Porous Three-Dimensional Scaffold Generation for 3D Printing

• Published in: Mathematics (Basel) Vol. 8; no. 6; p. 946
• Main Authors: Lee, Chaeyoung, Jeong, Darae, Yoon, Sungha, Kim, Junseok
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.06.2020
• Subjects: 3-D printers; 3D printing; Algorithms; Block copolymers; Bones; diblock copolymer; Discretization; Experiments; Fast Fourier transformations; Fourier transforms; Mathematical models; Mathematics; Methods; Morphology; Nonlinear differential equations; nonlocal Cahn–Hilliard equation; Numerical methods; Partial differential equations; Permeability; Phase separation; porous structure; Spectral methods; Three dimensional models; Three dimensional printing; Tissue engineering
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math8060946

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.