Generic separating sets for 3D elasticity tensors

Rodrigue Desmorat (1) , Nicolas Auffray (2) , Boris Desmorat (3) , Boris Kolev (1) , Marc Olive (1)

1 LMT - Laboratoire de Mécanique et Technologie
2 MSME - Laboratoire de Modélisation et Simulation Multi Echelle
3 SU - Sorbonne Université

We define what is a generic separating set of invariant functions (a.k.a. a weak functional basis) for tensors. We produce then two generic separating sets of polynomial invariants for 3D elasticity tensors, one made of 19 polynomials and one made of 21 polynomials (but easier to compute) and a generic separating set of 18 rational invariants. As a byproduct, a new integrity basis for the fourth-order harmonic tensor is provided.

Domaines: Théorie des représentations [math.RT]; Mécanique des matériaux [physics.class-ph]

Rodrigue Desmorat, Nicolas Auffray, Boris Desmorat, Boris Kolev, Marc Olive. Generic separating sets for 3D elasticity tensors. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2019, ⟨10.1098/rspa.2019.0056⟩. ⟨hal-01966221v1⟩