Another View on Planar Anisotropy: The Polar Formalism

Paolo Vannucci ()
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Paolo Vannucci: LMV - Laboratoire de Mathmatiques de Versailles - UMR8100, CNRS - UVSQ, University Paris-Saclay

A chapter in Variational Analysis and Aerospace Engineering, 2016, pp 489-524 from Springer

Abstract: Abstract The polar formalism is a mathematical method, based upon a complex variable transformation, proposed in 1979 by G. Verchery for representing plane tensors of any rank using invariants and angles. As such, it is particularly suited for representing anisotropic properties, in particular elasticity. In this paper, we give a brief account of the fundamentals of the polar formalism, stressing in particular the role played by the polar invariants on the characterization of elastic symmetries, that leads to a new classification of them, based upon an algebraic criterion and that has allowed for the discovery of two special orthotropies. Then, we focus on some special theoretical subjects: anisotropy of complex or rari-constant layers, some strange cases of interaction between geometry and anisotropy, the anisotropy of damaged layers initially isotropic.

Keywords: Special Orthotropy; Verchery; Polar Invariants; Isotropic Elasticity; Lamination Point (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-45680-5_19

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DOI: 10.1007/978-3-319-45680-5_19

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