We describe a general phase-field model for hyperelastic multiphase materials. The model features an elastic energy functional that depends on the phase-field variable and a surface energy term that depends in turn on the elastic deformation, as it measures interfaces in the deformed configuration. We prove the existence of energy minimizing equilibrium states and $\Gamma$-convergence of diffuse-interface approximations to the sharp-interface limit.

中文翻译：

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具有欧拉界面的多相固体的平衡

我们描述了超弹性多相材料的一般相场模型。该模型具有取决于相场变量的弹性能量函数和取决于弹性变形的表面能项，因为它测量变形配置中的界面。我们证明了能量最小化平衡状态和 $\Gamma$ - 扩散界面逼近锐界面极限的收敛性的存在。