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- W1966687966 abstract "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 ( $[mathbb {D}_{2}]$ ), trigonal ( $[mathbb {D}_{3}]$ ), tetragonal ( $[mathbb {D}_{4}]$ ), transverse isotropic ([SO(2)]) and cubic ( $[mathbb {O}]$ ) symmetry classes in $mathbb {H}^{4}$ , the highest-order irreducible component in the decomposition of $mathbb {E}mathrm {la}$ . We provide a bifurcation diagram which describes how one “travels” in $mathbb {H}^{4}$ 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." @default.
- W1966687966 created "2016-06-24" @default.
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- W1966687966 date "2013-06-19" @default.
- W1966687966 modified "2023-10-17" @default.
- W1966687966 title "On Anisotropic Polynomial Relations for the Elasticity Tensor" @default.
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- W1966687966 doi "https://doi.org/10.1007/s10659-013-9448-z" @default.
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