Acta Scientific Applied Physics

Research Article Volume 3 Issue 5

Two-dimensional Auxetic Structures from Rotating Squares

Julian Plewa* and Malgorzata Plonska

Silesia University, Katowice, Poland

*Corresponding Author:Julian Plewa, Silesia University, Katowice, Poland.

Received: February 28, 2023; Published: April 28, 2023


Mechanical metamaterials constructed from rotating squares connected in a new way by means of rotation axes on the surface of the squares exhibit a unique negative Poisson’s ratio (NPR) effect. This effect stems from the highly ordered geometric structure formed by the rigid squares. Under a tensile force, the tested auxetic structures expand horizontally and vertically, with the measure of the relative expansion in these linear dimensions not depending on the number of the elements and the size of the structure, but only on the position of the rotation axes on the surface of the squares.

The paper includes examples of planar and tubular structures made of rigid squares. The analyzed mechanism of the change in the structures’ dimensions upon stretching or compression involves both rotational motion and translation of the connected squares. The structures produced are an improved two-dimensional version of the well-known “rotating squares” model. They can find applications, e.g., in a wide range of adjustment mechanisms.

Keywords: Metamaterials; Auxetic Structures; Negative Poisson’s Ratio


  1. VG Veselago. “The electrodynamics of substances with simultaneously negative values of ε and μ”. Soviet Physics Uspekhi 47 (1968): 509-514.
  2. GS Rajni and A Marwaha. “A Review of Metamaterials and its Applications”. International Journal of Engineering Trends and Technology (IJETT): 6 (2015): 305-310.
  3. G Ma and P Sheng. “Acoustic metamaterials: From local resonances to broad horizons”. Science and Advances 2 (2016): 1-16.
  4. G Duan., et al. “Boosting magnetic resonance imaging signal-to-noise ratio using magnetic metamaterials”. Communications Physics 2 (2019): 1-7.
  5. JP Pendry., et al. “Magnetism from Conductors and Enhanced Nonlinear Phenomena”. IEEE. Trans. Microwave. Theory Technol. 47 (1999): 2075-2084.
  6. RS Lakes. “Foam structures with a negative Poisson’s ratio”. Science 235 (1987): 1038-1040.
  7. KW Wojciechowski. “Two-dimensional isotropic system with a negative Poisson ratio”. Physics Letters A 137 (1989): 60-64.
  8. K E Evans. “Auxetic polymers: a new range of materials”. Endeavour (151991): 170-174.
  9. JN Grima and KE Evans. “Auxetic behavior from rotating squares”. Journal of Materials Science Letters 19 (2000): 1563-1565.
  10. LJ Gibson., et al. “The mechanics of two- dimensional cellular materials”. Proceedings of the Royal Society of London. Series A 382 (1982): 25-42.
  11. AG Kolpakov. “Determination of the average characteristics of elastic frameworks”. Journal of Applied Mathematics and Mechanics 6 (1985): 739-745.
  12. RF Almgren. “An isotropic three-dimensional structure with Poisson’ s ratio -1”. Journal of Elasticity 15 (1985): 427-430.
  13. AV Mazaev., et al. “Auxetics materials: classification, mechanical properties and applications”. IOP Conf. Series: Mater. Sci. Eng. 747 (2020): 012008, 1-8.
  14. A Joseph., et al. “On the application of additive manufacturing methods for auxetic structures: a review”. Advances in Manufacturing 9 (2021): 342-368.
  15. E Barchiesi., et al. “Mechanical metamaterials: a state of the art”. Mathematics and Mechanics of Solids 24 (2019): 212-234.
  16. J Plewa., et al. “Experimental studies of auxetic structures from rotating squares”. Materials (2022).
  17. X Ren., et al. “A simple auxetic tubular structure with tuneable mechanical properties”. Smart Materials and Structures 25 (2016): 065012, 1-9.
  18. SK Bhullar., et al. “Design and Fabrication of Stent with Negative Poisson’s Ratio”. International Journal of Mechanical Engineering and Mechatronics 2 (2014): 448-454.
  19. F G J Broeren., et al. “Spatial pseudo-rigid body model for the analysis of a tubular mechanical Metamaterial”. Mathematics and Mechanics of Solids2 (2020): 305-316.
  20. C Luo., et al. “Design manufacturing and applications of auxetic tubular structures: A review”. Thin-Walled Structure 163 (2021): 7682, 1-12.


Citation: Julian Plewa and Malgorzata Plonska. “Two-dimensional Auxetic Structures from Rotating Squares". Acta Scientific Applied Physics 3.5 (2023): 10-20.


Copyright: © 2023 Julian Plewa and Malgorzata Plonska. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

News and Events

Contact US