Transient dynamic crack analysis in linear magnetoelectroelastic solids by a hypersingular time-domain BEM

This paper presents a hypersingular time-domain boundary element method (TDBEM) for transient dynamic crack analysis in two-dimensional (2D), homogeneous, anisotropic and linear magnetoelectroelastic solids. Stationary cracks in infinite and finite solids under impact loading are investigated. A combination of the strongly singular displacement boundary integral equations (BIEs) and the hypersingular traction boundary integral equations is used in the present analysis. The Galerkin-method is applied for spatial discretization, while a collocation method is implemented for the temporal discretization. The time-domain fundamental solutions for linear magnetoelectroelastic solids are derived. Both temporal and spatial integrations can be carried out analytically. The line integrals over the unit circle arising in the time-domain fundamental solutions are computed numerically by standard Gaussian quadrature. An explicit time-stepping scheme is obtained to compute the unknown boundary data including the generalized crack-opening-displacements (CODs) numerically. To ensure a direct and an accurate computation of the dynamic intensity factors (IFs) from the generalized CODs, special crack-tip elements are implemented. Several numerical examples are shown to confirm the accuracy and the efficiency of the present hypersingular time-domain BEM.