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MM: Fachverband Metall- und Materialphysik
MM 33: Structural Materials
MM 33.1: Vortrag
Mittwoch, 13. März 2013, 10:15–10:30, H26
Identifying isotropic auxetic modes in planar crystallographic frameworks — •Holger Mitschke1, Gerd E. Schröder-Turk1, Klaus Mecke1, Patrick W. Fowler2, and Simon D. Guest3 — 1Theoretische Physik, Univ. Erlangen — 2Depart. Chemistry, Univ. Sheffield, UK — 3Depart. Engineering, Univ. Cambridge, UK
Auxetic materials, i.e. with a negative Poisson’s ratio, possess typical microstructures enabling deformations with either rotating or re-entrant elements. Here we idealise planar auxetic microstructures by frameworks of j joints connected by b rigid bars and restrict our study to frameworks with crystallographic symmetry. An observation is that known auxetic microstructures map to non-rigid (floppy) frameworks [1]. Under this assumption an analysis of the types of mechanisms w.r.t. auxeticity seems a promising approach to identify and understand auxetic materials in a simplified but often sufficient manner. The two-dimensional Calladine-Maxwell counting rule m−s=2j−b+3 gives the net mobility where m is the number of mechanisms and s the number of self-stresses. This rule can be extended by taking crystallographic symmetries into account [2] and has recently been extended to allow for periodicity [3]. In this talk the application to planar hexagonal and square groups is presented which gives sufficient counts of the number of symmetry-detectable isotropic auxetic mechanisms.
[1] Mitschke H. et.al. (2013), Proc. R. Soc. A, 469.
[2] Fowler, P.W. and Guest, S.D. (2000), Int. J. Solids. Struct, 37.
[3] Symmetry-extended counting rules for periodic frameworks, S.D. Guest and P.W. Fowler, to be published in Phil Trans Roy Soc A.