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A Theory of Chiral Cosserat Elastic Plates

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Abstract

The mechanical behaviour of chiral materials is of interest for the investigation of carbon nanotubes, honeycomb structures, auxetic materials and bones. This paper is concerned with a theory of chiral Cosserat elastic plates. In this theory, in contrast with the case of achiral plates, the stretching and flexure cannot be treated independently of each other. First, we derive the basic equations which characterize the deformation of chiral plates. Then we establish a uniqueness result in the dynamical theory. In the equilibrium theory we establish conditions under which the Neumann problem admits solutions. Finally, the deformation of an infinite plate with a circular hole is studied. It is shown that, in contrast with the theory of Cosserat achiral plates a uniform pressure acting on the boundary of the hole produces a microrotation of the material particles.

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Acknowledgements

We express our gratitude to the referees for their helpful suggestions.

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Authors and Affiliations

  1. Dipartimento di Costruzioni e Metodi Matematici in Architettura, Università degli Studi di Napoli Federico II, Via Forno Vecchio 36, 80134, Naples, Italy

    S. De Cicco

  2. Octav Mayer Institute of Mathematics, Romanian Academy, Bd. Carol I, nr. 8, 700506, Iaşi, Romania

    D. Ieşan

Authors
  1. S. De Cicco
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  2. D. Ieşan
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Correspondence to S. De Cicco.

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De Cicco, S., Ieşan, D. A Theory of Chiral Cosserat Elastic Plates. J Elast 111, 245–263 (2013). https://doi.org/10.1007/s10659-012-9400-7

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  • DOI: https://doi.org/10.1007/s10659-012-9400-7

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