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A Minimal Integrity Basis for the Elasticity Tensor

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Abstract

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.

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

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