Recovering the normal form of an elasticity tensor

Sophie Abramian (1) , Boris Desmorat (2) , Rodrigue Desmorat (1) , Boris Kolev (1) , Marc Olive (1)

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

We propose an effective geometrical approach to recover the normal form of a given Elasticity tensor. We produce a rotation which brings an Elasticity tensor onto its normal form, given its components in any orthonormal frame, and this for any tensor of any symmetry class. Our methodology relies on the use of specific covariants and on the geometric characterization of each symmetry class using these covariants. An algorithm to detect the symmetry class of an Elasticity tensor is finally formulated.

Mots clés: Elasticity tensor; Anisotropy; Natural basis; Symmetry classes; Covariants

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des matériaux [physics.class-ph]

Sophie Abramian, Boris Desmorat, Rodrigue Desmorat, Boris Kolev, Marc Olive. Recovering the normal form of an elasticity tensor. Journal of Elasticity, 2020, 142 (1), pp.1-33. ⟨10.1007/s10659-020-09784-7⟩. ⟨hal-02410330v2⟩