Journal article
Finite auxetic deformations of plane tessellations
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol.469(2149), pp.20120465-20120465
2012
Abstract
We systematically analyse the mechanical deformation behaviour, in particular Poisson's ratio, of floppy bar-and-joint frameworks based on periodic tessellations of the plane. For frameworks with more than one deformation mode, crystallographic symmetry constraints or minimization of an angular vertex energy functional are used to lift this ambiguity. Our analysis allows for systematic searches for auxetic mechanisms in archives of tessellations; applied to the class of one- or two-uniform tessellations by regular or star polygons, we find two auxetic structures of hexagonal symmetry and demonstrate that several other tessellations become auxetic when retaining symmetries during the deformation, in some cases with large negative Poisson ratios ν<−1 for a specific lattice direction. We often find a transition to negative Poisson ratios at finite deformations for several tessellations, even if the undeformed tessellation is infinitesimally non-auxetic. Our numerical scheme is based on a solution of the quadratic equations enforcing constant edge lengths by a Newton method, with periodicity enforced by boundary conditions.
Details
- Title
- Finite auxetic deformations of plane tessellations
- Authors/Creators
- H. Mitschke (Author/Creator) - Friedrich-Alexander-Universität Erlangen-NürnbergV. Robins (Author/Creator) - Australian National UniversityK. Mecke (Author/Creator) - Friedrich-Alexander-Universität Erlangen-NürnbergG.E. Schröder-Turk (Author/Creator) - Friedrich-Alexander-Universität Erlangen-Nürnberg
- Publication Details
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol.469(2149), pp.20120465-20120465
- Publisher
- The Royal Society
- Identifiers
- 991005545226607891
- Murdoch Affiliation
- Murdoch University
- Language
- English
- Resource Type
- Journal article
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- Collaboration types
- Domestic collaboration
- International collaboration
- Citation topics
- 7 Engineering & Materials Science
- 7.63 Mechanics
- 7.63.980 Impact-Resistant Structures
- Web Of Science research areas
- Materials Science, Multidisciplinary
- ESI research areas
- Physics