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Mathematics and Mechanics of Solids
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Constant-Stress Inclusions in an Elastic Plate

S. Vigdergauz

R&D Division, The Israel Electric Corp., Ltd., PO. Box JO, Haifa 31000, Israel

A set of perfectly bonded inclusions in an elastic plate is considered. We employ the Kolosov-Muskhelishvili potentials to identify the interface shapes which provide a constant stress field inside the inclusions under a uniform loading at infinity. Coupled inequalities are explicitly derived for a single inclusion to prove that the only such contour is an ellipse. Within certain limits, these findings are extended to the multiconnected case.

Key Words: Plane elasticity • inclusion • phase transition • analytic functions • optimization

Mathematics and Mechanics of Solids, Vol. 5, No. 2, 265-279 (2000)
DOI: 10.1177/108128650000500205
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