Pattern Formation in a 2D Elastic Solid

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. Dynamical pattern formation, while canonically associated with fluid systems such as convection cells, or initially fluid systems, such as is the case in eutectic solidification, also occurs in fully coherent solid–to–solid structural phase transformations which are purely elastic in character. Such phase transformations, generally known as “Martensites”, involve the formation of regions of the solid which become permanently strained relative to their