Negative Poisson's ratio materials via isotropic interactions

TL;DR

This paper demonstrates that classical many-body systems with isotropic pair interactions can exhibit negative Poisson's ratio (auxetic behavior) under tension, including simple Lennard-Jones potentials and isotropic cubic materials.

Contribution

It derives conditions for negative Poisson's ratio in isotropic systems, showing auxetic behavior can arise from simple pair interactions in crystalline lattices.

Findings

Triangular lattice with Lennard-Jones potential can be auxetic.

Cubic symmetric lattices can be auxetic while remaining elastically isotropic.

Negative Poisson's ratio occurs under tension in these isotropic systems.

Abstract

We show that under tension, a classical many-body system with only isotropic pair interactions in a crystalline state can, counterintutively, have a negative Poisson's ratio, or auxetic behavior. We derive the conditions under which the triangular lattice in two dimensions and lattices with cubic symmetry in three dimensions exhibit a negative Poisson's ratio. In the former case, the simple Lennard-Jones potential can give rise to auxetic behavior. In the latter case, negative Poisson's ratio can be exhibited even when the material is constrained to be elastically isotropic.