Multiscale Optimization of 3D‐Printed Beam‐Based Lattice Structures through Elastically Tailored Unit Cells

Schwahofer, Oliver; Büttner, Sascha; Binder, Johannes; Colin, David; Drechsler, Klaus

doi:10.1002/adem.202201385

Adv Eng Mater

2022

DOI: 10.1002/adem.202201385

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Multiscale Optimization of 3D‐Printed Beam‐Based Lattice Structures through Elastically Tailored Unit Cells

Oliver Schwahofer

Sascha Büttner

Johannes Binder

et al.

Abstract: Herein, a numerical multiscale tool is developed to design 3D periodic lattice structures. The work is motivated by the high design freedom of additive manufacturing technologies, which enable complex multiscale lattice structures to be printed. A finite‐element‐based free‐material optimization method is used to determine the ideal orthotropic material properties of a 3D macrostructure space. Subsequently, a population‐based algorithm is established to design optimized microscopic lattice unit cells with the d… Show more

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Cited by 4 publications

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“…[15] The idea of designing a metamaterial with the desired structural properties based on a macroscopic periodic lattice composed of optimized microscopic unit cells has been proposed. [16] In recent publications, lattice metamaterials with mesoscale motifs (LMMM) were introduced. [3,17] They are characterized by a multiscale architecture with a regular lattice at the lowest length scale, which entails structural elements (rods, nodes) of more than one type.…”

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Lattice Metamaterials with Mesoscale Motifs: Exploration of Property Charts by Bayesian Optimization

et al. 2023

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Architectural materials at mesoscale open new opportunitiesfor the design of materials with unique combinations of properties. [1][2][3] One of the subclasses of this kind of material is lattice (meta)materials. Classical lattice materials have a mesh-like structure generated by translation in space of an elementary cell that comprises several, most commonly identical, elements, such as thin bars or rods. [4,5] It was found that materials with this type of inner architecture while having a low density, exhibit high values of stiffness, strength, and fracture toughness. [4][5][6] Great expectations in this field are connected with nanoscale lattices. [7,8] Two principal directions can be followed to get to more versatile behavior. First, lattice-based metamaterials can, of course, be built from more complex unit cells. Buckling elements in the unit cell can effectively give a plastic response, [9] chiral elements can show macroscopically chiral response, [10] and gear-based lattice structures can change connectivity and allow extreme adaptivity of elastic properties even in the built structure. [11] The second direction is to build lattice materials with a structure different from the classical one, which possesses new properties. [12] For example, it was shown that irregular mesh

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Lattice Metamaterials with Mesoscale Motifs: Exploration of Property Charts by Bayesian Optimization

et al. 2023

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Equivalent spring-like system for two nonlinear springs in series: application in metastructure units design

Cveticanin

2024

Acta Mech

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The paper deals with the problem of design of unit in auxetic metastructure. The unit is modeled as a two-part spring-like system where each part is with individual stiffness. To overcome the problem of analyzing of each of parts separately, the equivalent spring is suggested to be introduced. In the paper, a method for obtaining the equivalent elastic force of the unit is developed. The method is the generalization of the procedure suggested for substitution of a hard and a soft spring in series with an equivalent one. The nonlinearity of original springs is of quadratic order. As a results, it is obtained that the equivalent elastic force for two equal springs remains of the same type as of the original springs (soft or hard). For two opposite type springs in series with equal coefficients, the equivalent force is soft. The method is applicable for any hard and soft nonlinear springs or spring-like systems. Thus the hexagonal auxetic unit which contains a soft and a hard part in series is analyzed. In the paper, a new analytic method for determination of the frequency of vibration for the unit under action of a constant compression force acting along the unit axis is introduced. The method is applied for units which contain two parts: hard–hard, soft–soft, hard–linear, soft–linear and opposite. The obtained approximate vibration results are compared with numerically obtained ones and show good agreement. The advantage of the method is its simplicity as it does not require the nonlinear equation of motion to be solved.

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Tailored elastic properties of beam-based lattice unit structures

Schwahofer

Büttner

Colin

et al. 2023

Int J Mech Mater Des

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In this paper a structural optimization framework is developed to design three-dimensional periodic lattice unit cells that meets specific mechanical requirements. The work is motivated by the high design freedom of additive manufacturing technologies, which enable complex multiscale lattice structures to be printed. An optimized lattice unit cell delivers desired orthotropic elastic material properties, providing a tailored metamaterial. The design variables are the coordinates of lattice skeleton nodes defined within the three-dimensional lattice cell space, and the connectivities between them resulting a strut-skeleton. Genetic algorithm (GA) is combined with posterior particle swarm optimization (PSO) algorithm to establish an integrated topology and shape optimization tool. For the calculation of the elastic properties of the individual lattice cells, an effective Timoshenko beam-based finite element calculation method was developed. The novelty of the work stems from its free topology optimization nature, excluding the strut diameters from the optimization variables. The method is demonstrated by four lattice cell optimization cases, where extreme orthotropic elastic properties were targeted and achieved. The tailored lattice cells represent a metamaterial, that can be used to build a structural component on the macroscopic scale, by stacking the cells periodically together, to fill the macroscopic 3D design space. This framework is a strong basis that can be extended to meet further nonlinear metamaterial requirements, such as energy absorption.

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Multiscale Optimization of 3D‐Printed Beam‐Based Lattice Structures through Elastically Tailored Unit Cells

Cited by 4 publications

References 50 publications

Lattice Metamaterials with Mesoscale Motifs: Exploration of Property Charts by Bayesian Optimization

Lattice Metamaterials with Mesoscale Motifs: Exploration of Property Charts by Bayesian Optimization

Equivalent spring-like system for two nonlinear springs in series: application in metastructure units design

Tailored elastic properties of beam-based lattice unit structures

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