An ellipsoidal inclusion and an elliptical crack in the elastic media with ellipsoidal anisotropy

An isolated ellipsoidal inclusion and an elliptical crack in a homogeneous elastic medium with ellipsoidal anisotropy are considered. For constant external stress (strain) fields applied to the medium, the solutions of these problems are reduced to calculation of 2D-regular integrals. For materials with ellipsoidal anisotropy, the integrand functions in these integrals can be presented in explicit analytical forms that simplifies substantially construction of the numerical solutions of the problems. The stress intensity factors at the crack edge are expressed in the forms of 1D-integrals which integrand functions have also explicit analytical forms for media with ellipsoidal anisotropy.