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.
CITATION STYLE
Olive, M., Kolev, B., & Auffray, N. (2017). A Minimal Integrity Basis for the Elasticity Tensor. Archive for Rational Mechanics and Analysis, 226(1), 1–31. https://doi.org/10.1007/s00205-017-1127-y
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