General imperfect interface model for spherical-circular inclusion composites

From the compound sphere assemblage model involving the intermediate anisotropic coatings and appropriate limiting procedure, a general imperfect interface model for thermal conduction problem is constructed. This kind of interface includes both the highly conducting and lowly conducting ones as the specific cases. The analytical expressions of macroscopic conductivity, and microscopic fields in and around the inhomogeneities, are provided, with some comparisons with the results of another model in the literature. An equivalent inclusion approach is implemented in conjunction with a three-point correlation approximation to predict the effective conductivity of some periodic or random arrangements of imperfectly-bonded inclusions. The analytical model is also useful in the inverse problem to find the imperfect interface parameters from the available macroscopic experimental data.