An iterative-perturbation scheme for treating inhomogeneous elasticity in phase-field models

In this paper, we discuss a simple iterative-perturbation scheme for solving the elasticity equation in systems with strong elastic inhomogeneity. As an example, a thin film in contact with a gas and a substrate is considered. The scheme is demonstrated to be efficient through numerical experiments and reliable through rigorous mathematical justification. It is then applied to the study of the inhomogeneous shear modulus effect on the microstructure evolution in thin films based on the phase-field method.