Equilibrium Shape of Misfitting Precipitates with Anisotropic Elasticity and Anisotropic Interfacial Energy

Extended finite element method and anisotropic level set method are coupled to determine locally stable equilibrium shapes of homogeneous and inhomogeneous precipitates in a large matrix. The bulk elasticity and the interfacial energy density are both allowed to be anisotropic while the misfit strain is kept dilatational. The anisotropy in the crystalline interfacial energies, incorporated through a dependence on the orientation, renders the evolution equation unstable for certain orientation regimes. The equation is regularized by adding a curvature term in the interface energy density which in turn requires the level set method to be modified suitably. The developed methodology is verified for several existing solutions before obtaining new results in the presence of anisotropic interfacial energy. Equilibrium shapes are obtained both for single and multiple precipitates with an emphasis on the interplay between the anisotropies in bulk elasticity and interface energy density.