Long-time dynamics of the three-dimensional biaxial Grinfeld instability

Using a phase-field model including strain fields, we numerically investigate the melting-crystallization dynamics of a biaxially stressed semi-infinite solid. A multigrid algorithm is used to solve the elasticity part of the problem. Its efficiency allows us to explore the late stages of the full 3D Grinfeld instability. Recent analytical predictions [ P. Berger et al. Phys. Rev. Lett. 90 176103 (2003)] regarding stability and selection of patterns are confirmed and precised. It appears that, in the presence of a large scale stabilization mechanism, the system reaches an equilibrium state corresponding to a nontrivial striped pattern.