Circular Inclusion in Half-Plane: Effect of Boundary Conditions

Abstract

We consider an elastic circular inclusion embedded in a half-plane and subjected to uniform transformation strains (eigenstrains). The inclusion-matrix interface is either perfectly bonded or is allowed to slip without friction, while the straight edge of the half-plane is either fixed or frictionless (free to move in the horizontal direction). We compare the results with a recently obtained solution of an inclusion in a half-plane with a traction-free edge and show that the boundary conditions at both the inclusion-matrix interface and the half-plane edge have a significant effect on stress fields. Additionally, we observe that the effects of the interaction between the inclusion and the straight edge may be long range, i.e., may be observable when the inclusion is embedded several diameters away from the surface. We solve this plane elasticity problem using Papkovich-Neuber displacement potentials in the forms of infinite series and integrals.