A New Boundary Integral Equation Formulation for Elastodynamic and Elastostatic Crack Analysis

Abstract

An elastodynamic conservation integral, the J̃k integral, is employed to derive boundary integral equations for crack configurations in a direct and natural way. These equations immediately have lower-order singularities than the ones obtained in the conventional manner by the use of the Betti-Rayleigh reciprocity relation. This is an important advantage for the development of numerical procedures for solving the BIE’s, and for an accurate calculation of the strains and stresses at internal points close to the crack faces. For curved cracks of arbitrary shape the BIE’s presented here have simple forms, and they do not require integration by parts, as in the conventional formulation. For the dynamic case the unknown quantities are the crack opening displacements and their derivatives (dislocation densities), while for the static case only the dislocation densities appear in the formulation. For plane cracks the boundary integral equations reduce to the ones obtained by other investigators.