A phase field model of dynamic fracture: Robust field updates for the analysis of complex crack patterns
A phase field model of dynamic fracture: Robust field updates for the analysis of complex crack patterns
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DOI：
10.1002/nme.4387
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发表时间：
2013-01-20
影响因子：
2.9
通讯作者：
Miehe, C.
中科院分区：
文献类型：
--
作者：
Hofacker, M.;Miehe, C.
基于尖锐裂纹不连续面的固体动态断裂破坏机理的数值模拟在复杂裂纹拓扑结构的情况下会受到影响，并且需要制定额外的分支准则。这一缺陷可以通过基于引入裂纹相场的扩散裂纹模拟来克服。在我们最近对相场型脆性断裂的准静态模拟工作的基础上，我们提出了一个动态问题的扩散断裂的计算框架，该框架允许模拟复杂的扩展裂纹拓扑。它基于局部历史场的引入，其中包含在变形历史中获得的最大参考能量，该能量可以被认为是历史上最大拉伸应变的量度。这个局域变量驱动着裂纹相场的演化。它的介绍提供了控制扩散裂纹拓扑的平衡方程的一个非常透明的表示。特别是，它允许构建一个非常健壮的算法来处理扩散性断裂的弹性动力学问题。在这里，我们将最近提出的算子分裂方案从准静态问题推广到动态问题。在一个典型的时间步长内，它依次更新历史场、裂纹相场，最后是位移场。通过典型的数值算例，展示了动态载荷作用下复杂裂纹形态的演化过程，从而验证了断裂相场公式的有效性。版权所有(C)2012 John Wiley&Sons，Ltd.
The numerical modeling of dynamic failure mechanisms in solids due to fracture based on sharp crack discontinuities suffers in situations with complex crack topologies and demands the formulation of additional branching criteria. This drawback can be overcome by a diffusive crack modeling, which is based on the introduction of a crack phase field. Following our recent works on quasi-static modeling of phase-field-type brittle fracture, we propose in this paper a computational framework for diffusive fracture for dynamic problems that allows the simulation of complex evolving crack topologies. It is based on the introduction of a local history field that contains a maximum reference energy obtained in the deformation history, which may be considered as a measure of the maximum tensile strain in the history. This local variable drives the evolution of the crack phase field. Its introduction provides a very transparent representation of the balance equation that governs the diffusive crack topology. In particular, it allows for the construction of a very robust algorithmic treatment for elastodynamic problems of diffusive fracture. Here, we extend the recently proposed operator split scheme from quasi-static to dynamic problems. In a typical time step, it successively updates the history field, the crack phase field, and finally the displacement field. We demonstrate the performance of the phase field formulation of fracture by means of representative numerical examples, which show the evolution of complex crack patterns under dynamic loading. Copyright (c) 2012 John Wiley & Sons, Ltd.