Generic separating sets for three-dimensional elasticity tensors-Reference-Cited by-同舟云学术

Generic separating sets for three-dimensional elasticity tensors

Published:2019-06 Issue:2226 Volume:475 Page:20190056
ISSN:1364-5021
Container-title:Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Proc. R. Soc. A.

Author:

Desmorat R.¹^ORCID,Auffray N.²,Desmorat B.³⁴,Kolev B.¹,Olive M.¹

Affiliation:

1. LMT (ENS Paris-Saclay, CNRS, Université Paris Saclay), 94235 Cachan Cedex, France

2. MSME, Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallée, France

3. Sorbonne Université, UMPC Univ Paris 06, CNRS, UMR 7190, Institut d'Alembert, F-75252 Paris Cedex 05, France

4. Université Paris Sud 11, 91405 Orsay, France

Abstract

We define a generic separating set of invariant functions (a.k.a. a weak functional basis ) for tensors. We then produce two generic separating sets of polynomial invariants for three-dimensional elasticity tensors, one consisting of 19 polynomials and one consisting of 21 polynomials (but easier to compute), and a generic separating set of 18 rational invariants. As a by-product, a new integrity basis for the fourth-order harmonic tensor is provided.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2019.0056

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1. Material symmetry restrictions on constitutive equations

2. The geometry of spontaneous symmetry breaking

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