An edge dislocation interacting with an elliptical incompressible liquid inclusion

We use Muskhelishvili’s complex variable formulation to derive a closed-form solution to the plane strain problem of an elliptical incompressible liquid inclusion embedded in an infinite isotropic elastic matrix subjected to the action of an edge dislocation applied at an arbitrary position. The internal uniform hydrostatic tension within the liquid inclusion and the pair of analytic functions characterizing the elastic field in the matrix are completely determined. The image force acting on the edge dislocation is the sum of two parts: the first part has been obtained in previous studies and is due to the edge dislocation near a traction-free elliptical hole; the second modified part is caused by the induced uniform hydrostatic tension on the elliptical boundary: this part has not been considered previously and is given here explicitly.