Regensburg 2010 – wissenschaftliches Programm

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MM: Fachverband Metall- und Materialphysik

MM 38: Mechanical Properties III

MM 38.3: Vortrag

Mittwoch, 24. März 2010, 17:00–17:15, H16

Finite Auxetic Deformations of Plane Tessellations — •Holger Mitschke¹, Gerd E. Schroeder-Turk¹, Vanessa Robins², and Klaus Mecke¹ — ¹Theoretische Physik, Friedrich-Alexander Universität Erlangen-Nürnberg, Staudtstr. 7B, 91058 Erlangen — ²Applied Maths, School of Physics, The Australian National University, 0200 ACT, Canberra, Australia

We describe a systematic approach to study finite deformations of plane periodic symmetric skeletal structures or strut frameworks, consisting of stiff rods that pivot freely at the mutual joints. These skeletal structures are deformed by imposing a strain in one of the lattice directions and determining the response in the other lattice direction. A numerical Newton-Raphson scheme is used to find the deformation pathways that maintain constant strut lengths. The deformation behaviour is quantified by finite and instantaneous (or infinitesimal) Poissons ratios ν and ν_inst. This analysis allows in particular the analysis of skeletal structures based on tessellations of the plane. Applied to one- or two-uniform tesselations by regular or star polygons, this analysis reveals two as yet unknown structures with auxetic mechanisms. It also shows that a number of other periodic skeletal structure become auxetic at finite strain when retaining some or all symmetries during the deformation, some with Poisson’s ratios below −1. The approach can be generalized to three-dimensional skeletal structures.