Finding Auxetic Frameworks in Periodic Tessellations

Mitschke H, Schwerdtfeger J, Schury F, Stingl M, Körner C, Singer R, Robins V, Mecke K, Schröder-Turk G (2011)

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 2011

Journal

Advanced Materials Wiley-VCH Verlag

Publisher: Wiley-VCH Verlag

Book Volume: 23

Pages Range: 2669-2674

Journal Issue: 22-23

DOI: 10.1002/adma.201100268

Abstract

It appears that most models for micro-structured materials with auxetic deformations were found by clever intuition, possibly combined with optimization tools, rather than by systematic searches of existing structure archives. Here we review our recent approach of finding micro-structured materials with auxetic mechanisms within the vast repositories of planar tessellations. This approach has produced two previously unknown auxetic mechanisms, which have Poisson's ratio v(ss) = -1 when realized as a skeletal structure of stiff incompressible struts pivoting freely at common vertices. One of these, baptized Triangle-Square Wheels, has been produced as a linear-elastic cellular structure from Ti-6Al-4V alloy by selective electron beam melting. Its linear-elastic properties were measured by tensile experiments and yield an effective Poisson's ratio v(LE) approximate to -0.75, also in agreement with finite element modeling. The similarity between the Poisson's ratios v(SS) of the skeletal structure and v(LE) of the linear-elastic cellular structure emphasizes the fundamental role of geometry for deformation behavior, regardless of the mechanical details of the system. The approach of exploiting structure archives as candidate geometries for auxetic materials also applies to spatial networks and tessellations and can aid the quest for inherently three-dimensional auxetic mechanisms.

Authors with CRIS profile

Holger Mitschke Lehrstuhl für Theoretische Physik Jan Schwerdtfeger Lehrstuhl für Werkstoffwissenschaften (Werkstoffkunde und Technologie der Metalle) (WTM) Michael Stingl Lehrstuhl für Angewandte Mathematik (Kontinuierliche Optimierung) Carolin Körner Lehrstuhl für Werkstoffwissenschaften (Werkstoffkunde und Technologie der Metalle) (WTM) Robert Singer Lehrstuhl für Werkstoffwissenschaften (Werkstoffkunde und Technologie der Metalle) (WTM) Klaus Mecke Lehrstuhl für Theoretische Physik Gerd Schröder-Turk Lehrstuhl für Theoretische Physik

Additional Organisation(s)

Zentralinstitut für Neue Materialien und Prozesstechnik Exzellenz-Cluster Engineering of Advanced Materials (EAM)

Involved external institutions

Australian National University (ANU) AU Australia (AU)

How to cite

APA:

Mitschke, H., Schwerdtfeger, J., Schury, F., Stingl, M., Körner, C., Singer, R.,... Schröder-Turk, G. (2011). Finding Auxetic Frameworks in Periodic Tessellations. Advanced Materials, 23(22-23), 2669-2674. https://doi.org/10.1002/adma.201100268

MLA:

Mitschke, Holger, et al. "Finding Auxetic Frameworks in Periodic Tessellations." Advanced Materials 23.22-23 (2011): 2669-2674.

BibTeX: Download