Structures with polygonal prisms for three-dimensional auxetic behaviour

Junhyun Kim, Dongheok Shin, Do Sik Yoo, Kyoungsik Kim

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


We report here structures, constructed with regular polygonal prisms, that exhibit negative Poisson's ratios. In particular, we show how we can construct such a structure with regular n-gonal prism-shaped unit cells that are again built with regular n-gonal component prisms. First, we show that the only three possible values for n are 3, 4 and 6 and then discuss how we construct the unit cell again with regular n-gonal component prisms. Then, we derive Poisson's ratio formula for each of the three structures and show, by analysis and numerical verification, that the structures possess negative Poisson's ratio under certain geometric conditions.

Original languageEnglish
Article number3790000
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2202
Publication statusPublished - 2017

Bibliographical note

Funding Information:
Data accessibility. All data are completely provided in the paper. Authors’ contributions. K.K. conceived the idea of this study. J.K. designed and performed numerical evaluation and experiments. D.-S.Y. assisted in designing the structure. D.-S.Y. and K.K. helped in the analysis of the structures. J.K., D.-S.Y. and K.K. edited the manuscript. Competing interests. We declare we have no competing interests. Funding. This research was supported by Low Observable Technology Research Center program of the Defense Acquisition Program Administration and Agency for Defense Development. Acknowledgements. The authors would like to express their gratitude to referees for providing helpful comments.

Publisher Copyright:
© 2017 The Author(s).

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)


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