On the relation between extremal elasticity tensors with orthotropic symmetry and extremal polynomials

TL;DR

This paper establishes a link between extremal orthotropic elasticity tensors and extremal polynomials, showing that the extremality of the tensor is characterized by the determinant of its acoustic tensor being a non-square extremal polynomial.

Contribution

It provides a novel characterization of extremal orthotropic elasticity tensors through the properties of their acoustic tensor determinants.

Findings

Orthotropic elasticity tensors are extremal if their acoustic tensor determinant is an extremal polynomial.

The extremal polynomial must not be a perfect square for the tensor to be extremal.

The paper bridges tensor symmetry properties with polynomial extremality conditions.

Abstract

We prove that an elasticity tensor with orthotropic symmetry is extremal if the determinant of its acoustic tensor is an extremal polynomial that is not a perfect square.