Variational phase-field methods have been shown powerful for the modeling of complex crack propagation without a priori knowledge of the crack path or ad hoc criteria. However, phase-field models suffer from their energy functional being non-linear and non-convex, while requiring a very fine mesh to capture the damage gradient. This implies a high computational cost, limiting concrete engineering applications of the method. In this work, we propose an efficient and robust fully monolithic solver for phase-field fracture using a modified Newton method with inertia correction and an energy line-search. To illustrate the gains in efficiency obtained with our approach, we compare it to two popular methods for phase-field fracture, namely the alternating minimization and the quasi-monolithic schemes. To facilitate the evaluation of the time step dependent quasi-monolithic scheme, we couple the latter with an extrapolation correction loop controlled by a damage-based criteria. Finally, we show through four benchmark tests that the modified Newton method we propose is straightforward, robust, and leads to identical solutions, while offering a reduction in computation time by factors of up to 12 and 6 when compared to the alternating minimization and quasi-monolithic schemes.

中文翻译：

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使用改进的牛顿法处理相场准静态脆性断裂的有效且稳健的整体方法

变分相场方法已被证明可以有效地模拟复杂的裂纹扩展，而无需裂纹路径或特殊标准的先验知识。然而，相场模型的能量函数是非线性和非凸的，同时需要非常精细的网格来捕捉损伤梯度。这意味着高计算成本，限制了该方法的具体工程应用。在这项工作中，我们使用具有惯性校正和能量线搜索的改进牛顿法，提出了一种有效且稳健的全单片相场断裂求解器。为了说明使用我们的方法获得的效率增益，我们将其与两种流行的相场断裂方法进行比较，即交替最小化和准单片方案。为了便于评估与时间步长相关的准整体方案，我们将后者与由基于损伤的标准控制的外推校正循环相结合。最后，我们通过四个基准测试表明，我们提出的改进的 Newton 方法直接、稳健，并导致相同的解决方案，同时与交替最小化和准化相比，计算时间最多减少 12 和 6单体方案。