Fracture in magnetoelectroelastic materials using the extended finite element method

Abstract

SUMMARYStatic 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.

The extended finite element method with new crack-tip enrichment functions for an interface crack between two dissimilar piezoelectric materials

“…The geometrical enrichment with a larger radius of enriched domain performs better than that with a small one. All these phenomena are consistent with those previously observed in homogeneous piezoelectric materials [6] and magnetoelectroelastic materials [82,83]. Moreover, the accuracy of the new crack-tip enrichment functions specifically derived for piezoelectric bimaterials is superior to that of the standard isotropic ones if the same topological and/or geometrical enrichment is employed.…”

“…The convergence can be studied by comparing the analytical solution to a reference problem with the actual results of a numerical model; the error in the total energy norm is given by where " Ana ij and E Ana i correspond to the analytical (exact) solution for elastic strains and electric fields, respectively. The convergence of error in the total energy norm with respect to mesh density has been thoroughly investigated in [6,9,[82][83][84]. These all show that the convergence rate of topological enrichment is 0.5, whereas the geometrical one achieves a higher convergence rate, namely, 1.0.…”

Higher‐order extended FEM for weak discontinuities – level set representation, quadrature and application to magneto‐mechanical problems

“…Failure of electro‐mechanically coupled solids is analysed by elements with embedded discontinuities in . The problem of fracture in magnetoelastics is modelled by XFEM in . A comprehensive review of methodological issues of XFEM and various applications is given, for instance, in .…”

Extended material point method for the three‐dimensional crack problems

“…Generally, the Heaviside function is used as the enriched function for the crack surface. Many other enrichments such as bimaterial interface crack, 15 orthotropic material crack, 16 electromagnetic material crack, 17 V-notch crack 18 and cohesive crack 19,20 are also proposed for the different cases. In addition, Belytschko, 21 Daux, 22 Budyn, 23 and Taleghani et al 24 proposed the corresponding enriched functions for crack bifurcation and multiple cracks intersection respectively.…”