Porous Three-Dimensional Scaffold Generation for 3D Printing

Chaeyoung Lee, Darae Jeong, Sungha Yoon and Junseok Kim
Additional contact information
Chaeyoung Lee: Department of Mathematics, Korea University, Seoul 02841, Korea
Darae Jeong: Department of Mathematics, Kangwon National University, Gangwon-do 24341, Korea
Sungha Yoon: Department of Mathematics, Korea University, Seoul 02841, Korea
Junseok Kim: Department of Mathematics, Korea University, Seoul 02841, Korea

Mathematics, 2020, vol. 8, issue 6, 1-15

Abstract: In this paper, we present an efficient numerical method for arbitrary shaped porous structure generation for 3D printing. A phase-field model is employed for modeling phase separation phenomena of diblock copolymers based on the three-dimensional nonlocal Cahn–Hilliard (CH) equation. The nonlocal CH equation is a fourth-order nonlinear partial differential equation. To efficiently solve the governing equation, an unconditionally gradient stable convex splitting method for temporal discretization with a Fourier spectral method for the spatial discretization is adopted. The standard fast Fourier transform is used to speed up the computation. A new local average concentration function is introduced to the original nonlocal CH equation so that we can locally control the morphology of the structure. The proposed algorithm is simple to implement and complex shaped structures can also be implemented with corresponding signed distance fields. Various numerical tests are performed on simple and complex structures. The computational results demonstrate that the proposed method is efficient to generate irregular porous structures for 3D printing.

Keywords: 3D printing; diblock copolymer; porous structure; nonlocal Cahn–Hilliard equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/6/946/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/6/946/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:6:p:946-:d:369015

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().