This week's seminars
Applied Mathematics Seminars: Surface energies emerging in martensitic phase transformations
16 March 2018 14:00 in CM219
We will discuss microscopic modelling of a two-dimensional two-well problem which arises from the square-to-rectangular martensitic transformation in 2D shape-memory materials. In this discrete set-up, I will focus on the surface energy scaling regime and analyse the Hamiltonian incorporating two-body and three-body interactions on an atomistic lattice. This Hamiltonian allows for a direct control of the discrete second order deformation gradients as well as for a one-sided comparison with a two-dimensional spin system. Exploring this we will derive a (first order) continuum limit and show the emergence of surface energy in the form of a sharp-interface limiting model as well as the explicit structure of the minimisers to the latter. This is a joint work with Stephan Luckhaus and Angkana Rueland.
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