Finite auxetic deformations of plane tessellations
Mitschke H, Robins V, Mecke K, Schröder-Turk G (2013)
Publication Status: Published
Publication Type: Journal article
Publication year: 2013
Journal
Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences
Royal Society, The
Publisher: ROYAL SOC
Book Volume: 469
Journal Issue: 2149
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 nu < -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.
Authors with CRIS profile
Holger Mitschke
Lehrstuhl für Theoretische Physik
Klaus Mecke
Lehrstuhl für Theoretische Physik
Gerd Schröder-Turk
Professur für Theoretische Physik
Additional Organisation(s)
Involved external institutions
Australia (AU)How to cite
APA:
Mitschke, H., Robins, V., Mecke, K., & Schröder-Turk, G. (2013). Finite auxetic deformations of plane tessellations. Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 469(2149). https://doi.org/10.1098/rspa.2012.0465
MLA:
Mitschke, Holger, et al. "Finite auxetic deformations of plane tessellations." Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences 469.2149 (2013).
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