Interaction of thin inclusion with circular hole in the elastic isotropic medium

Abstract

The purpose of this paper is to analyze the interaction of thin elastic inclusions with globular defects in a solid structural element and develop technique to determine fracture parameters when the elastic inclusion of the structure is close to a circular hole and/or to its bonding layers. Procedures for determination of fracture parameters are based on the J‐integral relation with generalized stress intensity factors (GSIF) recently obtained by the authors and the boundary element method is adopted for studying thin shapes. The developed techniques, dominating GSIF and mutual integral method, are applied to two specific problems: the interaction of a traction‐free hole with a nearby, thin inclusion and the interaction of a constrained hole with the inclusion. The direct numerical solution was obtained for the two principal models which represent two different boundary conditions on the edge of the hole of the structural element. The study shows that if the hole is unstressed, the values of GSIF are approximately the same as the corresponding values of the fracture parameters and the presence of the hole and the rigid inclusion have only a small effect on GSIF. But if the hole is constrained along its boundary, the values of GSIF generally decrease with decreasing the distance between the inclusion and the hole. The stress concentration on the hole substantially depends on the presence of the inclusion and varies significantly with respect to its radius, the distance from the inclusion, and the relative rigidity of the inclusion.