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Research Papers: Design for Manufacture and the Life Cycle

Design of Three-Dimensional, Triply Periodic Unit Cell Scaffold Structures for Additive Manufacturing

[+] Author and Article Information
Mazher Iqbal Mohammed

School of Engineering,
Deakin University,
75 Pigdons Road,
Waurn Ponds,
Geelong 3216, VIC, Australia
e-mail: Mazher.mohammed@deakin.edu.au

Ian Gibson

School of Engineering,
Deakin University,
75 Pigdons Road,
Waurn Ponds,
Geelong 3216, VIC, Australia
e-mail: ian.gibson@deakin.edu.au

1Corresponding author.

Contributed by the Design for Manufacturing Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 2, 2017; final manuscript received April 17, 2018; published online May 23, 2018. Assoc. Editor: Paul Witherell.

J. Mech. Des 140(7), 071701 (May 23, 2018) (10 pages) Paper No: MD-17-1093; doi: 10.1115/1.4040164 History: Received February 02, 2017; Revised April 17, 2018

Highly organized, porous architectures leverage the true potential of additive manufacturing (AM) as they can simply not be manufactured by any other means. However, their mainstream usage is being hindered by the traditional methodologies of design which are heavily mathematically orientated and do not allow ease of controlling geometrical attributes. In this study, we aim to address these limitations through a more design-driven approach and demonstrate how complex mathematical surfaces, such as triply periodic structures, can be used to generate unit cells and be applied to design scaffold structures in both regular and irregular volumes in addition to hybrid formats. We examine the conversion of several triply periodic mathematical surfaces into unit cell structures and use these to design scaffolds, which are subsequently manufactured using fused filament fabrication (FFF) additive manufacturing. We present techniques to convert these functions from a two-dimensional surface to three-dimensional (3D) unit cell, fine tune the porosity and surface area, and examine the nuances behind conversion into a scaffold structure suitable for 3D printing. It was found that there are constraints in the final size of unit cell that can be suitably translated through a wider structure while still allowing for repeatable printing, which ultimately restricts the attainable porosities and smallest printed feature size. We found this limit to be approximately three times the stated precision of the 3D printer used this study. Ultimately, this work provides guidance to designers/engineers creating porous structures, and findings could be useful in applications such as tissue engineering and product light-weighting.

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Figures

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Fig. 1

(a) Various unit cell renderings, comprising (i) Schwarz P surface, (ii) Schwarz D surface, (iii) Schoen I-WP surface, (iv) Schwarz P branching unit, (v) Schwarz D branching unit, and (vi) Schoen I-WP branching unit. (b) A table summarizing the mathematical formula and boundary conditions used to render the respective unit cell.

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Fig. 2

(a) Methodology for the construction of surface style unit cells, (b) methodology for the construction of branching style unit cells, (c) a table illustrating the baseline properties of the unit cells developed in this study, and (d) methodology for the construction of a given scaffold structure, highlighting the wrapping methodology by which the porosity can be adjusted

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Fig. 3

(a) Thickness color maps for (i) the Schoen branching style unit cell and (ii) the resulting scaffold of the Schoen branching unit cell. (b) Graphs illustrating the change in porosity increases scaffold thickness for (i) the surface style unit cells and (ii) the branching style unit cells. (c) Graphs illustrating the change in surface area resulting from the changes in the scaffold porosity for (i) the surface style unit cells and (ii) the branching style unit cells.

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Fig. 4

(a) (i) Design of a test standard tessellation language file to examine the print precision for structures of varying widths and heights where vertical lines are of widths a = 600 μm, b = 400 μm, c = 200 μm, d = 100 μm and heights 1 = 400 μm, 2 = 200 μm, and 3 = 100 μm. Each “star” structure comprises lines of equal width and height, as stated in the diagram. (ii) The resulting print of the test structure on the examined FFF 3D printer, highlighting structures that were not printed. (b) Three-dimensional height color maps of a (i) flat and (ii) straight raised printed section of the test structures. (c) A table summarizing the designed and printed geometrical features found on the test structure.

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Fig. 5

(a) (i) Scaffold thickness tests using the Schwarz Primitive surface based unit cell for wrap closing distances of 0.1 = 0.38 mm, 0.2 = 0.53 mm, and 0.3 = 0.67 mm thickness scaffolds. (ii) Print tests of the lower precision limit for scaffold pore size, comprising the Schwarz Diamond branching unit cell for a uniform x = y = z unit cell size of 1 mm (pore of 0.9 mm), 2 mm (pore of 1.3 mm), and 3 mm (pore of 1.95 mm). (b) Test example prints for the designed Schwarz P, Schwarz D, and Schoen I-WP scaffolds for a unit cell size of 10 mm, within a cylinder of radius 25 mm, height 30 mm, and a wrap gap closing distance of 0.5.

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Fig. 6

(a) An example of a hybrid scaffold comprising a superimposed 2 × 2 and 3 × 3 unit cell derived cylindrical scaffold. (b) (i) CT scan image of a patients upper body, with the highlighted region of the bone in the arms and (ii) digital model of the extracted humerus, the segmented humerus with integrated anatomy specific scaffolds and the resulting 3D printed model of the scaffolds and bone.

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