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. 2015 Feb 11:5:8395.
doi: 10.1038/srep08395.

Hierarchical auxetic mechanical metamaterials

Ruben Gatt  1 , Luke Mizzi  1 , Joseph I Azzopardi  1 , Keith M Azzopardi  1 , Daphne Attard  1 , Aaron Casha  2 , Joseph Briffa  3 , Joseph N Grima  4
Affiliations

Hierarchical auxetic mechanical metamaterials

Ruben Gatt et al. Sci Rep. .

Abstract

Auxetic mechanical metamaterials are engineered systems that exhibit the unusual macroscopic property of a negative Poisson's ratio due to sub-unit structure rather than chemical composition. Although their unique behaviour makes them superior to conventional materials in many practical applications, they are limited in availability. Here, we propose a new class of hierarchical auxetics based on the rotating rigid units mechanism. These systems retain the enhanced properties from having a negative Poisson's ratio with the added benefits of being a hierarchical system. Using simulations on typical hierarchical multi-level rotating squares, we show that, through design, one can control the extent of auxeticity, degree of aperture and size of the different pores in the system. This makes the system more versatile than similar non-hierarchical ones, making them promising candidates for industrial and biomedical applications, such as stents and skin grafts.

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Figures

Figure 1
Figure 1. Diagram depicting some different types of hierarchical systems based on the rotating rigid units mechanism.
Note that the systems in (a) are all systems were an approximate ‘square' motif is being retained at all levels whilst the systems in (b) are dissimilar hierarchical systems which although being composed of the same level 0 and level 1 units, the sub-units making the level 2 have different shapes, sizes and/or connectivity. Note that in constructing such hierarchical structures care must be taken to avoid overlap, a property which may be partially controlled through changes in the geometric parameters related to the sub-units.
Figure 2
Figure 2. Graphs showing the Poisson's ratios in νyz and νzy planes for hierarchical structures with different θ0 values.
The missing values for θ0 = θ1 in both sets were due to unattainable geometries which resulted from mathematical constraints.
Figure 3
Figure 3. (a) Diagram showing the different points from which the Level 1 unit could be connected to other units (b) a two-level system with an acting rotating unit with a parallelogramic shape and (c) with a rectangular shape.
Figure 4
Figure 4. Stent based on a two level hierarchical rotating square geometry.
See this image and copyright information in PMC

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