, 2:15 PM → 4:15 PM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

Abstract:  

In this talk I will describe a class of minimization problems arising in
 modelling shape memory alloys.  I will start with a shape memory material illustration, followed by a simple one dimensional model of it. Its extensions in 2D and 3D will help us understand the energetic mechanism behind the formation of twin patterns in physical experiments. By means of sharp upper and lower bounds, we
show that certain experimentally observed  structures provide optimal energy scaling law, and - under certain assumptions - are true energy minimizers. I will also discuss the extension of the linear elastic models for two twins to model multiscale patterns, which appear in recent physical experiments and involve mixing of four
twins.