Pattern Formation in a 2D Elastic Solid

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.