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.
@article{arxiv.1605.09561,
title = {A minimal integrity basis for the elasticity tensor},
author = {Nicolas Auffray and Marc Olive and Boris Kolev},
journal= {arXiv preprint arXiv:1605.09561},
year = {2019}
}