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Fracture in magnetoelectroelastic materials using the extended finite element method

Static fracture analyses in two‐dimensional linear magnetoelectroelastic (MEE) solids is studied by means of the extended finite element method (X‐FEM). In the X‐FEM, crack modeling is facilitated by adding a discontinuous function and the crack‐tip asymptotic functions to the standard finite element approximation using the framework of partition of unity. In this study, media possessing fully coupled piezoelectric, piezomagnetic and magnetoelectric effects are considered. New enrichment functions for cracks in transversely isotropic MEE materials are derived, and the computation of fracture parameters using the domain form of the contour interaction integral is presented. The convergence rates in energy for topological and geometric enrichments are studied. Excellent accuracy of the proposed formulation is demonstrated on benchmark crack problems through comparisons with both analytical solutions and numerical results obtained by the dual boundary element method. Copyright © 2011 John Wiley & Sons, Ltd.