Journal
JOURNAL OF ELASTICITY
Volume 115, Issue 1, Pages 77-103Publisher
SPRINGER
DOI: 10.1007/s10659-013-9448-z
Keywords
Symmetry classes; Invariants; Anisotropy
Funding
- CNRS [PEPS Maths-ST2I 09-99]
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In this paper, we explore new conditions for an elasticity tensor to belong to a given symmetry class. Our goal is to propose an alternative approach to the identification problem of the symmetry class, based on polynomial invariants and covariants of the elasticity tensor C, rather than on spectral properties of the Kelvin representation. We compute a set of algebraic relations which describe precisely the orthotropic (), trigonal (), tetragonal (), transverse isotropic ([SO(2)]) and cubic () symmetry classes in , the highest-order irreducible component in the decomposition of . We provide a bifurcation diagram which describes how one travels in from a given isotropy class to another. Finally, we study the link between these polynomial invariants and those obtained as the coefficients of the characteristic or the Betten polynomials. We show, in particular, that the Betten invariants do not separate the orbits of the elasticity tensors.
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