A Circular Inclusion with Inhomogeneously Imperfect Interface in Plane Elasticity

ISSN： 0374-3535

Source： Journal of Elasticity, Vol.55, Iss.1, 1999-01, pp. : 19-41

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Abstract

A general method is presented for the rigorous solution of a circular inclusion embedded within an infinite matrix in plane elastostatics. The bonding at the inclusion-matrix interface is considered to be imperfect with the assumption that the interface imperfections are circumferentially inhomogeneous. Using analytic continuation, the basic boundary value problem for four analytic functions is reduced to two coupled first order differential equations for two analytic functions. The resulting closed-form solutions include a finite number of unknown constants determined by analyticity and certain 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 interface 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 within the inclusion.