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.
翻译:在不事先了解裂缝路径或临时标准的情况下,对复杂裂缝传播的模型采用变异阶段法已经证明,对于模拟复杂的裂缝传播而言,具有强大的影响力;然而,相场模型的能源功能是非线性和非线性,需要非常精细的网状才能捕捉损坏梯度。这意味着计算成本高,限制了该方法的具体工程应用。在这项工作中,我们建议采用经过惯性校正和能源线搜索的修改的牛顿法,为相场骨折提供一个高效和稳健的完全单一的解决器。为了说明我们采用的方法所取得的效率收益,我们将其比作两种流行的阶段-场骨折方法,即交替最小化和准蛋白质计划。为了便于评价取决于时间步骤的准毛质性计划,我们把后者与以损害为基础的标准控制的外推修正循环结合起来。最后,我们通过四个基准测试表明,我们提出的修正的牛顿法是直接、稳健的,并导致相同的解决办法。为了说明效率的提高,我们将其比喻到12和6个的计算时间因素减少至最低和准蛋质计划。