Abstract One major merit of phase-field models for fracture is that cracks nucleation, propagation, branching, merging, coalescence and even fragmentation, etc., can be accounted for seamlessly within a standalone regularized variational framework. This fascinating feature overcomes the cumbersomeness in the characterization of non-smooth crack surfaces and the tracking of complex crack paths. However, the numerical algorithms frequently adopted in solving the coupled governing equations are not robust or efficient enough, together with the high computational cost in resolving the fracture process zone, largely hindering application of these models to general 3D problems. In this work, several 3D benchmark problems involving mode I, I+II or I+III failure in brittle and quasi-brittle solids is addressed based on our recent theoretical and numerical progresses on the unified phase-field theory for damage and fracture (Wu, 2017). Complex 3D fracture problems with over 2 million elements and more than 6 million degrees of freedom (dofs) can be tackled using normal computation facilities within acceptable computational time. Moreover, we are able to not only reproduce qualitatively evolution of the complex fracture pattern, but also compare quantitatively the global responses against experimental results. With the need neither to characterize the non-smooth crack surface nor to track the twisting crack path, the 3D computer implementation is almost the same as the 2D counterpart, paving the way to the phase-field modeling of large scale engineering problems.

中文翻译：

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固体中 I + II/III 模式失效的三维相场建模

摘要 断裂相场模型的一个主要优点是裂纹的成核、扩展、分支、合并、合并甚至破碎等，可以在独立的正则化变分框架内无缝解释。这一引人入胜的功能克服了非光滑裂纹表面表征和复杂裂纹路径跟踪的繁琐性。然而，在求解耦合控制方程时经常采用的数值算法不够稳健或不够高效，再加上求解裂缝过程区的计算成本高，在很大程度上阻碍了这些模型在一般 3D 问题中的应用。在这项工作中，涉及模式 I 的几个 3D 基准问题，脆性和准脆性固体中的 I+II 或 I+III 失效基于我们最近在损伤和断裂的统一相场理论方面的理论和数值进展（Wu，2017）。具有超过 200 万个元素和超过 600 万个自由度 (dof) 的复杂 3D 断裂问题可以在可接受的计算时间内使用普通计算设施解决。此外，我们不仅能够定性地再现复杂断裂模式的演变，还能够定量地将全局响应与实验结果进行比较。由于不需要表征非光滑裂纹表面，也不需要跟踪扭曲裂纹路径，3D 计算机实现与 2D 对应物几乎相同，为大规模工程问题的相场建模铺平了道路。