An edge dislocation interacting with a hypotrochoidal compressible liquid inclusion

Abstract

We use Muskhelishvili’s complex variable formulation to derive a closed-form solution to the plane strain problem of a hypotrochoidal compressible liquid inclusion embedded in an infinite isotropic elastic matrix subjected to an edge dislocation located at an arbitrary position. The internal uniform hydrostatic tension within the hypotrochoidal liquid inclusion and all the unknown complex constants appearing in the two analytic functions characterizing the elastic field in the matrix are completely determined in an analytical manner. In principle, the solution to the problem of an edge dislocation interacting with an arbitrarily shaped compressible liquid inclusion can be obtained in closed-form as long as the adopted conformal mapping function which maps the exterior of the inclusion onto the exterior of the unit circle in the image plane contains a finite number of terms.