A unified treatment of the elliptic inhomogeneity with a slipping interface under line singularity loading

Most of the problems dealing with elliptic inhomogeneities may be grouped in two classes. The problems of the first class deal with a perfectly adhering matrix inhomogeneity interface, while those of the second class assume a slip¬ping (liquid like) interface. A further grouping level may be considered, accord¬ing whether the loading system is applied to the matrix (external loading) or to the inhomogene¬ity (internal loading). In the past, a number of works have considered elliptic inhomogeneities with slipping interfaces [1 6], but, to our knowledge, no solu¬tion has been provided for an internally loaded slipping inhomogeneity. The present paper is aimed to fill this gap by considering a line singularity (LS) as the loading system in plane elasticity. LS solutions are quite general, since they can be used for dislocations, dilatation centers, concentrated forces, and con¬centrated moments, and, more generally, lead to the Green functions for this kind of problems. In addition, the present solution has the advantage of includ¬ing both cases of internal or external LS, according to the value of a single parameter.