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A phase-field description for pressurized and non-isothermal propagating fractures

机译：用于加压和非等温繁殖裂缝的相位场描述

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摘要

In this work, we extend a phase-field approach for pressurized fractures to non-isothermal settings. Specifically, the pressure and the temperature are given quantities and the emphasis is on the correct modeling of the interface laws between a porous medium and the fracture. The resulting model is augmented with thermodynamical arguments and then analyzed from a mechanical perspective. The numerical solution is based on a robust semi-smooth Newton approach in which the linear equation systems are solved with a generalized minimal residual method and algebraic multigrid preconditioning. The proposed modeling and algorithmic developments are substantiated with different examples in two- and three dimensions. We notice that for some of these configurations manufactured solutions can be constructed, allowing for a careful verification of our implementation. Furthermore, crack-oriented predictor-corrector adaptivity and a parallel implementation are used to keep the computational cost reasonable. Snapshots of iteration numbers show an excellent performance of the nonlinear and linear solution algorithms. Lastly, for some tests, a computational analysis of the effects of strain-energy splitting is performed, which has not been undertaken to date for similar phase-field settings involving pressure, fluids or non-isothermal effects. (C) 2019 Elsevier B.V. All rights reserved.
机译：在这项工作中，我们扩展了对非等温环境的加压骨折的阶段方法。具体地，压力和温度是给定量的，重点是在多孔介质和骨折之间的界面定律的正确建模上。由此产生的模型以热力学参数增强，然后从机械角度分析。数值解决方案基于鲁棒的半平滑牛顿方法，其中线性方程系统以概括的最小残余方法和代数多重级预处理解决。所提出的建模和算法发展是用两维和三维的不同示例而证实。我们注意到，对于这些配置中的一些配置，可以构建制造的解决方案，允许仔细验证我们的实现。此外，面向裂缝的预测器校正器适应性和并行实现用于保持计算成本合理。迭代号的快照显示了非线性和线性解决方案算法的出色性能。最后，对于一些测试，执行应变节能分裂效应的计算分析，其迄今尚未进行涉及压力，流体或非等温效应的类似相位场设置。 （c）2019 Elsevier B.v.保留所有权利。

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