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Regularly configured structures with polygonal prisms for three-dimensional auxetic behaviour.

Junhyun Kim1, Dongheok Shin1, Do-Sik Yoo2

  • 1School of Mechanical Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Republic of Korea.

Proceedings. Mathematical, Physical, and Engineering Sciences
|July 11, 2017
PubMed
Summary
This summary is machine-generated.

Researchers designed novel structures using regular polygonal prisms to achieve negative Poisson's ratios. These structures, built from smaller polygonal prisms, demonstrate auxetic properties under specific geometric configurations.

Keywords:
auxeticdeformationnegative Poisson’s ratio

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Area of Science:

  • Materials Science
  • Solid Mechanics
  • Metamaterials

Background:

  • Poisson's ratio describes a material's tendency to deform in directions perpendicular to applied force.
  • Traditional materials typically exhibit positive Poisson's ratios.
  • Auxetic materials, with negative Poisson's ratios, offer unique mechanical properties.

Purpose of the Study:

  • To design and analyze structures with negative Poisson's ratios using regular polygonal prisms.
  • To identify the geometric constraints for achieving auxetic behavior in these structures.
  • To provide a theoretical and numerical basis for these novel materials.

Main Methods:

  • Construction of unit cells using regular n-gonal component prisms.
  • Mathematical derivation of the Poisson's ratio formula for specific n-gonal structures.
  • Analytical and numerical verification of the auxetic properties.

Main Results:

  • Identified n=3, 4, and 6 as the only possible values for regular n-gonal prism-based structures.
  • Derived specific Poisson's ratio formulas for these three configurations.
  • Demonstrated negative Poisson's ratios under defined geometric conditions through analysis and simulation.

Conclusions:

  • Regular polygonal prism-based structures can be engineered to exhibit negative Poisson's ratios.
  • The geometric parameters of the component prisms are critical for achieving auxetic behavior.
  • These findings open avenues for designing advanced metamaterials with tailored mechanical responses.