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New principles for auxetic periodic design.

Ciprian S Borcea1, Ileana Streinu2

  • 1Department of Mathematics, Rider University, Lawrenceville, NJ 08648, USA.

SIAM Journal on Applied Algebra and Geometry
|December 8, 2017
PubMed
Summary

The study reveals an infinite variety of periodic framework designs exhibiting auxetic properties in any dimension (d ≥ 2). This finding stems from a novel geometric analysis of auxetic deformation trajectories within these structures.

Keywords:
52C2574N10auxetic deformationmechanism designperiodic framework

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Area of Science:

  • Materials Science
  • Solid Mechanics
  • Geometry

Background:

  • Periodic frameworks are structural materials with repeating unit cells.
  • Auxetic materials exhibit a negative Poisson's ratio, expanding when stretched.
  • Understanding auxetic behavior in periodic frameworks is crucial for advanced material design.

Purpose of the Study:

  • To demonstrate the existence of an infinite number of distinct designs for periodic frameworks with auxetic capabilities.
  • To explore the geometric principles governing auxetic behavior in these structures.

Main Methods:

  • A purely geometric approach was employed to analyze auxetic trajectories.
  • The study is situated within a general theory of deformations of periodic frameworks.

Main Results:

  • For any dimension d ≥ 2, the number of unique periodic framework designs with auxetic properties is infinite.
  • The geometric approach provides a framework for understanding the diversity of auxetic designs.

Conclusions:

  • The design space for auxetic periodic frameworks is vast and theoretically unbounded.
  • Geometric analysis offers powerful insights into the fundamental mechanisms of auxeticity in periodic structures.