Porous three-dimensional scaffold generation for 3D printing

Chaeyoung Lee; Darae Jeong; Sungha Yoon; Junseok Kim

doi:10.3390/math8060946

Porous three-dimensional scaffold generation for 3D printing

Chaeyoung Lee, Darae Jeong, Sungha Yoon, Junseok Kim

Research output: Contribution to journal › Article › peer-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 language	English
Article number	946
Journal	Mathematics
Volume	8
Issue number	6
DOIs	https://doi.org/10.3390/math8060946
Publication status	Published - 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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10.3390/math8060946

Cite this

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title = "Porous three-dimensional scaffold generation for 3D printing",

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.",

keywords = "3D printing, Diblock copolymer, Nonlocal Cahn-Hilliard equation, Porous structure",

author = "Chaeyoung Lee and Darae Jeong and Sungha Yoon and Junseok Kim",

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: {\textcopyright} 2020 by the authors.",

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doi = "10.3390/math8060946",

language = "English",

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AU - Lee, Chaeyoung

AU - Jeong, Darae

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N1 - 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.

PY - 2020/6/1

Y1 - 2020/6/1

N2 - 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.

AB - 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.

KW - 3D printing

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KW - Nonlocal Cahn-Hilliard equation

KW - Porous structure

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JO - Mathematics

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ER -

Porous three-dimensional scaffold generation for 3D printing

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Bibliographical note

Keywords

ASJC Scopus subject areas

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