The fracture toughness of Schwarz Primitive triply periodic minimal surface lattice

Abdulla Almomani, Abdel Hamid I. Mourad

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Triply periodic minimal surface (TPMS) lattices have recently been shown to exhibit extraordinarily low densities and multi-functionalities. Nevertheless, the dependence of their fracture toughness KIc on relative density ρ¯, unit cell size l and the number of unit cells ahead of the crack tip suggest a lack of understanding of the governing parameters. This also extends to the adequacy of using the current conventional fracture testing protocols. Therefore, the objective of this work is threefold: (i) extract the minimum Schwarz Primitive unit cells for accurate toughness measurement, (ii) estimate KIc of polylactic acid Schwarz Primitive TPMS applying linear elastic fracture mechanics (LEFM) conditions, (iii) investigate the effect of relative density ρ¯ and unit cell size l on the fracture toughness. With 18 cells along the specimen width, KIc is shown to increase linearly with ρ¯ and with the square root of l. Outcomes from this work is aimed toward understanding the damage tolerance of TPMS lattices, and hence the reliability of such new emerging lightweight materials.

Original languageEnglish
Article number103924
JournalTheoretical and Applied Fracture Mechanics
Publication statusPublished - Jun 2023


  • Fracture toughness
  • Lattice structures
  • Metamaterials
  • Triply periodic minimal surface lattice

ASJC Scopus subject areas

  • General Materials Science
  • Condensed Matter Physics
  • Mechanical Engineering
  • Applied Mathematics


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