A time-domain collocation-Galerkin BEM for transient dynamic crack analysis in anisotropic solids

This paper presents a time-domain boundary element method (BEM) for transient elastodynamic crack analysis in homogeneous and linear elastic solids of general anisotropy. A finite crack subjected to a transient loading is investigated. Two-dimensional (2D) generalized plane-strain or plane-stress condition is considered. The initial-boundary value problem is described by a set of hypersingular time-dependent traction boundary integral equations (BIEs), in which the crack-opening displacements (CODs) are unknown quantities. The hypersingular time-domain BIEs are first regularized to weakly singular ones by using spatial Galerkin method, which transfers the derivatives of the fundamental solutions to the unknown CODs and the weight functions. To solve the time-domain BIEs numerically, a time-stepping scheme is developed. The scheme applies the collocation method for temporal discretization of the time-domain BIEs. As spatial shape-functions, two different functions are implemented. For elements away from crack-tips, linear spatial shape-function is used, while for elements near the crack-tips a special 'crack-tip shape-function' is applied to describe the local 'square-root' behavior of the CODs at the crack-tips properly. Special attention of the analysis is devoted to the numerical computation of the transient elastodynamic stress intensity factors for cracks in general anisotropic and linear elastic solids. Numerical examples are presented to verify the accuracy of the present time-domain BEM.