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Anisotropic structure of two-dimensional linear Cosserat elasticity

Nicolas Auffray, Saad El Ouafa, Giuseppe Rosi and Boris Desmorat
Vol. 10 (2022), No. 4, 321–356
DOI: 10.2140/memocs.2022.10.321
Abstract

In the present contribution the anisotropic structure of the two-dimensional linear Cosserat elasticity is investigated. The symmetry classes of this model are derived and detailed in a synthetic way. Particular attention is paid to specific features of Cosserat elasticity: sensitivity to non-centrosymmetry and to chirality. These aspects are important for the application of this continuum theory to the mechanical modelling of lattices and metamaterials. In order to give a parameterisation to the Cosserat constitutive law, an explicit harmonic decomposition of its constitutive tensors is provided. Finally, using an algorithm introduced in a side paper, a minimal integrity basis, which is the minimal set of polynomial invariants generating the algebra of O ⁡ (2)-invariant polynomials, is reported.

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Keywords
anisotropy, Cosserat elasticity, symmetry classes, invariants
Mathematical Subject Classification
Primary: 74E10, 74Q15
Milestones
Received: 6 July 2021
Revised: 16 November 2021
Accepted: 27 December 2021
Published: 30 April 2023

Communicated by Emilio Barchiesi
Authors
Nicolas Auffray
MSME,
Univ Gustave Eiffel,
CNRS UMR 8208,
Marne-la-Vallée,
France
Saad El Ouafa
LMSME, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR
Université Gustave Eiffel
8208 CNRS, 5 bd Descartes
77454 Champs-sur-Marne Cedex 2
France
Giuseppe Rosi
Laboratoire de Modélisation et Simulation Multi Echelle, Equipe de Mécanique
Université Paris Est Créteil
Créteil Marne-la-Vallée
France
Boris Desmorat
Institut d’Alembert
Sorbonne Université
Paris
France
© 2022 MSP (Mathematical Sciences Publishers).