Stiff auxetics: Hierarchy as a route to stiff, strong lattice based auxetic meta-materials

Abstract

Using a combination of analytic and computational methods, we examine the effect of adding hierarchical substructure to an auxetic lattice. Our novel methodology, involving a coarse grain approach, allows for the analysis of hierarchically sub-structured lattices where direct computation would prove intractable. We show that through hierarchy one can create ultra-lightweight auxetic meta-materials of high strength and stiffness. Through scaling law arguments, we show that the benefits of hierarchical design can also be obtained in the general class of bending-dominated lattices. Furthermore, we show that the hierarchical structures presented show a wide range of tailorability in their mechanical properties, and exhibit increased strength when optimised for buckling resistance. Auxetic materials have a broad range of potential applications, and thus the creation of ultra-light auxetic meta-materials with enhanced stiffness and strength is undoubtedly of practical importance.

Meta-biomaterials

“…Indeed, the limitations of the two length scales approach have been also recognized by other metamaterials communities. For example, a number of hierarchical mechanical metamaterials 25,26 with extraordinary and otherwise impossible combination of properties, such as high stiffness and auxetic behavior 27 have recently appeared in the literature.…”

Lightweight mechanical metamaterials designed using hierarchical truss elements

“…The investigation was primarily focused on exploring the merits of introducing hierarchical triangular truss-like components within the rotating unit and analysing the effects of these structural frameworks on the mechanical properties of the studied systems. Previous studies on other hierarchical auxetic systems have shown that the introduction of hierarchy in such structures may be used to obtain enhanced mechanical properties and/or provide structural stability through smart design [23][24][25][26][27][28][29][30]. Hierarchical structures, which are defined as structures which are themselves made from structures [31], are not limited solely to fractal or fractal-like systems [25,32,33], but may also include the use of different geometries and mechanisms at separate hierarchical levels aimed at conferring additional enhanced properties to the system.…”

Delocalized Nonlinear Vibrational Modes in Graphene: Second Harmonic Generation and Negative Pressure

“…It should be noted that materials with negative Poisson's ratio, negative thermal expansion, negative compressibility, and other anomalous characteristics attract considerable attention of researchers because they are interesting from the theoretical standpoint and have a potential in applications …”