Abstract

Surface instabilities driven by stress

Chaouqi Misbah
Centre National de la Recherche Scientifique (CNRS)

A review on surface instabilities driven by stress is presented.Various examples from different contexts (MBE, solidification, stylolithes in geophysics, cell motility) where surface stress instabilities play a decisive role are discussed. We then focus on the study of the nonlinear regime by means of a phase-field formulation. We discuss the basic questions of the formulation and especially how the reference state is properly chosen. We show that the phase field causes a regularization of the finite time singularity associated with the instability.We discuss also the fact that the phase field implicitly introduces
a yield-like stress. We present the main outcomes obtained to date by the phase-field formulation. Preliminary results on the coarsening dynamics are briefly outlined.