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Deformation behavior of re-entrant auxetic metamaterials considering shape transformation effects

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Abstract

A re-entrant hexagonal structure is the most popularly-used auxetic metamaterial providing unique deformation behavior with a negative Poisson’s ratio. In the re-entrant auxetic structure, the Poisson’s ratio varies depending on the design of the re-entrant shape and the order of deformation. In this study, the deformation behavior of re-entrant auxetic structures was investigated through experimental and numerical analyses, with a variation of the reentrant angle. The experimental results showed that the Poisson’s ratio increased as the reentrant angle decreased, and the auxetic property was maintained only while a re-entrant cell remained in a concave shape. Finite element analyses (FEAs) were also conducted to investigate the deformation behavior of the re-entrant structures, using ID-beam and 2D-continuum elements. Compared to the experimental findings, the 2D-FEA showed similar results both in the concave and convex deformation regimes whereas the 1D-FEA showed a reliable prediction only in the concave regime. Additionally, consideration of the cell curvature in the 2D-FEA provided better simulation accuracy by appropriately describing the transformation from the concave to convex regimes. The relevant Poisson’s ratio data were then statistically analyzed to obtain a bilinear regression equation as a function of the axial strain and re-entrant angle, which provides insights into the deformation behavior of re-entrant structures.

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Abbreviations

\({\nu ^ \ast }\) :

Apparent Poisson’s ratio

\({\varepsilon ^ \ast }\) :

Apparent strain

θ :

Re-entrant angle

a :

Inclined ligament length

b :

Vertical ligament length

l :

Cell size

w :

Ligament width

R 1 :

Concave edge round

R 2 :

Convex edge round

P (x,y) :

Position vector

c n :

Coefficients of the bilinear regression equation

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Acknowledgments

This research was financially supported the National Research Foundation of Korea (NRF) grant funded by the Ministry of Science and ICT, Republic of Korea (Grant number: 2022 R1A4A1032030).

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Authors and Affiliations

  1. Department of Mechanical System Design Engineering, Seoul National University of Science and Technology, Seoul, 01811, Korea

    Hong-Gap Choi & Keun Park

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  1. Hong-Gap Choi
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Correspondence to Keun Park.

Additional information

Hong-Gap Choi is a M.Sc. candidate of the Department of Mechanical Design and Robot Engineering, Seoul National University of Science and Technology (SeoulTech), Seoul, Korea. He received his B.S in Mechanical System Design Engineering from SeoulTech. His research interests include additive manufacturing and automatic design.

Keun Park received his B.S. and M.Sc. degrees in Precision Engineering and Mechatronics from KAIST, Korea, in 1992 and 1994, respectively. He received his Ph.D. degree in Mechanical Engineering from KAIST in 1999. He is currently a Professor of the Department of Mechanical System Design Engineering at SeoulTech, Korea. His research interests are finite element analysis and optimization, additive manufacturing, and design for additive manufacturing (DfAM).

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Choi, HG., Park, K. Deformation behavior of re-entrant auxetic metamaterials considering shape transformation effects. J Mech Sci Technol 37, 6143–6151 (2023). https://doi.org/10.1007/s12206-023-2407-0

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  • DOI: https://doi.org/10.1007/s12206-023-2407-0

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