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

• The X-FEM is extended to investigate interface crack problems of MEE bimaterials.
• New enrichment functions for interface crack problems of MEE bimaterials are derived.
• The validity of the formulas of X-FEM is proved by comparing with analytical results.
• The proposed new enrichment functions are able to lead to most accurate results.
• The use of geometrical enrichment can also achieve higher accuracy.

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.