Fracture analysis of cracked 2D planar and axisymmetric problems of magneto–electro-elastic materials by the MLPG coupled with FEM

The fracture behaviors of two-dimensional (2D) planar and axisymmetric problems of magneto–electro-elastic materials are investigated by the method of the meshless local Petrov–Galerkin (MLPG) coupled with finite element method (FEM). In the coupled method, the physical domain is divided into two parts, which are formulated with the MLPG and FEM, respectively. In the MLPG region, the moving least squares (MLS) method is adopted to approximate the physical quantities, and the Heaviside step function is taken as a test function. The interface elements with a novel shape function in present study are introduced. For the axisymmetric case, the annular volumetric elements are applied to obtain the simpler discretized equations than those derived by the planar elements. The validity and efficiency of the MLPG/FEM method are verified by comparing the results obtained here with the ones in the previous literature. The extended crack open displacements (CODs), especially the field intensity factors (FIFs) of the crack tips including the stress intensity factor (SIF), electric displacement intensity factor (EDIF) and magnetic induction intensity factor (MIIF) for magneto–electro-elastic materials are calculated and analyzed.