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Interdisciplinary Applications of Kinematics pp 197–204Cite as

Auxetic Regions in Large Deformations of Periodic Frameworks

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Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 71))

Abstract

In materials science, auxetic behavior refers to lateral widening upon stretching. We investigate the problem of finding domains of auxeticity in global deformation spaces of periodic frameworks. Case studies include planar periodic mechanisms constructed from quadrilaterals with diagonals as periods and other frameworks with two vertex orbits. We relate several geometric and kinematic descriptions.

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Acknowledgements

This work was supported by the National Science Foundation (awards no. 1319389 and 1704285 to C.S.B., awards no. 1319366 and 1703765 to I.S.) and the National Institutes of Health (award 1R01GM109456 to C.S.B. and I.S.).

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Authors and Affiliations

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

    Ciprian S. Borcea

  2. Department of Computer Science, Smith College, Northampton, MA, 01063, USA

    Ileana Streinu

Authors
  1. Ciprian S. Borcea
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  2. Ileana Streinu
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Corresponding authors

Correspondence to Ciprian S. Borcea or Ileana Streinu .

Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, University of Duisburg-Essen, Duisburg, Germany

    Andrés Kecskeméthy

  2. Chair of Mechanics and Robotics, University of Duisburg-Essen, Duisburg, Nordrhein-Westfalen, Germany

    Francisco Geu Flores

  3. Faculty of Engineering, University of Piura, Piura, Peru

    Eliodoro Carrera

  4. Department of Engineering, Pontifical Catholic University of Peru, Lima, Peru

    Dante A. Elias

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Borcea, C.S., Streinu, I. (2019). Auxetic Regions in Large Deformations of Periodic Frameworks. In: Kecskeméthy, A., Geu Flores, F., Carrera, E., Elias, D. (eds) Interdisciplinary Applications of Kinematics. Mechanisms and Machine Science, vol 71. Springer, Cham. https://doi.org/10.1007/978-3-030-16423-2_18

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