The Stress State of an Elastic Medium with an Elliptic Crack and Two Ellipsoidal Cavities

This paper is a study into the interaction of two triaxial ellipsoidal cavities whose surfaces are under different pressures with an elliptic crack in an infinite elastic medium. The stress state in the elastic space is represented by a superposition of perturbed states due to the presence and interaction of the cavities and the crack. The exact solution of the problem is constructed by using a modified method of equivalent inclusion, the potential of an inhomogeneous ellipsoid, and a system of harmonic functions for the elliptic crack. A numerical analysis is carried out to find how the geometry of the cavities and the crack, the distance between them, and the pressure on their surfaces affect the stress intensity factors