A multilayered circular inhomogeneity with interfacial diffusion and sliding

We study the time-dependent and plane strain deformations of a circular inhomogeneity bonded to an infinite matrix through a multilayer interphase when subjected to uniform remote stresses. Both interfacial diffusion and rate-dependent sliding occur on all the existing interfaces between two neighboring phases. The problem is solved effectively and elegantly by means of the complex variable method together with the state-space approach. The state variables are just the unknown coefficients appearing in the analytic functions defined in all the phases of the composite. Numerical results are presented to demonstrate the obtained solution.