Analysis of cracked magnetoelectroelastic composites under time-harmonic loading

This paper presents a numerical model for the analysis of cracked magnetoelectroelastic materials subjected to in-plane mechanical, electric and magnetic dynamic time-harmonic loading. A traction boundary integral equation formulation is applied to solve the problem in combination with recently obtained time-harmonic Green’s functions (Rojas-Diaz et al., 2008). The hypersingular boundary integral equations appearing in the formulation are first regularized via a simple change of variables that permits to isolate the singularities. Relevant fracture parameters, namely stress intensity factors, electric displacement intensity factor and magnetic induction intensity factor are directly evaluated as functions of the computed nodal opening displacements and the electric and magnetic potentials jumps across the crack faces. The method is checked by comparing numerical results against existing solutions for piezoelectric solids. Finally, numerical results for scattering of plane waves in a magnetoelectroelastic material by different crack configurations are presented for the first time. The obtained results are analyzed to evaluate the dependence of the fracture parameters on the coupled magnetoelectromechanical load, the crack geometry and the characteristics of the incident wave motion.