Fracture in magnetoelectroelastic materials using the extended finite element method

• Published in: International journal for numerical methods in engineering Vol. 88; no. 12; pp. 1238 - 1259
• Main Authors: Rojas-Díaz, R., Sukumar, N., Sáez, A., García-Sánchez, F.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 23-12-2011; Wiley
• Subjects: Asymptotic properties; Boundary element method; Computational techniques; Enrichment; Exact sciences and technology; Finite element method; Finite-element and galerkin methods; Fracture mechanics; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); interaction integral; magnetoelectroelasticity; Mathematical analysis; Mathematical methods in physics; Mathematical models; Mathematics; Methods of scientific computing (including symbolic computation, algebraic computation); Numerical analysis; Numerical analysis. Scientific computation; partition of unity enrichment; Physics; Sciences and techniques of general use; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; X-FEM; Enrichment; Modeling; Finite element method; X-FEM; Dimensional analysis; Static analysis; Piezoelectricity; Convergence rate; Crack tip; Magnetoelastic effect; Boundary element method; Magnetoelectric properties; Piezomagnetic effect; Rupture; partition of unity enrichment; Topology; Electroelasticity; magnetoelectroelasticity; interaction integral; Magnetomechanical properties; Asymptotic approximation; Unity partition; Crack; eXtended Finite Element Method; Electromechanical properties
• ISSN: 0029-5981; 1097-0207; 1097-0207
• DOI: 10.1002/nme.3219

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.