Journal of Materials Science

, Volume 46, Issue 2, pp 372–384 | Cite as

A generalised three-dimensional tethered-nodule model for auxetic materials

  • N. GasparEmail author
  • C. W. Smith
  • A. Alderson
  • J. N. Grima
  • K. E. Evans


Models for the nano/micro-structural deformation and mechanical properties of auxetic materials (i.e. materials with a negative Poisson’s ratio) have been previously developed. However, most of these models have been two-dimensional, were usually designed specifically to describe some particular class of auxetic materials, and generally only described the behaviour of one particular plane whilst completely ignoring the out-of-plane behaviour of the material. A three-dimensional model has been developed which can be applied to several classes of auxetic materials, including microporous expanded polymers such as e-PTFE, e-UHMWPE and e-PA, body-centered cubic metals and foams. It is generalised that its underlying structure is not specific to a lengthscale or material as the previous list shows. The new model offers a better insight into the underlying principles behind the observed auxetic behaviour and offers a significant improvement in the agreement of the models with existing experimental data. It is shown that there are geometric limitations to the number of planes that can simultanesously display auxetic behaviour. This has ramifications on the design of ordered auxetic materials.


Fibril Strain Increment Elastic Cylinder Tangential Interaction Interaction Ratio 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors acknowledge Brian Caddock of Liverpool University for his contribution to the model at the inital stages of this work.


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • N. Gaspar
    • 1
    Email author
  • C. W. Smith
    • 2
  • A. Alderson
    • 3
  • J. N. Grima
    • 4
  • K. E. Evans
    • 2
  1. 1.AWE plcReadingUK
  2. 2.School of Engineering, Computing and MathematicsUniversity of ExeterExeterUK
  3. 3.Centre for Materials Research & InnovationUniversity of BoltonBoltonUK
  4. 4.Department of Chemistry, Faculty of ScienceUniversity of MaltaMsidaMalta

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