A circular inclusion with inhomogeneously imperfect interface in plane elasticity

A general method is presented for the rigorous solution of a circular inclu sion embedded within an infinite matrix in plane elastostatics. The bonding at the inclusion-matrix interface is considered to be imperfect with the a ssumption that the interface imperfections are circumferentially inhomogene ous. Using analytic continuation, the basic boundary value problem for four analytic functions is reduced to two coupled first order differential equa tions for two analytic functions. The resulting closed-form solutions inclu de a finite number of unknown constants determined by analyticity and certa in other auxiliary conditions. The method is illustrated using a particular class of inhomogeneous interface. The results from these calculations are compared to the corresponding results when the imperfections in the interfa ce are circumferentially homogeneous. These comparisons illustrate, for the first time, how the circumferential variation of the parameter describing the imperfection has a pronounced effect on the average stresses induced wi thin the inclusion.