%0 Journal Article
%T A minimal integrity basis for the elasticity tensor
%+ Laboratoire de Mécanique et Technologie (LMT)
%+ Institut de Mathématiques de Marseille (I2M)
%+ Laboratoire de Modélisation et Simulation Multi Echelle (MSME)
%A Olive, Marc
%A Kolev, Boris
%A Auffray, Nicolas
%< avec comité de lecture
%@ 0003-9527
%J Archive for Rational Mechanics and Analysis
%I Springer Verlag
%V 226
%N 1
%P 1-31
%8 2017-10
%D 2017
%Z 1605.09561
%R 10.1007/s00205-017-1127-y
%K Elasticity tensor
%K Integrity Basis
%K Classical Invariant Theory
%K Gordan Algorithm
%Z MSC 2010: 74E10 (15A72 74B05)
%Z Engineering Sciences [physics]/MaterialsJournal articles
%X 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.
%G English
%2 https://hal.science/hal-01323543v2/document
%2 https://hal.science/hal-01323543v2/file/OKA16.pdf
%L hal-01323543
%U https://hal.science/hal-01323543
%~ CNRS
%~ UNIV-AMU
%~ ENS-CACHAN
%~ EC-MARSEILLE
%~ MSME
%~ MSME_MECA
%~ UPEC
%~ LMT
%~ I2M
%~ I2M-2014-
%~ UNIV-PARIS-SACLAY
%~ ENS-CACHAN-SACLAY
%~ SORBONNE-UNIVERSITE
%~ SU-SCIENCES
%~ LMT-SACLAY
%~ SU-TI
%~ FARMAN
%~ ENS-PARIS-SACLAY
%~ GS-ENGINEERING
%~ TEST-ANAIS
%~ ALLIANCE-SU
%~ UNIV-EIFFEL
%~ UPEM-UNIVEIFFEL
%~ LMPS