Circular inclusion in an infinite elastic medium with a circular inhomogeneity

Abstract

AbstractIn a previous paper ((l)) the authors gave the solution for the two-dimensional circular inclusion problem in a medium containing a circular cavity. This paper seeks to solve the more general problem of a similar inclusion when the cavity is replaced by an inhomogeneity which could be of a different elastic material. The solution consists in finding three sets of suitable complex potential functions ø(z) and ψ(z) for three regions: the inhomogeneity, the inclusion and the rest of the material. The solution depends upon the evaluation of the complex potentials for a material containing the inhomogeneity when on the former a finite force is acting at some fixed point. It may be noted that two sets of ø(z) and ψ(z) have to be found in this case: one for the inhomogeneity and the other for the rest of the material. This may be taken as an auxiliary problem.