Nov 17, 2023
Summary
Oleksandr Misiats (VCU)
Full Description
Title: Patterns in Shape Memory Alloys: Variational Perspective
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 with a simple one dimensional model. Its extensions in 2D and 3D will help us understand the energetic mechanism behind the formation of multiscale patterns in physical experiments. By means of sharp upper and lower bounds, we show that certain experimentally observed structures provide optimal energy scaling law. Despite the fact that the problem is highly nonconvex due to the presence of phase constraints and the singular perturbation, in my talk, I will describe a relaxation method which allows the use of the convex duality technique for the purpose of obtaining a sharp lower bound.
