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Finding Auxetic Frameworks in Periodic Tessellations

Authors

  • Holger Mitschke,

    1. Institut für Theoretische Physik, Friedrich-Alexander Universität Erlangen-Nürnberg, Staudtstr. 7, 91058 Erlangen, Germany
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  • Jan Schwerdtfeger,

    1. Friedrich-Alexander Universität Erlangen-Nürnberg, Institute of Advanced Materials and Processes (ZMP), Dr.-Mack-Str. 81, 90762 Fürth, Germany
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  • Fabian Schury,

    1. Department Mathematik, Lehrstuhl Angewandte Mathematik II, Friedrich-Alexander Universität Erlangen-Nürnberg, Martenstr. 3, 91058 Erlangen, Germany
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  • Michael Stingl,

    1. Department Mathematik, Lehrstuhl Angewandte Mathematik II, Friedrich-Alexander Universität Erlangen-Nürnberg, Martenstr. 3, 91058 Erlangen, Germany
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  • Carolin Körner,

    1. Friedrich-Alexander Universität Erlangen-Nürnberg, Institute of Materials Science and Technology (WTM), Martensstr. 5, 91058 Erlangen, Germany
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  • Robert F. Singer,

    1. Friedrich-Alexander Universität Erlangen-Nürnberg, Institute of Materials Science and Technology (WTM), Martensstr. 5, 91058 Erlangen, Germany
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  • Vanessa Robins,

    1. Applied Maths, Research School of Physics, The Australian National University, Canberra, 0200 ACT, Australia
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  • Klaus Mecke,

    1. Institut für Theoretische Physik, Friedrich-Alexander Universität Erlangen-Nürnberg, Staudtstr. 7, 91058 Erlangen, Germany
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  • Gerd E. Schröder-Turk

    Corresponding author
    1. Institut für Theoretische Physik, Friedrich-Alexander Universität Erlangen-Nürnberg, Staudtstr. 7, 91058 Erlangen, Germany
    • Institut für Theoretische Physik, Friedrich-Alexander Universität Erlangen-Nürnberg, Staudtstr. 7, 91058 Erlangen, Germany.
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Abstract

It appears that most models for micro-structured materials with auxetic deformations were found by clever intuition, possibly combined with optimization tools, rather than by systematic searches of existing structure archives. Here we review our recent approach of finding micro-structured materials with auxetic mechanisms within the vast repositories of planar tessellations. This approach has produced two previously unknown auxetic mechanisms, which have Poisson's ratio νss = -1 when realized as a skeletal structure of stiff incompressible struts pivoting freely at common vertices. One of these, baptized Triangle-Square Wheels, has been produced as a linear-elastic cellular structure from Ti-6Al-4V alloy by selective electron beam melting. Its linear-elastic properties were measured by tensile experiments and yield an effective Poisson's ratio νLE ≈ -0.75, also in agreement with finite element modeling. The similarity between the Poisson's ratios νSS of the skeletal structure and νLE of the linear-elastic cellular structure emphasizes the fundamental role of geometry for deformation behavior, regardless of the mechanical details of the system. The approach of exploiting structure archives as candidate geometries for auxetic materials also applies to spatial networks and tessellations and can aid the quest for inherently three-dimensional auxetic mechanisms.

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