动态断裂相场法的异步变分积分器
An asynchronous variational integrator for the phase field approach to dynamic fracture
摘要：
相场方法由于不需要跟踪裂纹拓扑结构和预测裂纹成核和分支的能力而被广泛用于模拟断裂行为。在这项工作中，异步变分积分器（AVI）适用于动态脆性断裂的相场方法。AVI是从Hamilton原理中推导出来的，它允许网格中的每个单元都有自己的本地时间步长，可以与其他单元的时间步长不同。当位移场被显式更新时，相位场被隐式求解，并且严格且方便地执行上界和下界。特别是，AT1和AT2变体同样容易实现。三个基准问题被用来研究两个AT 1和AT 2模型的性能和结果表明，AVI相场方法显着加快了计算效率，并成功地捕捉到复杂的动态断裂行为。
英文摘要：
The phase field approach is widely used to model fracture behaviors due to the absence of the need to track the crack topology and the ability to predict crack nucleation and branching. In this work, the asynchronous variational integrators (AVI) is adapted for the phase field approach of dynamic brittle fractures. The AVI is derived from Hamilton's principle and allows each element in the mesh to have its own local time step that may be different from others'. While the displacement field is explicitly updated, the phase field is implicitly solved, with upper and lower bounds strictly and conveniently enforced. In particular, the AT1 and AT2 variants are equally easily implemented. Three benchmark problems are used to study the performances of both AT1 and AT2 models and the results show that AVI for phase field approach significantly speeds up the computational efficiency and successfully captures the complicated dynamic fracture behavior.
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