An Edge Dislocation in an Epitrochoidal Domain

We use the techniques of conformal mapping and analytic continuation to derive a closed‐form solution to the plane elasticity problem of an edge dislocation in an isotropic elastic epitrochoidal finite domain. The epitrochoidal boundary of the finite domain is traction‐free. All of the complex constants appearing in the pair of analytic functions characterizing the elastic field in the epitrochoidal domain are determined in an analytical manner. In particular, when the edge dislocation is in a finite domain bounded by a Pascal's limaçon, an explicit expression for the image force acting on the edge dislocation is obtained. Moreover, in this case, our numerical results indicate that the edge dislocation can find a stable equilibrium position, a phenomenon in direct contrast to the existence of a sole unstable equilibrium position at the center of a circular domain for an edge dislocation.