Dresden 2009 – scientific programme

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MM: Fachverband Metall- und Materialphysik

MM 35: Poster Session II

MM 35.25: Poster

Wednesday, March 25, 2009, 16:30–18:30, P4

Deformations of auxetic periodic strut frameworks — •Holger Mitschke, Klaus Mecke, and Gerd E. Schröder-Turk — Institut für Theoretische Physik, Universität Erlangen-Nürnberg, Staudtstr. 7, D-91058 Erlangen

We study the deformation behaviour, in particular Poisson ratios, of planar periodic strut frameworks with rigid struts connected at flexible joints. We systematically search for yet unknown auxetic frameworks (i.e. with negative Poisson ratio) and to understand the relationship between structure morphology (quantified by integral geometric Minkowski measures) and deformation behaviour.

These frameworks are defined by their symmetry group with two lattice vectors a^→ and b^→, the position of joints p_i^→ and strut vectors of length l_ij. A deformation of an initially rigid network is obtained, if possible, by changing the lattice vector a^→→ (1+δ)a^→ with δ ∈ R, |δ| ≪ 1 but maintaining all initial strut lengths l_ij and translational periodicity. The Poisson ratio is extracted from the relative change in the resulting new b^→. The deformed network is numerically obtained by a multi-dimensional Newton-Raphson method. Here we present an analysis of strut frameworks based on Archimedean tilings and tilings of star polygons [1].

[1] B. Grünbaum and G.C. Shephard, : Tilings and patterns, W.H. Freeman, 1987.