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MM: Fachverband Metall- und Materialphysik

MM 18: Mechanical Properties I

MM 18.6: Vortrag

Dienstag, 15. März 2011, 15:15–15:30, IFW B

Tilings as models for auxetic cellular structures — •Holger Mitschke¹, Jan Schwerdtfeger², Vanessa Robins³, Carolin Körner², Robert F. Singer², Klaus Mecke¹, and Gerd E. Schröder-Turk¹ — ¹Theoretische Physik I, Universität Erlangen-Nürnberg — ²Insitute of Advanced Materials and Processes, University of Erlangen-Nuremberg — ³Applied Maths, School of Physical Sciences, Australian National University, Australia

In most auxetic materials, the negative Poisson’s ratio is a consequence of the geometry of the microstructure. This motivates the search for auxetic structures in archives of mathematical models, such as planar tiling or spatial periodic networks. Here we study the deformation of planar tilings, interpreted as skeletal structures. Our numerical study of their deformations reveals several new auxetic structures and examples with different degrees of freedom, i.e. rigid, unique-flexible or flexible with several deformation modes. In the latter case, we show that the conservation of initial symmetries are a possibility to enforce a unique deformation corresponding to the energy minimum of an energy functional, e.g. given by harmonic angular springs at the vertices. Furthermore we show that elastic cellular structures, built by Ti-6Al-4V selective electron-beam melting rapid prototyping precisely on the basis of the newly found auxetic skeletal structures, possess the same deformation behaviour, namely a negative Poisson’s ratio. Finally, the analysis of repositories of three-dimensional tilings or networks (such as www.epinet.anu.edu) is equally possible and has the potential to yield conceptually new truly-3D auxetic deformation mechanisms.