Induced damage by ellipsoidal cracks in an anisotropic medium

This paper is concerned with an estimation of the effective elastic properties of an anisotropic body permeated by ellipsoidal cracks following the Eshelbys method. The classical integral expression of the P-tensor, the symmetrised derivative of the Greens tensor, is given for a 3D defined crack embedded in an anisotropic medium. The numerical evaluation of the P-tensor is validated with several limiting cases of simplified geometry cracks. The interest of a 3D representation of the cracks is shown with several applications: influence of the ellipticity and crack thickness aspect ratios, growing cracks. To conclude, a comparison between theoretical results and experimental data is done for the load-induced change of the compliance tensor for a damaged composite material.