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arXiv · 1502.03418

Bending of thin periodic plates

Mikhail Cherdantsev·Kirill Cherednichenko
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Abstract

We show that nonlinearly elastic plates of thickness $h\to 0$ with an $\varepsilon$-periodic structure such that $\varepsilon^{-2}h\to 0$ exhibit non-standard behaviour in the asymptotic two-dimensional reduction from three-dimensional elasticity: in general, their effective stored-energy density is "discontinuously anisotropic" in all directions. The proof relies on a new result concerning an additional isometric constraint that deformation fields must satisfy on the microscale.

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Mikhail Cherdantsev, Kirill Cherednichenko. 2015-02-11. Bending of thin periodic plates. https://arxiv.org/abs/1502.03418

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