A minimal integrity basis for the elasticity tensor

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

1 MSME - Laboratoire de Modélisation et Simulation Multi Echelle
2 I2M - Institut de Mathématiques de Marseille
3 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]

We definitively solve the old problem of finding a minimal integrity basis of polynomial invariants of the fourth-order elasticity tensor C. Decomposing C into its SO(3)-irreducible components we reduce this problem to finding joint invariants of a triplet (a, b, D), where a and b are second-order harmonic tensors, and D is a fourth-order harmonic tensor. Combining theorems of classical invariant theory and formal computations, a minimal integrity basis of 297 polynomial invariants for the elasticity tensor is obtained for the first time.

Mots clés: Elasticity tensor; Classical Invariant Theory; Integrity Basis; Gordan Algorithm

Domaines: Physique mathématique [math-ph]

Nicolas Auffray, Boris Kolev, Marc Olive. A minimal integrity basis for the elasticity tensor. 2016. ⟨hal-01323543v1⟩