An integral equation approach to the inclusion-crack interactions in three-dimensional infinite elastic domain

Abstract

In this paper, an integral equation method to the inclusion-crack interaction problem in three-dimensional elastic medium is presented. The method is implemented following the idea that displacement integral equation is used at the source points situated in the inclusions, whereas stress integral equation is applied to source points along crack surfaces. The displacement and stress integral equations only contain unknowns in displacement (in inclusions) and displacement discontinuity (along cracks). The hypersingular integrals appearing in stress integral equation are analytically transferred to line integrals (for plane cracks) which are at most weakly singular. Finite elements are adopted to discretize the inclusions into isoparametric quadratic 10-node tetrahedral or 20-node hexahedral elements and the crack surfaces are decomposed into discontinuous quadratic quadrilateral elements. Special crack tip elements are used to simulate the ffiffi r p variation of displacements near the crack front. The stress intensity factors along the crack front are calculated. Numerical results are compared with other available methods.

A new integral equation formulation of two-dimensional inclusion–crack problems

“…The price paid is that the inclusions have to discretized into some finite elements. The domain integral equation method was also used to investigate the propagation of the crack near the inclusion (Dong et al, 2003b) and 3D inclusion-crack interaction (Dong et al, 2002).…”