We present an effective mechanical equilibrium solution algorithm suitable for finite strain consideration within the phase-field method. The proposed algorithm utilizes a Fourier space solution in its core. The performance of the proposed algorithm is demonstrated using the St. Venant–Kirchhoff hyperelastic model, but the algorithm is also applicable to other hyperelastic models. The use of the fast Fourier transformation routines and fast convergence within several iterations for most common simulation scenarios makes the proposed algorithm suitable for phase-field simulations of rapidly evolving microstructures. Additionally, the proposed algorithm allows using different strain measures depending on the requirements of the underlying problem. The algorithm is implemented in the OpenPhase phase-field simulation library. A set of example simulations ranging from simple geometries to complex microstructures is presented. The effect of different externally applied mechanical boundary conditions and internal forces is also demonstrated. The proposed algorithm can be considered a straightforward update to already existing small strain solvers based on Fourier space solutions.

我们提出了一种有效的机械平衡求解算法，适用于相场方法中的有限应变考虑。所提出的算法在其核心中利用傅里叶空间解决方案。使用圣维南-基尔霍夫超弹性模型证明了所提出算法的性能，但该算法也适用于其他超弹性模型。对于大多数常见的模拟场景，使用快速傅立叶变换例程和多次迭代内的快速收敛使得所提出的算法适用于快速演化的微观结构的相场模拟。此外，所提出的算法允许根据潜在问题的要求使用不同的应变测量。该算法在OpenPhase相场仿真库中实现。提供了一组从简单几何形状到复杂微观结构的示例模拟。还证明了不同的外部施加机械边界条件和内力的影响。所提出的算法可以被认为是对基于傅立叶空间解的现有小应变求解器的直接更新。