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On the elliptic inclusion in anti-plane shear. (English) Zbl 1001.74509

Summary: 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.

MSC:

74B05 Classical linear elasticity
74E05 Inhomogeneity in solid mechanics
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