Abstract
A family of confocal ellipses may be characterized by a single parameter, ρ> 1. In the limit as ρ→1, the ellipse degenerates into a straight line of length 2. It tends to a circle of infinite radius as ρ→ ∞. The geometry of the title problem is fixed by the crack (ρ = 1) and the size of an elliptic inhomogeneity (ρ = ρ0). Both the inhomogeneity and the infinite medium are assumed to be homogeneous and isotropic. Plane and anti-plane solutions associated with remote loading conditions are obtained. The solutions depend, among other parameters, on the size of the inhomogeneity ρ0. Special attention is placed on determining the various limits as ρ0→1.
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