Eshelby tensor for a penny-shaped inclusion with limited thickness in transversely isotropic elastic medium

The present work is devoted to get the Eshelby Tensor of a penny-shape inclusion with small but nonzero thickness in transversely isotropic elastic solid under uniform stress at infinity. Based on the integral representation, explicit expressions of Eshelby tensor will be present as the linear function of aspect ratio when the inclusion is lay on the isotropic plane of the transversely isotropic solid. With Crack is treated as a special case of penny-shape inclusion, the Griffith fracture criterion, stress intensity factors of cracks and the crack opening displacement are given the explicit expressions. Also the solution could be used to calculate the effective properties of solid with many parallel cracks, lamellated plate with debond, transversely rock with cracks.