On two hypersingular time-domain BEM for dynamic crack analysis in 2D anisotropic elastic solids

This paper presents a comparison of two hypersingular time-domain boundary element methods for transient dynamic crack analysis in two-dimensional, homogeneous, anisotropic and linear elastic solids. Stationary cracks in infinite and finite elastic solids of general anisotropy under impact loading are investigated. A combination of the classical displacement boundary integral equations and the hypersingular traction boundary integral equations is applied. Two different numerical solution procedures are developed to solve the time-domain boundary integral equations. The spatial discretization is performed by a Galerkin-method in both solution procedures. A collocation method is adopted for the temporal discretization in the first solution procedure, while a convolution quadrature is implemented for the temporal discretization in the second procedure. An explicit time-stepping scheme is developed to compute the unknown boundary data and the crack-opening-displacements. Numerical examples for the dynamic stress intensity factors are presented and discussed.