It is well known that continuum models for the evolution by surface diffusion of material surfaces in an elastic solid can become mathematically ill-posedness when the surface energy is highly anisotropic. In some cases,this ill-posedness has been associated with the formation of corners alongthe interface. In this talk, we consider a regularization of the ill-posedness which incorporates higher order terms in the surface energy. An accurate and efficient numerical method is devised for computing interface motion in the regularized model, based on the “small scale decomposition” originally developed in the context of interfacial fluid dynamics. Numerical results are presented for the specific example of a material void in a stressed solid, with an emphasis on inferring trends in the zero regularization limit. A previously formulated conjecture concerning the effect of elastic stresses on the steady interfacial corner angles (Wulff angles) is investigated within the context of the model.
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