Semi-permeable crack analysis in magnetoelectroelastic solids

This paper discusses various electromagnetic boundary conditions on the crack-faces in two-dimensional magnetoelectroelastic materials. For this purpose, a meshless method based on the local Petrov–Galerkin approach is developed to solve the initial-boundary value problems of two-dimensional cracked magnetoelectroelastic solids with nonlinear electrical and magnetic boundary conditions on the crack-faces. A Heaviside step function as the test function is applied in the weak form to derive local integral equations. Nodal points are spread on the analyzed domain and each node is surrounded by a small circle for simplicity. The spatial variations of the displacements, electric and magnetic potentials are approximated by the moving least-squares (MLS) scheme. After performing the spatial integrations, one obtains a system of ordinary differential equations for certain nodal unknowns. That system is solved numerically by the Houbolt finite-difference scheme as a time-stepping method. An iterative solution algorithm is developed to consider nonlinear electromagnetic crack-face boundary conditions. (paper)