Pattern Formation in a 2D Elastic Solid

TL;DR

This paper develops a dynamical theory for pattern formation during a 2D martensitic transition in an elastic solid, revealing surface nucleation and pattern length scale selection.

Contribution

It introduces a global mode-based Galerkin method to simulate the transition based on a nonlinear Ginzburg-Landau framework including sound-wave viscosity.

Findings

Observation of surface nucleation phenomena.

Identification of dynamical pattern length scale selection.

Simulation of martensitic transition dynamics.

Abstract

We present a dynamical theory of a two-dimensional martensitic transition in an elastic solid, connecting a high-temperature phase which is nondegenerate and has triangular symmetry, and a low-temperature phase which is triply degenerate and has oblique symmetry. A global mode-based Galerkin method is employed to integrate the deterministic equation of motion, the latter of which is derived by the variational principle from a nonlinear, nonlocal Ginzburg-Landau theory which includes the sound-wave viscosity. Our results display (i) the phenomenon of surface nucleation, and (ii) the dynamical selection of a length scale of the resultant patterns.