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On the Elliptic Inclusion in Anti-Plane Shear

Peter Schiavone

Department of Mechanical Engineering, University of Alberta, Edmonton, Alberta, Canada T6G 2G8

In this paper, we consider the anti-plane shear problem of an elliptic inclusion embedded in an infinite, isotropic, elastic medium, subjected at infinity to a uniform stress field. Using complex variable methods and the theory of analytic functions, we prove that the state of deformation in the inclusion is a simple shear if and only if the curve enclosing the inclusion is an ellipse.

Mathematics and Mechanics of Solids, Vol. 1, No. 3, 327-333 (1996)
DOI: 10.1177/108128659600100304


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