Comment on: I-Shih Liu: Constitutive theory of anisotropic rigid heat conductors

TL;DR

This paper critiques Liu's analysis of anisotropic rigid heat conductors, emphasizing the importance of including the deformation gradient in the constitutive modeling to accurately capture anisotropy and frame indifference.

Contribution

It clarifies the role of the deformation gradient in constitutive theories for anisotropic rigid heat conductors, challenging previous assumptions about isotropy.

Findings

Including the deformation gradient is essential for modeling anisotropy.

The usual omission leads to misleading conclusions about isotropy.

Material frame indifference does not imply isotropy when deformation gradient is considered.

Abstract

In I-Shih Liu's paper \C{1}, the compatibility of anisotropy and material frame indifference of a rigid heat conductor is investigated. For this purpose, the deformation gradient is introduced into the domain of the constitutive mapping. Because of the presupposed rigidity, the deformation gradient is here represented by an orthogonal tensor. The statement, that the usual procedure -- not to introduce the deformation gradient into the state space of rigid heat conductors -- causes isotropy because of the material frame indifference, is misleading.