Soft neutral elastic inhomogeneities with membrane-type interface conditions

A foreign body, called an "inhomogeneity," when introduced in a host solid disturbs the stress field which is present in it. One can explore the possibility of modifying the contact mechanism between the inhomogeneity and the host body so as to leave the stress field in the host solid undisturbed. If such a procedure succeeds, then the inhomogeneity is called "neutral." Modification of the contact mechanism between the inhomogeneity and the host solid can be achieved, for example, by a suitably designed thick or thin interphase between them. When the interphase is thin, it can be represented by an "imperfect interface" model. In the present study we consider "soft" inhomogeneities which are more compliant than the host body. A "membrane-type interface" which models a thin and stiff interphase is used in rendering such inhomogeneities neutral. Illustrative examples are constructed for cylindrical neutral inhomogeneities of elliptical cross section under a triaxial loading, and for spheroidal inhomogeneities subjected to an axisymmetric loading.