In this work, phase-field modeling of hydraulic fractures in porous media is extended towards a Global–Local approach. Therein, the failure behavior is solely analyzed in a (small) local domain. In the surrounding medium, a simplified and linearized system of equations is solved. Both domains are coupled with Robin-type interface conditions. The fractures inside the local domain are allowed to propagate and consequently, both subdomains change within time. Here, a predictor–corrector strategy is adopted, in which the local domain is dynamically adjusted to the current fracture pattern. The resulting framework is algorithmically described in detail and substantiated with some numerical tests.

在这项工作中，将多孔介质中水力压裂的相场建模扩展到了全局-局部方法。其中，仅在（小型）本地域中分析故障行为。在周围的介质中，求解了简化的线性化方程组。两个域都与Robin类型的接口条件耦合。局部区域内部的裂缝被允许传播，因此，两个子区域都随时间变化。在这里，采用了一种预测-校正策略，其中局部域被动态地调整为当前的裂缝模式。由此产生的框架在算法上进行了详细描述，并通过一些数值测试得到了证实。