Negative Poisson's Ratio Materials via Isotropic Interactions

Negative Poisson’s Ratio Materials via Isotropic Interactions

Mikael C. Rechtsman, Frank H. Stillinger, and Salvatore Torquato

Phys. Rev. Lett. 101, 085501 – 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.

Received 19 April 2008

DOI:https://doi.org/10.1103/PhysRevLett.101.085501

Authors & Affiliations

Mikael C. Rechtsman¹, Frank H. Stillinger², and Salvatore Torquato^2,3,4,5

¹Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
²Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
³Program in Applied and Computational Mathematics and PRISM, Princeton, New Jersey 08544, USA
⁴Princeton Center for Theoretical Science, Princeton, New Jersey 08544, USA
⁵School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08544, USA

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Issue

Vol. 101, Iss. 8 — 22 August 2008

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