Hierarchical honeycomb metamaterials based on monohedral triangular, square and hexagonal tessellations

Hierarchical mechanical metamaterials are a class of architectured materials characterised by structures within structures. In this work we present a new class of honeycomb-based hierarchical metamaterials which incorporate irregular honeycombs within the three class of regular monohedral 2D tessellations; namely the triangle, square and hexagonal tessellations. The introduction of hierarchy within these frameworks imparts a high level of versatility in terms of permissible mechanical properties, including anomalous properties such as auxeticity and zero Poisson's ratio, which are not found in the original tessellations. Furthermore, by preserving the original symmetry characteristics of the base tessellations, other advantageous properties, such as transverse isotropy in the case of the triangular and hexagonal tessellations, are retained as well. A wide range of systems were analysed using Finite Element simulations, followed by experimental tests on three additively-manufactured prototypes; one representative architecture of each hierarchical tessellation. The findings of this study demonstrate the transformative effect which the introduction of hierarchy can have on the mechanical properties and deformation behaviour of even the most basic of tessellations as well as opening up new avenues for further studies on the development of novel mechanical metamaterials.