Geometry: The leading parameter for the Poisson's ratio of bending-dominated cellular solids

Journal article


Publication Details

Author(s): Mitschke H, Schury F, Mecke K, Wein F, Stingl M, Schroder-Turk GE
Journal: International Journal of Solids and Structures
Publisher: PERGAMON-ELSEVIER SCIENCE LTD
Publication year: 2016
Volume: 100
Pages range: 1-10
ISSN: 0020-7683


Abstract

Control over the deformation behaviour that a cellular structure shows in response to imposed external forces is a requirement for the effective design of mechanical metamaterials, in particular those with negative Poisson's ratio. This article sheds light on the old question of the relationship between geometric microstructure and mechanical response, by comparison of the deformation properties of bar-and-joint frameworks with those of their realisation as a cellular solid made from linear-elastic material. For ordered planar tessellation models, we find a classification in terms of the number of degrees of freedom of the framework model: first, in cases where the geometry uniquely prescribes a single deformation mode of the framework model, the mechanical deformation and Poisson's ratio of the linearly-elastic cellular solid closely follow those of the unique deformation mode; the result is a bending-dominated deformation with negligible dependence of the effective Poisson's ratio on the underlying material's Poisson's ratio and small values of the effective Young's modulus. Second, in the case of rigid structures or when geometric degeneracy prevents the bending-dominated deformation mode, the effective Poisson's ratio is material-dependent and the Young's modulus (E) over tilde (cs) large. All analysed structures of this type have positive values of the Poisson's ratio and large values of (E) over tilde (cs). Third, in the case, where the framework has multiple deformation modes, geometry alone does not suffice to determine the mechanical deformation. These results clarify the relationship between mechanical properties of a linear-elastic cellular solid and its corresponding bar-and-joint framework abstraction. They also raise the question if, in essence, auxetic behaviour is restricted to the geometry-guided class of bending-dominated structures corresponding to unique mechanisms, with inherently low values of the Young's modulus. (C) 2016 Elsevier Ltd. All rights reserved.


FAU Authors / FAU Editors

Mecke, Klaus Prof. Dr.
Lehrstuhl für Theoretische Physik
Mitschke, Holger
Lehrstuhl für Theoretische Physik
Stingl, Michael Prof. Dr.
Professur für Angewandte Mathematik (Kontinuierliche Optimierung)
Wein, Fabian Dr.
Lehrstuhl für Angewandte Mathematik


Additional Organisation
Exzellenz-Cluster Engineering of Advanced Materials


External institutions with authors

Murdoch University


Research Fields

A3 Multiscale Modeling and Simulation
Exzellenz-Cluster Engineering of Advanced Materials


How to cite

APA:
Mitschke, H., Schury, F., Mecke, K., Wein, F., Stingl, M., & Schroder-Turk, G.E. (2016). Geometry: The leading parameter for the Poisson's ratio of bending-dominated cellular solids. International Journal of Solids and Structures, 100, 1-10. https://dx.doi.org/10.1016/j.ijsolstr.2016.06.027

MLA:
Mitschke, Holger, et al. "Geometry: The leading parameter for the Poisson's ratio of bending-dominated cellular solids." International Journal of Solids and Structures 100 (2016): 1-10.

BibTeX: 

Last updated on 2018-08-08 at 13:53