Interaction between an edge dislocation and a partially debonded circular elastic inhomogeneity with the debonded portion occupied by a liquid slit inclusion

We study the plane strain problem of a circular elastic inhomogeneity partially debonded from an infinite elastic matrix subjected to an edge dislocation at an arbitrary position. The debonded portion of the circular interface is occupied by an incompressible liquid slit inclusion. The original boundary value problem is reduced to a standard Riemann-Hilbert problem with discontinuous coefficients which can be solved analytically. The two unknown constants appearing in the analytical solution are determined by imposing the incompressibility condition of the liquid inclusion. Closed-form expressions for the internal uniform hydrostatic stress field within the liquid slit inclusion, the average mean stress within the circular elastic inhomogeneity, the rigid body rotation at the center of the circular inhomogeneity, and the two complex stress intensity factors at the two tips of the debonded portion induced by the edge dislocation are obtained.