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Crack tip enrichment functions for extended finite element analysis of two-dimensional interface cracks in anisotropic magnetoelectroelastic bimaterials

机译：各向异性磁电双材料二维界面裂纹扩展有限元分析的裂纹尖端富集函数

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摘要

In this paper, the extended finite element method (X-FEM) is employed to present a static fracture analysis of two-dimensional interfacial crack problems in linear magnetoelectroelastic (MEE) bimaterials. Magnetoelectrically impermeable crack-face boundary conditions are adopted and the multi-field coupled effect in MEE bodies is considered. In order to capture the oscillating singularity of the extended stresses near the interfacial crack tip, suitable crack tip enrichment functions for anisotropic and transversely isotropic MEE bimaterials are newly derived and further applied to perform X-FEM analysis. As the fracture parameter, the J-integral is evaluated using the domain form of the contour integral. By comparing yielded results with the analytical and numerical solutions of the corresponding interfacial crack problems, the validity of the proposed formulation is verified. Moreover, it is shown that the results obtained by way of the new enrichment functions are superior to those obtained by the fourfold enrichment functions and twelvefold enrichment functions, especially in the case of topological enrichment. If there is no special requirement for precision, the fourfold enrichment functions with less computational cost can also be used to conduct X-FEM analysis for the present problem. (C) 2016 Elsevier Ltd. All rights reserved.
机译：本文采用扩展有限元方法（X-FEM）对线性磁电弹性（MEE）双材料中的二维界面裂纹问题进行了静态断裂分析。采用磁电不透性裂纹面边界条件，并考虑了MEE体内的多场耦合效应。为了捕获界面裂纹尖端附近的扩展应力的振荡奇异性，新推导了适用于各向异性和横向各向同性的MEE双材料的合适裂纹尖端富集功能，并将其进一步应用于X-FEM分析。使用轮廓积分的域形式评估J积分作为断裂参数。通过将产生的结果与相应的界面裂纹问题的解析解和数值解进行比较，验证了所提出配方的有效性。此外，表明通过新的富集函数获得的结果优于通过四倍富集函数和十二倍富集函数获得的结果，尤其是在拓扑富集的情况下。如果对精度没有特殊要求，则可以使用计算量较小的四倍富集函数对当前问题进行X-FEM分析。 （C）2016 Elsevier Ltd.保留所有权利。

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