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Review Article

The Design Process of Additively Manufactured Mesoscale Lattice Structures: A Review

[+] Author and Article Information
Francesco Tamburrino

Department of Mechanical Engineering,
Politecnico di Milano,
Milan 20156, Italy
e-mail: francesco.tamburrino@polimi.it

Serena Graziosi

Department of Mechanical Engineering,
Politecnico di Milano,
Milan 20156, Italy
e-mail: serena.graziosi@polimi.it

Monica Bordegoni

Mem. ASME
Department of Mechanical Engineering,
Politecnico di Milano,
Milan 20156, Italy
e-mail: monica.bordegoni@polimi.it

1Corresponding author.

Contributed by the Computers and Information Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received January 2, 2018; final manuscript received April 26, 2018; published online July 3, 2018. Assoc. Editor: Charlie C. L. Wang.

J. Comput. Inf. Sci. Eng 18(4), 040801 (Jul 03, 2018) (16 pages) Paper No: JCISE-18-1004; doi: 10.1115/1.4040131 History: Received January 02, 2018; Revised April 26, 2018

This review focuses on the design process of additively manufactured mesoscale lattice structures (MSLSs). They are arrays of three-dimensional (3D) printed trussed unit cells, whose dimensions span from 0.1 to 10.0 mm. This study intends to detail the phases of the MSLSs design process (with a particular focus on MSLSs whose unit cells are made up of a network of struts and nodes), proposing an integrated and holistic view of it, which is currently lacking in the literature. It aims at guiding designers' decisions with respect to the settled functional requirements and the manufacturing constraints. It also aims to provide an overview for software developers and researchers concerning the design approaches and strategies currently available. A further objective of this review is to stimulate researchers in exploring new MSLSs functionalities, consciously considering the impact of each design phase on the whole process, and on the manufactured product.

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Gladman, A. S. , Matsumoto, E. A. , Nuzzo, R. G. , Mahadevan, L. , and Lewis, J. A. , 2016, “ Biomimetic 4D Printing,” Nat. Mater., 15(4), pp. 413–418. [CrossRef] [PubMed]
Meisel, N. A. , Elliott, A. M. , and Williams, C. B. , 2015, “ A Procedure for Creating Actuated Joints Via Embedding Shape Memory Alloys in Polyjet 3D Printing,” J. Intell. Mater. Syst. Struct., 26(12), pp. 1498–1512. [CrossRef]
Wagner, M. , Chen, T. , and Shea, K. , 2017, “ Large Shape Transforming 4D Auxetic Structures,” 3D Printing Addit. Manuf., 4(3), pp. 133–142. [CrossRef]
Truby, R. L. , and Lewis, J. A. , 2016, “ Printing Soft Matter in Three Dimensions,” Nature, 540(7633), pp. 371–378. [CrossRef] [PubMed]
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Figures

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Fig. 1

The concept of lattice applied to different dimensional scales: structures defining the atoms arrangement in the microscale; structures of cellular materials in the mesoscale; specific architectural structures in the macroscale

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Fig. 2

Cellular structures can be divided into stochastic and nonstochastic ones. Both the arrangement as well as the geometry of the unit cells of 2D and 3D nonstochastic structures can be designed. This paper is focused on the design process of 3D strut-and-node based lattice structures. This type of cellular structure is highlighted in the image. This figure is inspired by Tao and Leu [4], while the TPMS structure has been modeled using the software, developed at the University of Nottingham, mentioned in Ref. [14].

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Fig. 3

The MSLSs design workflow. Starting from the available design space and the functional targets to be reached, the design process is then structured into five main phases. During these phases manufacturing constraints will also be taken into account to guarantee the printability of the structure.

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Fig. 4

Two examples of unit cells: a TPMS (cell modeled using the software, developed at the University of Nottingham, mentioned in Ref. [14]) and a 3D strut-and-node based cell

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Fig. 5

The qualitative stress/strain curves of stretch-dominated and bending-dominated unit cells. The stress/strain curve of stretch-dominated unit cells is characterized by high stiffness and high initial strength, followed by postyield softening. The stress/strain curve of bending-dominated unit cells is characterized by a lower stiffness, a lower initial strength and a large deformation at relatively low and constant stress (plateau stress). The last part of both curves shows the densification phase, that is the moment when the struts merge. The image is inspired by the work [1].

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Fig. 6

Maxwell's Criterion (see Eq. (2)). The unit cell on the left has M < 0: it is bending-dominated (nodes are all locked). The unit cell in the center has M = 0: it is stretch-dominated. Adding a further strut to this cell will make M > 0. In this case, if nodes are unlocked there is a state of self-stress: the struts carry stress also if no external loads are applied. If nodes are locked, the cell is still stretch-dominated and can be manufactured using AM technologies. Figure inspired by Ashby [1].

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Fig. 7

Unit cell optimization according to six loading conditions (xx, yy, zz, yz, xy, xz). Considering, as design requirements, the stiffness and the strength as well as the loading conditions, the unit cell is optimized through a proper strut positioning for each loading condition. The combined results lead to the final cell developed and optimized in all directions. Figure inspired by Nguyen et al. [3].

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Fig. 8

The aspect ratio of a BCC unit cell. When W and, thus, the aspect ratio (W/H) decreases, the unit cell shows higher stiffness and yield stress. In particular, the amplitude of the angles between the struts changes. The amplitude of the angles at the bottom, and at the top of the unit cell, decreases while, for the angles at the sides (α) of the unit cell, the amplitude increases. This figure is used to summarize some considerations provided in Ref. [34].

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Fig. 9

The total area moment of inertia values (I) of the cells about centroid coordinate axes. The figure shows how three different geometric configurations of unit cells, having the same W, H, and D values (respectively 10 mm, 10 mm, and 1 mm), but a different struts number and arrangement, have different I values.

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Fig. 10

The figure shows the deviation between the thickness of the virtual model of the struts and the additively manufactured ones (dashed lines) as discussed in Ref. [20]: both for horizontal and sloped struts such deviation is related to the change of the D value. For horizontal struts, this value can vary between tmax and tmin. For sloped struts the cross section is no more a circle but it can vary between ta and tb. This figure has been inspired by the work [20].

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Fig. 11

The uniform population is based on a periodic unit cell distribution. The figure shows how all unit cells have the same shape and dimensions. Dashed lines are used to highlight that the unit cells integrity, at the boundary, is accidental.

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Fig. 12

The conformal population is based on a distribution of the unit cells that is conformal to the boundaries of the design space. The figure shows that the unit cells do not have the same shape and dimensions. The dashed lines and the box highlight that they are fully conformal to the boundaries and their integrity is preserved.

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Fig. 13

The figure shows the application of a heterogeneous gradient through the use of a gray scale image that is overlaid to a uniform lattice structure. The darker areas have a higher relative density (through the struts thickening), while the clearer ones have a lower relative density. Both the uniform and graded structures were modeled using the software, developed at the University of Nottingham, mentioned in Ref. [14].

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Fig. 15

The figure shows how shear bands (dashed lines) can occur when an array of unit cells less regular, like BCC-Z with the characteristic vertical strut in the middle, is loaded (see also Fig. 14). In these cases, a simulation performed on a single unit cell can be not sufficient to get information on the deformability of a lattice structure. This image has been inspired by the work [34].

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Fig. 14

The figure shows the model that has been used in Ref. [34] for performing a FEA on BCC and BCC-Z unit cells. The solid model is based on the use of struts wholly straight and with a constant diameter. A compression test is simulated applying the same loading conditions on the planar face at the top of each unit cell and using a rigid plate to crush the same unit cells progressively.

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