A practical algorithm for the design of multiple-sized porous scaffolds with triply periodic structures

Yibao Li, Qing Xia, Seungyoon Kang, Soobin Kwak, Junseok Kim

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


In this study, we present a practical volume-merging method for generating multiple-sized porous structures that exhibit geometries with triply periodic minimal surface (TPMS) lattice structures. The proposed method consists of three stages: (1) designing the physical models with a signed distance field, (2) performing a merging operation for the porous scaffolds, and (3) assembling different units into a composite structure. The significant advantages of the proposed algorithm can be summarized as follows: Our method is independent of the model shape; the designed structures maintain a smooth surface with a constant mean curvature, and the mathematical computational complexity is low. We can join two different-sized triply periodic minimal surface lattices in the radial direction, where the transition region is obtained by smooth interpolation between the two lattice structures with different cell sizes or types. However, constructing large-sized models is only conceptually possible due to computational cost and memory storage constraints. To overcome these limitations, we present a practical method that can efficiently assemble large-scaled models at a low computational cost. The proposed method is based on a Boolean union operation of basic units of TPMS. Thus, it is simple to generate large-scale three-dimensional multiple-sized porous volumes based on our proposed method, which can be applied to many applications in mechanical and electrical engineering. The produced multi-scale compound scaffolds have smooth surfaces without fractures, making them suitable for straightforward application in additive manufacturing. Several numerical tests are conducted to validate the efficiency of the proposed algorithm.

Original languageEnglish
Pages (from-to)481-495
Number of pages15
JournalMathematics and Computers in Simulation
Publication statusPublished - 2024 Jun

Bibliographical note

Publisher Copyright:
© 2024 International Association for Mathematics and Computers in Simulation (IMACS)


  • Implicit surfaces
  • Numerical design procedure
  • Porous scaffolds
  • Triply periodic minimal surfaces
  • Volume merging algorithm

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science
  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics


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