The aim of the MetaTes project is to develop a general analytical framework for the design of auxetic
metamaterials based solely on geometric considerations. Auxetics are structured-materials which
exhibit a negative Poisson’s ratio. This anomalous property has the ability to impart a number of
advantageous characteristics making these systems ideal candidates for implementation in niche
applications in biomedical and aerospace engineering.
Auxetics are typically characterised by a representative geometry which is periodically replicated in
space to form a tessellation. The majority are based on the three forms of regular classic
tessellations: triangles, squares and hexagons; intertwined with local geometric characteristics such
as chirality, re-entrancy and rotating unit modes. However, recently, other forms based on irregular
monohedral and polyhedral tilings have also been proposed. This extension of the design space of
auxetic metamaterials opens up a vast number of possibilities for the development of novel
structures since in mathematical literature a large number of tessellations exist with a near-infinite
amount of possible configurations.
This development, while providing greater impetus for the design of new auxetic systems is,
however, somewhat qualified by the fact that not all of these tessellations can give rise to auxeticity.
Preliminary studies have shown that while chiral honeycombs based on certain polyhedral tilings are
auxetic, others exhibit solely a positive Poisson’s ratio regardless of the degree of geometric
variation. This gives rise to the main research question of this project: What exactly is it that makes a
tessellation suitable for the design of an auxetic metamaterial? And is it possible to qualitatively
predict the auxeticity of a generic tessellation without testing it?
In this project we aim to answer these questions by employing a two-pronged approach. Since the
mechanical properties of metamaterials are geometry-dependent, we aspire to utilise analytical
methods used to predict the deformation behaviour of generic truss systems. The first step involves
employing Maxwell’s Criterion, which is typically used to characterise bending vs stretch-dominated
lattice structures in terms of stiffness and apply it to periodic tessellations. This should allow us to
classify these systems in terms of permissible degrees of freedom and enable us to move on to the
second step; a wide ranging parametric simulation run, validated by experimental tests, on
representative tessellations of each class. This will involve both original tessellations per se as well
as transformed variants based on the same tilings.
We believe that this work will allow us to obtain a comprehensive understanding of the structural
mechanics which drive the deformation behaviour of Euclidean tessellations and, in the future, allow
us to qualitatively predict the suitability of generic tessellations for the design of auxetic
metamaterials.