Reduced algebraic conditions for plane or axial tensorial symmetries

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

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

In this article, we formulate necessary and sufficient polynomial equations for the existence of a symmetry plane or an order-two axial symmetry for a totally symmetric tensor of order n ≥ 1. These conditions are effective and of degree n (the tensor's order) in the components of the normal to the plane (or the direction of the axial symmetry). These results are then extended to obtain necessary and sufficient polynomial conditions for the existence of such symmetries for an Elasticity tensor, a Piezo-electricity tensor or a Piezo-magnetism pseudo-tensor.

Mots clés: Anisotropy; Elasticity; Piezo-magnetism; Piezo-electricity

Domaines: Mécanique des matériaux [physics.class-ph]; Physique mathématique [math-ph]

Marc Olive, Boris Desmorat, Boris Kolev, Rodrigue Desmorat. Reduced algebraic conditions for plane or axial tensorial symmetries. Mathematics and Mechanics of Solids, 2020, 25 (12), pp.2155-2177. ⟨10.1177/1081286520920691⟩. ⟨hal-02291487v3⟩