Stress concentration tensors of inhomogeneities with interface effects

The effects of the interface bonding conditions simulated by four interface models on the stress fields of spherical and circular inhomogeneities in infinite media are investigated for general loading conditions. The four interface models are the free sliding model, linear spring model, dislocation-like model and interface stress model. Based upon the solutions of the elastostatic problems, the local and average stress concentration tensors are derived for the inhomogeneities with these interface effects. It is shown that when the linear spring interface model and the interface stress model are considered, the inhomogeneities exhibit a size effect. Moreover, unlike the case of a perfect bonding interface, a sort of “local anisotropy” appears when the interface effects come into play, namely, the normal (shear) stresses in the inhomogeneities are coupled with the remote shear (normal) stresses. However, the coupling disappears in the average stress concentration tensors.