Crack propagation simulation without crack tracking algorithm: embedded discontinuity formulation with incompatible modes
Crack propagation simulation without crack tracking algorithm: embedded discontinuity formulation with incompatible modes
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DOI：
10.1016/j.cma.2021.114090
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发表时间：
2020-12
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影响因子：
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通讯作者：
A. Stanic;B. Brank;A. Ibrahimbegovic;H. Matthies
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文献类型：
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作者：
A. Stanic;B. Brank;A. Ibrahimbegovic;H. Matthies
我们表明，在准脆性，二维固体的裂纹扩展的模拟，可以得到很好的结果与嵌入式强不连续四边形有限元，具有不兼容的模式。更重要的是，我们证明了这些结果可以在不使用裂纹跟踪算法的情况下获得。因此，模拟多个裂纹的裂纹图案，包括分支，成为可能。避免跟踪算法主要是通过应用一种新的局部（基于高斯点）裂纹成核标准来实现的，该标准确定了嵌入定位线的时间以及其位置和方向。我们把裂纹演化的一个critical框架，软化变量描述内部耗散机制的材料退化。如数值例子所示，网格中的许多单元可能产生裂纹，但只有其中一些单元实际上打开和/或滑动，耗散断裂能，并最终形成裂纹图案。新方法已被实现的静力学和动力学，计算困难的例子（包括Kalthoff的测试）的结果表明，其非常令人满意的性能。它有效地克服了标准嵌入式强不连续性公式的不利限制，即仅模拟单个裂纹的扩展。此外，它是计算快速和简单的实施。我们的数值解匹配的结果，实验测试和以前报道的数值结果的裂纹图案，耗散断裂能，和负载-位移曲线。
We show that for the simulation of crack propagation in quasi-brittle, two-dimensional solids, very good results can be obtained with an embedded strong discontinuity quadrilateral finite element that has incompatible modes. Even more importantly, we demonstrate that these results can be obtained without using a crack tracking algorithm. Therefore, the simulation of crack patterns with several cracks, including branching, becomes possible. The avoidance of a tracking algorithm is mainly enabled by the application of a novel, local (Gauss-point based) criterion for crack nucleation, which determines the time of embedding the localisation line as well as its position and orientation. We treat the crack evolution in terms of a thermodynamical framework, with softening variables describing internal dissipative mechanisms of material degradation. As presented by numerical examples, many elements in the mesh may develop a crack, but only some of them actually open and/or slide, dissipate fracture energy, and eventually form the crack pattern. The novel approach has been implemented for statics and dynamics, and the results of computed difficult examples (including Kalthoff’s test) illustrate its very satisfying performance. It effectively overcomes unfavourable restrictions of the standard embedded strong discontinuity formulations, namely the simulation of the propagation of a single crack only. Moreover, it is computationally fast and straightforward to implement. Our numerical solutions match the results of experimental tests and previously reported numerical results in terms of crack pattern, dissipated fracture energy, and load–displacement curve.