Internal Rotations and Stress Tensor Symmetry in Theories of Nematic Liquids and Solids

TL;DR

This paper investigates how internal rotations affect stress tensor symmetry in nematic liquids and solids, showing that neglecting rotational inertia simplifies the models and enables direct calculation of internal rotation variables.

Contribution

It demonstrates that ignoring rotational inertia and director gradients makes stress symmetric and simplifies the calculation of internal rotations in nematic materials.

Findings

Neglecting rotational inertia leads to symmetric stress tensors.

Simplified models allow direct computation of internal rotations.

Theories become more tractable with assumptions on director gradients.

Abstract

The paper analyses kinematics and dynamics of internal rotations with spin and their effects on the constitutive relations for uniaxial (nematic) liquids and for weakly elastic nematic solids. It is shown that neglecting the internal rotational inertia terms and effects of director gradient made the stress symmetric. This not only highly simplifies the theories but also allows calculating all the kinematic variables of internal rotations without any additional constants, other than those presented in the simplified theory with symmetric stress.