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

Abstract : We produce a minimal set of 70 generators for the covariant algebra of a fourth-order harmonic tensor, using an original generalized cross product on totally symmetric tensors. This allows us to formulate coordinate-free conditions using polynomial covariant tensors for identifying all the symmetry classes of the elasticity tensor and prove that these conditions are both necessary and sufficient. Besides, we produce a new minimal set of 297 generators for the invariant algebra of the Elasticity tensor, using these tensorial covariants.
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Submitted on : Friday, July 20, 2018 - 3:29:14 PM
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  • HAL Id : hal-01845691, version 1
  • ARXIV : 1807.08996

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Marc Olive, Boris Kolev, R. Desmorat, Boris Desmorat. Characterization of the symmetry class of an Elasticity tensor using polynomial covariants. 2018. ⟨hal-01845691⟩

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