The problem of two plastic and heterogeneous inclusions in an anisotropic medium
We demonstrate an integral equation for the total local strain \(\epsilon^ T\) in an anisotropic heterogeneous medium with incompatible strain \(\epsilon^ P\) and which is at the same time submitted to an exterior field. The integral equation is solved in the case of an heterogeneous and plastic pair of inclusions, for which we calculate the average fields in each inclusion as well as the different parts of the elastic energy stocked in the medium. The solution is applied to the case of two isotropic and spherical inclusions in an isotropic matrix loaded in shear. The results are compared with those deduced from a more approximate method based on Born's approximation of the integral equation. In appendix we give a numerical method for calculating the interaction tensors between anisotropic inclusions in an anisotropic medium as well as the analytic solution in the case of two spherical inclusions located in an isotropic medium.
heterogeneous and plastic pair of inclusions
scientific article; zbMATH DE number 3990957