Simulation of cracks in a Cosserat medium using the extended finite element method
Simulation of cracks in a Cosserat medium using the extended finite element method
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DOI：
10.1177/1081286514533120
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发表时间：
2016-05
影响因子：
2.6
通讯作者：
M. Kapiturova;R. Gracie;S. Potapenko
中科院分区：
文献类型：
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作者：
M. Kapiturova;R. Gracie;S. Potapenko
与经典弹性理论相比，Cosserat(微极，非对称)弹性能更好地预测具有特征长度尺度的材料的力学行为。然而，在Cosserat介质中建立裂缝模型的领域在文献中并没有被广泛介绍。本文用扩展有限元方法对Cosserat介质中的裂纹进行了数值模拟。适当的裂纹尖端平移场和微位移场的丰富对于XFE/Cosserat模型的稳健性和效率是重要的。本文以I型边裂纹为例，证明了Cosserat固体的J积分值高于等效的经典弹性固体的J积分值。对于具有强微极性质的材料，这种差异变得显著。不同尺寸裂纹的断裂行为对Cosserat弹性常数有显著的依赖关系。因此，建议对微位移场考虑特殊的尖端浓缩，并对材料参数进行仔细的分析，以便模拟Cosserat介质中的断裂。
Cosserat (micropolar, asymmetric) elasticity can better predict the mechanical behavior of the materials with a characteristic length scale than the classical theory of elasticity. However, the area of fracture modelling in a Cosserat medium is not widely presented in the literature. The simulation of cracks in a Cosserat medium using the eXtended Finite Element Method (XFEM) is presented in this paper. The proper crack tip enrichment of the translational and microrotational fields is important for the robustness and efficiency of the XFEM/Cosserat model. Using the example of an edge crack of the Mode I in this paper, we have shown that the values of the J-integral for the Cosserat solid are higher than those for the equivalent classical elastic solid. The difference becomes significant for the cases of materials with strong micropolar properties. The dependence of the fracture behavior of the crack of different sizes on the Cosserat elastic constants was found to be significant. Therefore, it is recommended that the special tip enrichment is considered for the microrotational field, and a careful analysis of the material parameters is performed in order to model fracture in a Cosserat medium.