A SPHERICAL INCLUSION IN AN ELASTIC HALF-SPACE UNDER SHEAR

We find the elastic fields in a half-space (matrix) having a spherical inclusion and subjected to either a remote shear stress parallel to i ts traction-free boundary or to a uniform shear transformation strain (eigenstrain) in the inclusion. The inclusion has distinct properties from those of the matrix, and the interface between the inclusion and the surrounding matrix is either perfectly bonded or is allowed to sli p without friction. We obtain an analytical solution to this problem u sing displacement potentials in the forms of infinite integrals and in finite series. We include numerical examples which give the local elas tic fields due to the inclusion and the traction-free surface.