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

Marc Olive (1) , Boris Kolev (1) , R. Desmorat (1) , Boris Desmorat (2)

1 LMT - Laboratoire de Mécanique et Technologie
2 DALEMBERT - Institut Jean Le Rond d'Alembert

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.

Domaines: Matériaux; Théorie des représentations [math.RT]

Marc Olive, Boris Kolev, R. Desmorat, Boris Desmorat. Characterization of the symmetry class of an Elasticity tensor using polynomial covariants. 2018. ⟨hal-01845691v2⟩