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arXiv · 1807.08996

Characterization of the symmetry class of an Elasticity tensor using polynomial covariants

Marc Olive·Boris Kolev·R. Desmorat·Boris Desmorat
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Abstract

We formulate effective necessary and sufficient conditions to identify the symmetry class of an elasticity tensor, a fourth-order tensor which is the cornerstone of the theory of elasticity and a toy model for linear constitutive laws in physics. The novelty is that these conditions are written using polynomial covariants. As a corollary, we deduce that the symmetry classes are affine algebraic sets, a result which seems to be new. Meanwhile, we have been lead to produce a minimal set of 70 generators for the covariant algebra of a fourth-order harmonic tensor and introduce an original generalized cross product on totally symmetric tensors. Finally, using these tensorial covariants, we produce a new minimal set of 294 generators for the invariant algebra of the elasticity tensor.

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BibTeXRIS

Marc Olive, Boris Kolev, R. Desmorat, Boris Desmorat. 2018-07-24. Characterization of the symmetry class of an Elasticity tensor using polynomial covariants. https://arxiv.org/abs/1807.08996

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