Search
Talk

Analysis of microstructures in martensite-austenite phase transitions using sharp variational bounds

  • Oleksandr Misiats (Perdue University)
A3 01 (Sophus-Lie room)

Abstract

We consider a singularly perturbed variational problem of minimizing the sum of the surface and elastic energies of the order parameter $u$ in a two-dimensional rectangular domain. This model, originally suggested by Kohn and Muller, comes from martensitic phase transitions, in which two distinct phases of the martensite correspond to $u_y(x,y)=1$ and $u_y(x,y)=-1$. It was observed that minimizers develop self-similar branched microstructures in the case when the boundary condition is not compatible with either of the phases, and may have zigzag microstructures otherwise. In my talk, I will describe several patterns of the behavior of minimizers depending on the choice of boundary conditions, derive sharp global and local energy bounds, and discuss the applications to 2D and 3D linear elasticity models.

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

Upcoming Events of This Seminar

  • Mar 12, 2024 tba with Theresa Simon
  • Mar 26, 2024 tba with Phan Thành Nam
  • Mar 26, 2024 tba with Dominik Schmid
  • May 7, 2024 tba with Manuel Gnann
  • May 14, 2024 tba with Barbara Verfürth
  • May 14, 2024 tba with Lisa Hartung
  • Jun 25, 2024 tba with Paul Dario
  • Jul 16, 2024 tba with Michael Loss