Planar isotropic structures with negative Poisson's ratio

Igor Shufrin, Elena Pasternak, Arcady V. Dyskin

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


A new design principle is suggested for constructing auxetic structures - the structures that exhibit negative Poisson's ratio (NPR) at macroscopic level. We propose 2D assemblies of identical units made of a flexible frame with a sufficiently rigid reinforcing core at the centre. The core increases the frame resistance to the tangential movement thus ensuring high shear stiffness, whereas the normal stiffness is low being controlled by the local bending response of the frame. The structures considered have hexagonal symmetry, which delivers macroscopically isotropic elastic properties in the plane perpendicular to the axis of the symmetry. We determine the macroscopic Poisson's ratio as a ratio of corresponding relative displacements computed using the direct microstructural approach. It is demonstrated that the proposed design can produce a macroscopically isotropic system with NPR close to the lower bound of -1. We also developed a 2D elastic Cosserat continuum model, which represents the microstructure as a regular assembly of rigid particles connected by elastic springs. The comparison of values of NPRs computed using both structural models and the continuum approach shows that the continuum model gives a healthy balance between the simplicity and accuracy and can be used as a simple tool for design of auxetics.

Original languageEnglish
Pages (from-to)2239-2253
Number of pages15
JournalInternational Journal of Solids and Structures
Issue number17
StatePublished - 1 Sep 2012
Externally publishedYes


  • Auxetic isotropic structures
  • Cosserat continuum
  • Homogenisation
  • Reinforcing core

ASJC Scopus subject areas

  • Modeling and Simulation
  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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