Mikael C. Rechtsman
Department of Physics, Princeton University, Princeton, New Jersey 08544, USA

Frank H. Stillinger
Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA

Salvatore Torquato
Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
Program in Applied and Computational Mathematics and PRISM, Princeton, New Jersey 08544, USA
Princeton Center for Theoretical Science, Princeton, New Jersey 08544, USA
School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08544, USA

Phys. Rev. Lett. 101, 085501 (2008).

Received 19 April 2008; published 18 August 2008.

Abstract

We show that under tension a classical many-body system with only isotropic pair interactions in a crystalline state can, counterintuitively, 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, a negative Poisson’s ratio can be exhibited even when the material is constrained to be elastically isotropic.