Mitchell Luskin

Metastability and Microstructure in Structural Phase Transformations

Abstract:

Phase transformation, microstructure, and metastability offer great challenges to the development of mathematical models, analysis, and computation. I will present some solutions to these problems in the context of martensitic structural phase transformations. Martensitic crystals undergo a first order structural phase transformation between a high symmetry crystalline phase and several variants of a low symmetry crystalline phase (such as the cubic to orthorhombic transformation in some CuAlNi alloys). These crystals are observed to be in metastable states (local minima) exhibiting a fine-scale spatial oscillation (microstructure) between the variants of the low symmetry phase, and hysteresis is observed as the temperature or boundary forces are varied. I will present computational methods and a numerical analysis for this microstructure, and I will discuss several multiscale methods and the different metastable states that they compute.

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