On Universal Deformations and Material Preferred Directions in Anisotropic Cauchy Elasticity

TL;DR

This paper investigates universal deformations in anisotropic Cauchy elasticity, revealing that for certain symmetry classes, universal deformations and preferred directions are identical regardless of hyperelasticity, extending previous isotropic results.

Contribution

It demonstrates the equivalence of universality constraints in hyperelastic and Cauchy elasticity for specific anisotropic classes, showing independence from strain energy functions.

Findings

Universal deformations are identical in hyperelastic and Cauchy elasticity for certain classes.

Material preferred directions are consistent across hyperelastic and Cauchy models.

Results extend previous isotropic findings to anisotropic materials.

Abstract

In this paper we study universal deformations in anisotropic Cauchy elasticity. We show that the universality constraints of hyperelasticity and Cauchy elasticity for transversely isotropic, orthotropic, and monoclinic solids are equivalent. This implies that for each of these symmetry classes the universal deformations and the corresponding universal material preferred directions of hyperelastic and Cauchy elastic solids are identical. This is consistent with previous findings for isotropic solids. Universal deformations and material preferred directions are therefore independent of the existence or absence of a strain energy function.