Archive for Rational Mechanics and Analysis

, Volume 226, Issue 1, pp 1–31 | Cite as

A Minimal Integrity Basis for the Elasticity Tensor

  • M. Olive
  • B. Kolev
  • N. AuffrayEmail author


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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© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.LMT-Cachan (ENS Cachan, CNRS, Université Paris Saclay)Cachan CedexFrance
  2. 2.CNRS, Centrale Marseille, I2M, UMR 7373Aix Marseille UniversitéMarseilleFrance
  3. 3.Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd DescartesMSME, Université Paris-EstMarne-la-ValléeFrance

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