Minimal functional bases for elasticity tensor symmetry classes

TL;DR

This paper introduces minimal functional bases tailored to specific symmetry classes of elasticity tensors, enabling more precise analysis within each symmetry stratum.

Contribution

It develops low-cardinality minimal bases for various symmetry classes of elasticity tensors, focusing on symmetry strata rather than the entire tensor space.

Findings

Minimal bases for tetragonal, trigonal, cubic, and transversely isotropic classes

Enhanced ability to analyze elasticity tensors within specific symmetry classes

Reduction in complexity of tensor symmetry analysis

Abstract

Functional bases, synonymous with separating sets, are usually formulated for an entire vector space, such as the space Ela of elasticity tensors. We propose here to define functional bases limited to symmetry strata, i.e. sets of tensors of the same symmetry class. We provide such lowcardinal minimal bases for tetragonal, trigonal, cubic or transversely isotropic symmetry strata of the elasticity tensor.