Design and analysis of a thick Miura-ori folded structure with large negative Poisson’s ratio

Abstract

In this article, effective properties of Miura-ori patterned sheets are studied. The thickness of the facets is allowed to have considerably large values; hence, the structural response of the system cannot be determined by considering only the kinematics of the folding. In particular, large negative values of the Poisson’s ratio have been observed for particular sets of parameters. Numerical outcomes, for periodic and finite systems, have been validated by an experimental campaign, where several specimens with different geometries and materials have been tested. The elastic fields of the specimens have been measured with the digital image correlation method.

Keywords:

• Negative Poisson’s ratio
• auxetic structure
• Miura-ori folded sheet
• metamaterial
• digital image correlation

Acknowledgements

GC’s and MB’s work has been performed under the auspices of GNFM-INDAM.

Notes

1 The mesh has been chosen in order to have at least four elements along the thickness, even though convergence could be reached with fewer elements. As an example, for t = 1 mm, the mesh assuring convergence of results consists of a total number of degrees of freedom of the order $3.6\times {10}^4.$ It has also been checked that with a different type of finite elements, namely, hexahedral, a mesh with a similar number of degrees of freedom leads to very close results.

2 The chosen mesh of the shell model, consisting of triangular elements, is characterized by around $1.0\times {10}^4$ degrees of freedom.

3 Note that γ, θ, and ν_SL in [88] correspond to $\phi ,\hspace{0.17em}(\pi -{\theta }_2)/2,$ and ν_xy in this article.

Additional information

Funding

Financial support from Fondazione di Sardegna, project ADVANCING 2018 (MB, PMS, AB), is gratefully acknowledged.