Computational and Applied Mathematics seminar

Abstrakt finns enbart på engelska: 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. 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. I will also describe the extension of the linear elastic models of two twins to model multiscale patterns, which appear in recent physical experiments and involve mixing of four twins.