# Regensburg 2013 – wissenschaftliches Programm

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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 Mitschke^{1}, Gerd E. Schröder-Turk^{1}, Klaus Mecke^{1}, Patrick W. Fowler^{2}, and Simon D. Guest^{3} — ^{1}Theoretische Physik, Univ. Erlangen — ^{2}Depart. Chemistry, Univ. Sheffield, UK — ^{3}Depart. 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*=2*j*−*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.