Hypersingular and Mixed Boundary Elements in Fracture Mechanics

Abstract

The general Hypersingular and Mixed Boundary Element approach for threedimensional fracture mechanics is presented in this chapter. It is based on the traction (hypersingular) boundary integral equation for infinite domain problems and on a combined use of the traction boundary integral equation and the classical displacement boundary integral equation (mixed formulation) for bounded domain problems. The approach is formulated and implemented for static and time harmonic dynamic loading conditions. The hypersingular and strongly singular kernels appearing in the formulation are regularized by simple analytical transformations. Nine-node quadrilateral and six-node triangular continuous quadratic elements are used for external boundaries and crack surfaces. The crack front elements have their mid node at one quarter of the element length allowing for a proper representation of the crack surface displacement. The present approach is intended for the analysis of fracture mechanics problems of any general 3-D geometry; i.e. boundless or bounded regions, single or multiple, surface or internal cracks. Transient dynamic problems are studied using the FFT algorithm. The numerical results presented show the robustness and accuracy of the approach which requires a moderate number of elements and degrees of freedom.