An edge dislocation interacting with a compressible liquid inclusion of arbitrary shape

We derive a closed-form solution to the plane strain problem of a compressible liquid inclusion of arbitrary shape embedded in an infinite isotropic elastic matrix subjected to an edge dislocation. The arbitrary shape of the liquid inclusion is reflected in the fact that the conformal mapping function that maps the exterior of the liquid inclusion onto the exterior of the unit circle in the image plane contains an arbitrary number of terms. Using a modified form of analytic continuation, we develop a set of coupled linear algebraic equations with quite simple structure. Once the set of linear algebraic equations is solved, the internal uniform hydrostatic stress field within the liquid inclusion and the elastic field in the matrix induced by the edge dislocation are completely determined.