A minimal integrity basis for the elasticity tensor

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

1 LMT - Laboratoire de Mécanique et Technologie
2 I2M - Institut de Mathématiques de Marseille
3 MSME - Laboratoire de Modélisation et Simulation Multi Echelle

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; Integrity Basis; Classical Invariant Theory; Gordan Algorithm

Domaines: Matériaux

Marc Olive, Boris Kolev, Nicolas Auffray. A minimal integrity basis for the elasticity tensor. Archive for Rational Mechanics and Analysis, 2017, 226 (1), pp.1-31. ⟨10.1007/s00205-017-1127-y⟩. ⟨hal-01323543v2⟩