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Normal and shear behaviours of the auxetic metamaterials: homogenisation and experimental approaches

Abstract

The auxetic metamaterials exhibit attractive mechanical properties, including negative Poisson’s ratio and compressional resistance. Although auxetic metamaterials have been extensively investigated using experimental and computational approaches, the consistent estimation of shear properties has still not been clarified. According to Cauchy elasticity, the shear properties of an auxetic structure should be enhanced owing to the negative Poisson’s ratio. However, this study used homogenisation and experimental approaches to demonstrate that the shear elasticity is highly non-linear with respect to the characteristic geometrical parameters of a unit cell and that shear properties, particularly normal elasticity, are not always improved. Furthermore, the estimation of the shear elasticity based on the classical isotropic continuum elasticity relations can result in misleading values and should be avoided.

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Acknowledgements

This work was supported by the Ministry of Education, Youth and Sports of the Czech Republic and the European Union - European Structural and Investment Funds in the frames of Operational Programme Research, Development and Education - project Hybrid Materials for Hierarchical Structures (HyHi, Reg. No. CZ.02.1.01/0.0/0.0/16_019/0000843).

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Correspondence to L. Čapek.

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Appendix: Parameterisation of auxetic structures

Appendix: Parameterisation of auxetic structures

See Figs. 6 and 7.

Fig. 6
figure6

Parametrisation of structure A

Fig. 7
figure7

Parametrisation of structure B

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Henyš, P., Vomáčko, V., Ackermann, M. et al. Normal and shear behaviours of the auxetic metamaterials: homogenisation and experimental approaches. Meccanica 54, 831–839 (2019). https://doi.org/10.1007/s11012-019-01000-8

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Keywords

  • Auxetic metamaterial
  • Linear elasticity
  • Computational homogenization
  • Finite element
  • Optical measurement
  • Shear modulus