The ellipsoidal inhomogeneity with imperfect interface

Presents an exact solution to the problem of an ellipsoidal inhomogeneity embedded in an infinitely extended body with imperfect interface subject to uniform shear stress at infinity. A kind of new boundary condition similar to the dislocation- like model is used. The tractions are assumed continuous across the interface, and the displacements may be discontinuous from one side to the other. With the help of Lam6 functions, Papkowich-Neuber displacement potential functions are introduced. In the end, the displacements fields inside and outside the ellipsoid are obtained in explicit form, respectively. Then the stress field in the whole domain will be concluded relevantly.