The phase-field method is a very effective way to simulate arbitrary crack nucleation, propagation, bifurcation, and the formation of complex crack networks. The diffusion-based method is suitable for multi-field coupling fracture problems. In this paper, a parallel algorithm of the thermo-elastic coupled phase-field model is implemented in commercial finite element code Abaqus/Explicit. The algorithm is applied to simulate the dynamic and quasi-static brittle fracture of thermo-elastic materials. Further, it is adopted on a structured mesh combined with first-order explicit integrators. Several examples of the quasi-static and dynamic cases of single crack, as well as multi-crack initiation and propagation under thermal shock, are given to demonstrate the robustness of the algorithm. The source code and tutorials provide an effective way to simulate crack nucleation and propagation in multi-field coupling problems.

中文翻译：

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具有显式时间积分的热弹耦合脆性断裂相场模型

相场法是一种非常有效的方法来模拟任意裂纹的形核、扩展、分叉和复杂裂纹网络的形成。基于扩散的方法适用于多场耦合断裂问题。在本文中，热弹性耦合相场模型的并行算法在商业有限元代码 Abaqus/Explicit 中实现。该算法用于模拟热弹性材料的动态和准静态脆性断裂。此外，它被用于与一阶显式积分器相结合的结构化网格。给出了单裂纹的准静态和动态情况，以及热冲击下的多裂纹萌生和扩展的几个例子，以证明算法的鲁棒性。