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....

中文翻译：

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具有各向异性弹性和各向异性界面能的失配沉淀物的平衡形状

结合扩展有限元法和各向异性能级集方法，可以确定大型基体中均匀和不均匀沉淀的局部稳定平衡形状。体弹性和界面能密度都是各向异性的，而失配应变保持膨胀。通过依赖于取向而结合的晶体界面能中的各向异性使演化方程对于某些取向状态不稳定。通过在界面能量密度中添加曲率项来对方程进行正则化，这反过来又需要对水平设置方法进行适当的修改。在各向异性界面能的存在下获得新结果之前，已对几种现有解决方案的方法进行了验证。