Porous three-dimensional scaffold generation for 3D printing

Chaeyoung Lee, Darae Jeong, Sungha Yoon, Junseok Kim

    Research output: Contribution to journalArticlepeer-review

    8 Citations (Scopus)

    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 transformis used to speed up the computation. A newlocal 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.

    Original languageEnglish
    Article number946
    JournalMathematics
    Volume8
    Issue number6
    DOIs
    Publication statusPublished - 2020 Jun 1

    Bibliographical note

    Funding Information:
    The first author (C.L.) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2019R1A6A3A13094308). The author (D.J.) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2017R1E1A1A03070953). The corresponding author (J.K.) expresses thanks for the support from the BK21 PLUS program. The authors thank the editor and the reviewers for their constructive and helpful comments on the revision of this article.

    Publisher Copyright:
    © 2020 by the authors.

    Keywords

    • 3D printing
    • Diblock copolymer
    • Nonlocal Cahn-Hilliard equation
    • Porous structure

    ASJC Scopus subject areas

    • General Mathematics

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