Analytical solutions for coated circular inhomogeneity with non-uniform axisymmetric eigenstrain distribution

In this paper, a general model for coated circular inhomogeneous inclusion problems is proposed and studied, where non-uniform axisymmetric eigenstrains are independently distributed within the circular zone and annular zone (coating layer). The main difficulties are from the dissimilarity of three-phase materials, the non-uniform axisymmetric eigenstrain distribution, and the presence of intermediate annularity, which are hardly treated within the classical Eshelby inclusion mechanics. By employing the equivalent eigenstrain principle, these challenges can be completely tackled, and a general explicitly analytical solution is obtained. From this solution, a couple of solutions for typical inclusion problems are readily degenerated, which have been derived with great efforts in literature. With the general model and its solution, the analytical solution for the coated hollow-cored inhomogeneous inclusion problem with non-uniform axisymmetric eigenstrain is provided, and an eigenstrain-based nano-inclusion model is subsequently proposed. The applications of coated circular inhomogeneity with eigenstrains can be found in coated fiber composites, thermoelastic problems, and micro- & nano-mechanics.