Shape optimization of additively manufactured lattices based on triply periodic minimal surfaces

Research output: Contribution to journalResearch articleContributedpeer-review



Additively manufactured lattice structures based on triply periodic minimal surfaces (TPMS) offer desirable structure–property relationships for seminal industries such as bone tissue engineering. However, increasingly complex morphologies raise the question of their integrity. Structural optimization can be a powerful design tool, but preserving biomimetic TPMS mesostructure remains a challenge, as conventional shape optimization techniques are limited to strut-based cell designs. Therefore, the present study focuses on shape optimization of promising TPMS based bone substitutes. Here, various load cases relevant to implant applications are numerically considered, including compression, compression–shear and shear. Optimized lattices are manufactured using laser powder bed fusion from the beta-type Ti-42Nb alloy and tested under compression. The results indicate significant potential for coupling TPMS lattices and shape optimization in the context of additive manufacturing. Specifically, stiffness increases of up to 80% and strength increases of up to 61% are experimentally demonstrated, while maintaining the inherent TPMS morphology. Therefore, the presented shape optimization procedure could be a key factor to exploit the combination of biocompatible Ti-42Nb alloy and TPMS based biomimetic design for future implant applications.


Original languageEnglish
Article number103659
Number of pages9
JournalAdditive Manufacturing
Publication statusPublished - 5 Jul 2023

External IDs

ORCID /0000-0002-0584-0565/work/161116681
ORCID /0000-0003-3358-1545/work/161407664



  • Additive manufacturing, Bone tissue engineering, Lattice structures, Shape optimization, Triply periodic minimal surfaces