Interface mechanics can significantly govern the evolution of multiple phases on smaller scales, e.g., determining the properties of TWIP- and TRIP-steels, geopolymers or Li-ion batteries. The present contribution is specifically centered around the influence of interface elasticity on mechanically induced phase transformations. A geometrically exact finite element framework is developed for this purpose based on incremental energy minimization. It is set up in three-dimensional space and comprises an Allen-Cahn type phase field formulation based on a Modica-Mortola double-well functional, as well as a Ginzburg-Landau type viscosity formulation. The phase field approximation of the interface deformation gradient is derived by means of homogenization theory. A monolithic solver is employed for the resulting set of non-linear coupled equations. The example of coalescing spheres shows that larger interface energies can amplify and accelerate coalescence. Lower interface energies, in contrast, allow for distinct spreading of the energetically favorable bulk phase. Deformation-dependent interface energies particularly add stress peaks to this process that are localized at the phase transition zone. The relaxation of a stepped interface shape showed that deformation-dependent interface energies favor a plane partition of the bulk phases. Yet, they also delay breakup events compared to simple constant interface energies. This peculiarity can be beneficial for calibration purposes. Strain dependence moreover causes an additional elastic stiffness in the direction of the interface tangent plane and constitutes thus another origin for anisotropy of the overall structure.

中文翻译：

---

超弹性材料界面的相场建模——相变的理论、实现和应用

界面力学可以显着控制较小尺度上多个相的演化，例如确定 TWIP 和 TRIP 钢、地质聚合物或锂离子电池的性能。目前的贡献特别集中于界面弹性对机械诱导相变的影响。为此，基于增量能量最小化，开发了几何精确的有限元框架。它建立在三维空间中，包括基于 Modica-Mortola 双井泛函的 Allen-Cahn 型相场公式以及 Ginzburg-Landau 型粘度公式。利用均质化理论推导了界面变形梯度的相场近似。采用单片求解器来求解非线性耦合方程组的结果。聚结球体的例子表明，较大的界面能可以放大和加速聚结。相反，较低的界面能允许能量上有利的体相的明显扩散。与变形相关的界面能尤其会在该过程中增加位于相变区的应力峰值。阶梯界面形状的松弛表明，变形相关的界面能有利于体相的平面划分。然而，与简单的恒定界面能相比，它们也会延迟分解事件。这种特性对于校准目的可能是有益的。此外，应变依赖性导致界面切平面方向上的额外弹性刚度，并因此构成整体结构各向异性的另一个来源。