Finding Auxetic Frameworks in Periodic Tessellations

Journal article
(Original article)

Publication Details

Author(s): Mitschke H, Schwerdtfeger J, Schury F, Stingl M, Körner C, Singer R, Robins V, Mecke K, Schröder-Turk G
Journal: Advanced Materials
Publisher: Wiley-VCH Verlag
Publication year: 2011
Volume: 23
Journal issue: 22-23
Pages range: 2669-2674
ISSN: 0935-9648


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.

FAU Authors / FAU Editors

Körner, Carolin Prof. Dr.-Ing.
Lehrstuhl für Werkstoffwissenschaften (Werkstoffkunde und Technologie der Metalle)
Mecke, Klaus Prof. Dr.
Lehrstuhl für Theoretische Physik
Mitschke, Holger
Lehrstuhl für Theoretische Physik
Schröder-Turk, Gerd PD Dr.
Lehrstuhl für Theoretische Physik
Schwerdtfeger, Jan
Lehrstuhl für Werkstoffwissenschaften (Werkstoffkunde und Technologie der Metalle)
Singer, Robert Prof. Dr.-Ing.
Lehrstuhl für Werkstoffwissenschaften (Werkstoffkunde und Technologie der Metalle)
Stingl, Michael Prof. Dr.
Professur für Mathematische Optimierung

Additional Organisation
Zentralinstitut für Neue Materialien und Prozesstechnik
Exzellenz-Cluster Engineering of Advanced Materials

External institutions
Australian National University (ANU)

How to cite

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.

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


Last updated on 2018-17-07 at 11:23