Mechanical characterisation of novel aperiodic lattice structures

Abstract

This paper compares the mechanical properties of a class of lattice metamaterials with aesthetically-pleasing patterns that are governed by the mathematics of aperiodic order. They are built up of ordered planar rod networks and exhibit higher non-crystallographic rotational symmetries. However, they lack the translational symmetry associated with periodic lattice metamaterials. We present schematics illustrating their development based on pattern-unique mathematical substitution rules and exploit a numerical framework from previous work to demonstrate that they exhibit fascinating near-isotropic properties. The lattice structures are compared to the well-known hexagonal lattice with respect to their elastic anisotropy measure and the proximity of their bulk and shear moduli to Hashin–Shtrikman-Walpole limits. The study lends insight into the cost-constrained benefits of introducing additional connectivities between aperiodically-ordered point sets. The results show that aperiodic lattices have the potential to yield superior mechanical properties to periodic ones subject to the mechanical rigidity of the underlying shapes that constitute the pattern. The inherent ‘near-isotropy’ associated with these aperiodic structures, even with uniform strut thicknesses and at low fractional densities, and the ordered and varied orientation of their lattice struts present them as promising mesoscale architecture for solving complex multi-axially loaded structural optimization problems, providing inspiration for this study.

Keywords

• Aperiodic order
• Penrose tiling
• Quasiperiodic
• Lattice