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.

References in corpus (2)

• Quadratic invariants of elastic moduli
• Remarks on Tsfasman-Boguslavsky Conjecture and Higher Weights of Projective Reed-Muller Codes

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• Rational invariants of even ternary forms under the orthogonal group
• An Irreducible Function Basis of Isotropic Invariants of A Third Order Three-Dimensional Symmetric Tensor
• Reduced polynomial invariant integrity basis for in-plane magneto-mechanical loading
• Construction of minimal integrity basis for anisotropic hyperelasticity via structural tensors