Generic separating sets for 3D elasticity tensors

Abstract

We define what is a generic separating set of invariant functions (a.k.a. a weak functional basis) for tensors. We produce then two generic separating sets of polynomial invariants for 3D elasticity tensors, one made of 19 polynomials and one made of 21 polynomials (but easier to compute) and a generic separating set of 18 rational invariants. As a byproduct, a new integrity basis for the fourth-order harmonic tensor is provided.

References in corpus (3)

• A minimal integrity basis for the elasticity tensor
• Harmonic factorization and reconstruction of the elasticity tensor
• Rational invariants of even ternary forms under the orthogonal group

Cited by in corpus (7)

• Symmetry classes in piezoelectricity from second-order symmetries
• Minimal functional bases for elasticity tensor symmetry classes
• Computation of minimal covariants bases for 2D coupled constitutive laws
• Irreducible matrix resolution of the elasticity tensor for symmetry systems
• Recovering the normal form of an elasticity tensor
• Upper bounds estimates of the distance to cubic or orthotropic elasticity
• Preserving elastic anisotropy with tessellations of granular packings