Equivalent inclusion solution adapted to particle debonding with a non-linear cohesive law

Starting from Eshelby’s solution of the equivalent inclusion problem, an approximate solution is proposed in order to model interface debonding of a spherical inhomogeneity isolated in a uniform matrix. Both phases are linear elastic but the interface traction-separation law is non-linear. A semi-analytical incremental model is developed which is suitable for any type of loading. For computational efficiency, the model relies on two simplifying assumptions: (i) the eigenstrain is uniform inside the inhomogeneity and (ii) the interface compliance is averaged over inhomogeneity’s surface when computing the average strain within the inhomogeneity. An extensive parametric study is conducted for three loading modes and 144 combinations of non-dimensional parameters. The predictions are assessed against full-field finite element solutions based on two error measures of the mean stress field inside the inhomogeneity. The results show that the mean error value is acceptable in all cases and indicate the parameter ranges for which the model is most accurate.