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arXiv · 1807.09981

An extension of the Eshelby conjecture to domains of general shape in anti-plane elasticity

Doosung Choi·Kyoungsun Kim·Mikyoung Lim
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Abstract

According to the Eshelby conjecture, an ellipse or ellipsoid is the only shape that induces an interior uniform strain under a uniform far-field loading. We extend the Eshelby conjecture to domains of general shape for anti-plane elasticity. Specifically, we show that for each positive integer $N$, an inclusion induces an interior uniform strain under a polynomial loading of degree $N$ if and only if the exterior conformal map of the inclusion is a Laurent series of degree $N$. Furthermore, for the isotropic case, we characterize the shape of an inclusion by only using the first-degree polynomial loading and explicitly solve the interior potential of the inclusion in terms of the Grunsky coefficients.

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Doosung Choi, Kyoungsun Kim, Mikyoung Lim. 2018-07-26. An extension of the Eshelby conjecture to domains of general shape in anti-plane elasticity. https://arxiv.org/abs/1807.09981

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