Systematic design of Cauchy symmetric structures through Bayesian optimization

Sheikh, Haris Moazam; Meier, Timon; Blankenship, Brian; Vangelatos, Zacharias; Zhao, Naichen; Marcus, Philip; Grigoropoulos, Costas P.

doi:10.1016/j.ijmecsci.2022.107741

Cited by 36 publications

(21 citation statements)

References 60 publications

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“…Meta-structure optimisation methods have previously employed finite element analysis (FEA) as a basis for structure-property enhancements [16,17]. These include non-linear programming [18], gradient-descent [19,20,21], Bayesian optimisation [22,23], deep learning [24,25] and various evolutionary algorithms [26,27,28,29,30] as a basis for the optimisation frameworks. These optimisation frameworks rely on topology [31,3,17,25] and parametric design approaches [22,26,32,33,34,5] to alter the arrangement of metamaterial lattices [23,4], chiral structures [34,32] and thin-walled cellular solids [6,7,8].…”

Section: Introductionmentioning

confidence: 99%

“…These include non-linear programming [18], gradient-descent [19,20,21], Bayesian optimisation [22,23], deep learning [24,25] and various evolutionary algorithms [26,27,28,29,30] as a basis for the optimisation frameworks. These optimisation frameworks rely on topology [31,3,17,25] and parametric design approaches [22,26,32,33,34,5] to alter the arrangement of metamaterial lattices [23,4], chiral structures [34,32] and thin-walled cellular solids [6,7,8]. While there are a few reports detailing the design of mechanical metamaterials based on fractal substructures [35,36,37,34], 3D projections of 4th dimensional geometries (4-polytopes, or, polychorons) have not as yet been considered as baselines for the design of novel, structural mechanical metamaterials.…”

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: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Cerniauskas¹,

Alam²

2023

Preprint

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“…These are commonly structural optimization models, which are coupled with finite element simulations (FEA) [25,23,8,13]. Advanced optimized methods use meta-heuristic methods and machine learning algorithms, to aid the exploration of the metamaterial design space by either carrying out parametric optimization [26,27] of the metamaterial structures, or by enabling the exploration of inverse design approaches [7,26]. Such approaches include evolutionary algorithms [28,29], as well as Bayesian optimization [15,27], gradient-descent [30,31,32] and neural-network-powered techniques [33,7,26].…”

Section: Introductionmentioning

confidence: 99%

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

Cerniauskas¹,

Alam²

2023

Preprint

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In this paper, we explore the mechanical behavior of a new class of mechanical metamaterials based on the 3D projections of 4-dimensional geometries (4-polytopes) subjected to loading in tension. We demonstrate that the specific properties of mechanical metamaterials can be enhanced by more than 4-fold when optimized within a framework powered by an evolutionary algorithm. Optimized metamaterial structures were manufactured using the low-forcestereolithography prototyping technique and mechanically tested in tension. The experimental results show that the best-performing metamaterial structure, the 8-cell (tesseract), has specific yield strength and specific stiffness values in a similar range to those of hexagonal honeycombs tested out-of-plane. Nevertheless, the 8-cell structures are also cubically symmetrical and have the same mechanical properties in three orthogonal axes. The effect of structure is quantified by comparing the tensile strength against the Young's modulus of bulk solid material. We find that the final value of the 8-cell structures exceeds that of the hexagonal honeycomb by 76%. The 5-cell (pentatope) and 16-cell (orthoplex) metamaterials are shown to be more effective in bearing tensile loads than the gyroid structures, while the 24-cell (octaplex) structures exhibit the lowest ratio and possess the least optimal structure-properties relationships. The findings presented in this paper showcase the importance of macro-scale architecture and highlight the potential of 3D projections of 4-polytopes as the basis for a new class of mechanical metamaterials.

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“…These are commonly structural optimization models, which are coupled with finite-element (FE) simulations. [8,13,28,30] Advanced optimization methods use meta-heuristics and machine-learning algorithms, to aid the exploration of the metamaterial design space by either carrying out parametric optimization [31,32] of the metamaterial structures, or by enabling the exploration of inverse design approaches. [7,31] Such approaches include evolutionary algorithms, [33,34] as well as Bayesian optimization, [20,32,35] gradientdescent, [36][37][38] and neural-network-powered techniques.…”

mentioning

confidence: 99%

“…[8,13,28,30] Advanced optimization methods use meta-heuristics and machine-learning algorithms, to aid the exploration of the metamaterial design space by either carrying out parametric optimization [31,32] of the metamaterial structures, or by enabling the exploration of inverse design approaches. [7,31] Such approaches include evolutionary algorithms, [33,34] as well as Bayesian optimization, [20,32,35] gradientdescent, [36][37][38] and neural-network-powered techniques. [7,31,39] Following from our previous work, [40] this paper focuses on 3D-projected 4D polytopes (4-polytopes) that have inherently similar fractal substructures with superior mechanical properties.…”

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confidence: 99%

Tensile Properties of 3D‐Projected 4‐Polytopes: A New Class of Mechanical Metamaterial

Cerniauskas,

Alam

2023

Adv Eng Mater

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In this article, we research the tensile behavior mechanical metamaterial based on the 3D projections of 4D geometries (4‐polytopes). The specific properties of these mechanical metamaterials can be enhanced by more than fourfold when optimized within a framework powered by an evolutionary algorithm. We show that the best‐performing metamaterial structure, the 8‐cell (tesseract), has specific yield strength and specific stiffness values in a similar range to those of hexagonal honeycombs tested out‐of‐plane. The 8‐cell structures are also cubically symmetrical and have the same mechanical properties in three orthogonal axes. The effect of structure is quantified by comparing metamaterial tensile strength against the Young's modulus of constituent solid material. We find that the strength‐to‐modulus value of the 8‐cell structures exceeds that of the hexagonal honeycomb by 76%. The 5‐cell (pentatope) and 16‐cell (orthoplex) metamaterials are shown to be more effective under tensile loading than gyroid structures, while 24‐cell (octaplex) structures display the least optimal structure‐properties relationships. The findings presented in this paper showcase the importance of macro‐scale architecture and highlight the potential of 3D projections of 4‐polytopes as the basis for a new class of mechanical metamaterial.

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Systematic design of Cauchy symmetric structures through Bayesian optimization

Cited by 36 publications

References 60 publications

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

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

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

Tensile Properties of 3D‐Projected 4‐Polytopes: A New Class of Mechanical Metamaterial

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