Mass lumping strategies for X‐FEM explicit dynamics: Application to crack propagation
Mass lumping strategies for X‐FEM explicit dynamics: Application to crack propagation
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DOI：
10.1002/nme.2180
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发表时间：
2008-04
影响因子：
2.9
通讯作者：
T. Menouillard;J. Réthoré;Nicolas Moes;A. Combescure;Harridh Bung
中科院分区：
文献类型：
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作者：
T. Menouillard;J. Réthoré;Nicolas Moes;A. Combescure;Harridh Bung
本文使用扩展有限元方法处理动态情况下裂纹的数值模拟。更确切地说，我们对显式算法感兴趣。我们证明，通过使用一种特定的集中技术，临界时间步长与没有裂纹时完全相同。这在一定程度上改进了先前的结果，先前的结果是临界时间步长比无裂纹情况减少了\(\sqrt{2}\)倍。新的集中技术是通过使用一种最初为处理包含孔洞的单元而开发的集中策略获得的。确切地说，所得到的结果仅在裂纹由海维赛德富集建模时才有效。还需注意，所得的集中矩阵是块对角的（块大小为\(2×2\)）。对于常应变单元（线性单纯形单元），当单元被切割时临界时间步长不变。由于集中质量矩阵，临界时间步长永远不会趋于零。此外，集中技术在刚体运动中能保持动能。另外，拉应力波不会通过不连续处传播。因此，集中技术既不会在刚体运动的动能守恒上产生误差，也不会使波通过裂纹传播。这两种技术都将用于数值实验。版权所有©2007约翰威立父子有限公司
This paper deals with the numerical modelling of cracks in the dynamic case using the extended finite element method. More precisely, we are interested in explicit algorithms. We prove that by using a specific lumping technique, the critical time step is exactly the same as if no crack were present. This somewhat improves a previous result for which the critical time step was reduced by a factor of square root of 2 from the case with no crack. The new lumping technique is obtained by using a lumping strategy initially developed to handle elements containing voids. To be precise, the results obtained are valid only when the crack is modelled by the Heaviside enrichment. Note also that the resulting lumped matrix is block diagonal (blocks of size 2 × 2). For constant strain elements (linear simplex elements) the critical time step is not modified when the element is cut. Thanks to the lumped mass matrix, the critical time step never tends to zero. Moreover, the lumping techniques conserve kinetic energy for rigid motions. In addition, tensile stress waves do not propagate through the discontinuity. Hence, the lumping techniques create neither error on kinetic energy conservation for rigid motions nor wave propagation through the crack. Both these techniques will be used in a numerical experiment. Copyright © 2007 John Wiley & Sons, Ltd.