A minimal integrity basis for the elasticity tensor

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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Submitted on : Monday, May 15, 2017 - 4:16:18 PM
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Marc Olive, Boris Kolev, Nicolas Auffray. A minimal integrity basis for the elasticity tensor. Archive for Rational Mechanics and Analysis, Springer Verlag, 2017, 226 (1), pp.1-31. ⟨https://link.springer.com/article/10.1007%2Fs00205-017-1127-y⟩. ⟨10.1007/s00205-017-1127-y⟩. ⟨hal-01323543v2⟩

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