On the weak nematic elasticity

TL;DR

This paper develops a simplified theoretical framework for weak nematic elasticity, analyzing stability, stress symmetry, and conditions for soft deformations in incompressible non-classical elastic materials.

Contribution

It introduces a reduced formulation of the theory that simplifies calculations while maintaining stability conditions, and analyzes soft deformation conditions in weak nematic elasticity.

Findings

Stress tensor can be considered symmetric under certain conditions.

Reduced free energy expressions facilitate stress-strain calculations.

Conditions for soft deformations are derived and exemplified.

Abstract

The paper considers the general case of incompressible non-classical elasticity with small deformations and rotations. The thermodynamic stability is analysed for free energy density with three rotational degrees of freedom. Although the theory generally predicts the stress to be non-symmetric, the stress tensor can still be considered as symmetrical in the absence of external fields and when the inertia effects of internal rotations and couple stresses are neglected. When the condition of stress tensor symmetry is applied, it results in simplified, "reduced" expressions for the free energy density and stress, which preserve the general stability conditions and allow easy calculations of stress-strain relations and rotations. Using this reduced formulation, a general condition of existence of soft deformations is analysed for the weak nematic elasticity. The reduction procedure is exemplified using the infinitesimal Warner potential derived from a molecular model.