# On static chiral Milton-Briane-Willis continuum mechanics

## TL;DR

This paper compares the static behavior of Milton-Briane-Willis continuum mechanics to micropolar Eringen models, showing that the former captures chiral twist effects with fewer parameters and aligns qualitatively with experimental observations.

## Contribution

It demonstrates that Milton-Briane-Willis equations require only one additional parameter for static cubic cases, effectively modeling chiral effects in metamaterials.

## Key findings

- Milton-Briane-Willis equations have one extra parameter influencing chirality.
- These equations qualitatively match observed chiral twist effects.
- The behavior relates to a characteristic length scale.

## Abstract

Recent static experiments on twist effects in chiral three-dimensional mechanical metamaterials have been discussed in the context of micropolar Eringen continuum mechanics, which is a generalization of Cauchy elasticity. For cubic symmetry, Eringen elasticity comprises nine additional parameters with respect to Cauchy elasticity, of which three directly influence chiral effects. Here, we discuss the behavior of the static case of an alternative generalization of Cauchy elasticity, the Milton-Briane-Willis equations. We show that in the homogeneous static cubic case only one additional parameter with respect to Cauchy elasticity results, which directly influences chiral effects. We show that the Milton-Briane-Willis equations qualitatively describe the experimentally observed chiral twist effects, too. We connect the behavior to a characteristic length scale.