Experimental validation of theoretical models for hypercube models made by fused deposition modelling technology

Choi, Jeongho; Lee, Sang-ik

doi:10.1007/s12206-019-1140-1

Cited by 3 publications

(2 citation statements)

References 33 publications

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“…Both 8-cell and 24-cell metamaterials, as well as gyroids, retain relative closeness between their C and D constants, indicating that both strength and stiffness are equally reduced from the bulk material properties due to pore space. Nevertheless, the optimised 8-cell metamaterial structures have significantly higher C and D constants than have previously been reported [47] exceeding the previous constants for tesseracts by ca. 20fold and 44-fold in terms of stiffness and strength, respectively.…”

Section: Experimental Testing Resultscontrasting

confidence: 69%

“…Due to their geometrical symmetry and self-repeating features when projected as 3D structures, 4-polytopes have been of interest in aesthetic design and can be seen in some patterned materials, ornaments and creative sculptures [39,40,41]. While there also are numerous reports on the more technical utility of 4-polytopes, for example as space discretising finite elements [42,43,44,45], and even one as an additively manufactured high-porosity potential bone replacement material [46], Choi and Lee [47] provide the only report detailing relationships between the porosity and stiffness, and the porosity and strength of hypercubes, or, tesseracts. In their work, they discuss the strength and stiffness of strut-based hypercubes in terms of E * E s = C ρ * ρ s a and σ * σ s = D ρ * ρ s b , respectively, where E, σ and ρ are the Young's modulus, the strength in compression and the density, respectively.…”

Section: Introductionmentioning

confidence: 99%

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

Cerniauskas¹,

Alam²

2023

Preprint

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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.

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Section: Experimental Testing Resultscontrasting

confidence: 69%