Compressive properties of parametrically optimised mechanical metamaterials based on 3D projections of 4D geometries

Abstract

The design process of 3D mechanical metamaterials is still an emerging field and in this paper, we propose for the first time, a new design and optimisation approach based on 3D projections of 4D geometries (4-polytopes) and evolutionary algorithms. We find that through iterative parametric optimisation, 4-polytope projected mechanical metamaterials can be optimised to achieve both high specific stiffness and high specific yield strengths. Samples manufactured using a low-stereolithography method were tested in compression. We find that optimised tesseracts (8-cell structures) had a higher specific yield strength (22.8 kNm/kg) than that of honeycomb structures tested out-ofplane (19.4 kNm/kg) and a specific stiffness of (0.68 MNm/kg) which is more than 3-fold that of gyroid structures. The compressive strength to solid-modulus ratio of the 8-cell tesseract is very high (3×10 −3 ), exceeding that of out-ofplane honeycombs, which are themselves closer in value to 5-cell pentatopes (2×10 −3 ). 8-cell and 5-cell structures are in the region of one order of magnitude higher than 16-cell and 24-cell structures (∼ 2 × 10 −4 − 8 × 10 −4 ) and are hence comparable to nanostructured metamaterials. The 8-cell tesseracts are 18% stiffer, 43% stronger, and 19% tougher in compression than out-of-plane honeycomb structures, but unlike honeycombs, 8-cell tesseracts are 3D structures with cubic symmetry. Architecture has a profound effect on the relative consistency of properties with cubically symmetric structures displaying the greatest levels of consistency in terms of both strength and stiffness reduction as a function of pore space. The results presented in this paper showcase the potential of this new class of mechanical metamaterial based on 3D projected 4-polytopes.

Tensile properties of 3D projected 4-polytopes: a new class of mechanical metamaterial

“…Table 5: Parametric design variables for 5, 8, 16 and 24-cell designs as illustrated in Figure 7, adapted from [34]. 5 The structures were discretized using a free (unstructured) meshing technique as it was found to be more reliable for auto-generated structures rather than swept and structured meshes.…”

“…Following from our previous work [34], this paper focuses on 3D projected 4-dimensional polytopes (4-polytopes) that have inherently similar fractal substructures with superior mechanical properties [35,36,37,38]. 3D projected 4-polytopes have geometrical features which are self-repeating and hierarchical, and therefore show great potential in applications where high stiffness and lightweightness are required [38,39,35].…”

“…3D projected 4-polytopes have geometrical features which are self-repeating and hierarchical, and therefore show great potential in applications where high stiffness and lightweightness are required [38,39,35]. While our previous work [34] considered the effects of compression on parametrically optimized 3D projected 4D polytopes, this paper will apply an optimization framework powered by a single objective evolutionary algorithm to enhance their specific tensile stiffnesses. In addition, we discuss how maximising the specific tensile stiffness affects other mechanical properties of these metamaterials.…”

Improved mechanical performance of quasi-cubic lattice metamaterials with asymmetric joints

“…In the present paper, we focus on the strut-based artificial cellular structures – hereafter referred to as lattice metamaterials 4 . Modern 3d-printing technologies allow to produce the lattice metamaterials with complex geometry of the unit cells that provides their unique mechanical properties such as the ultra-high and tailorable specific stiffness and strength 5 , 6 , high impact strength 7 – 9 and wide band gaps in the dynamic response 10 – 12 , negative Poisson’s ratio, thermal expansion or stiffness 13 – 15 , pronounced non-classical Cosserat-type and Mindlin-type macroscale behavoir 16 – 19 , etc. The design of the unit cells in the lattice structures usually defines the position, size and orientation of the struts to provide some desired topology and related macroscopic response such that the stretch-dominated behavior 20 – 22 , the quasi-isotropic averaged properties 23 , 24 , the prescribed anisotropy and the symmetric groups 25 , 26 or the functionally graded structure 27 , 28 .…”