Phonons in lattices with rod-like particles

TL;DR

This paper investigates vibrational modes in lattices with rod-like particles, revealing complete bandgaps and auxetic-like behavior in two-dimensional structures with coupled translational and rotational dynamics.

Contribution

It introduces a continuum model for lattices with rigid rods, highlighting the coupling of degrees of freedom and the existence of complete bandgaps in auxetic-like materials.

Findings

Complete bandgaps observed between acoustic and optical modes.

Rigid rods prevent membrane collapse under stretching.

Auxetic-like behavior with negative Poisson ratio in 2D lattices.

Abstract

The paper studies the modes of vibrations of a lattice with rod-like particles, in a continuum model where the sites of the lattice are the connections among strings and rigid rods. In these structures then, translational and rotational degrees of freedom are strongly coupled. We will discuss in particular two-dimensional lattices with auxetic-like behaviour. Auxetics are materials with a negative Poisson elastic parameter, meaning that they have a lateral extension, instead to shrink, when they are stretched. We assume as "auxetic-like" two-dimensional structures, structures which do not collapse, when stretched in one of the in-plane directions. The presence of rigid rod-like particles in the lattice prevents the shrinking of the membrane. Complete bandgaps between acoustic and optical modes are observed in analogy with the behaviour of crystalline materials.