# Comparative Torsional Properties via Numerical Simulation of Triply Periodic Minimal Surfaces (TPMS): Diamond, Gyroid and Primitive Structures

## TL;DR

This paper compares torsion properties of three TPMS structures using simulations, finding that Primitive structures perform best under certain conditions.

## Contribution

The study provides new insights into torsional behavior of Diamond, Gyroid, and Primitive TPMS structures using finite element simulations.

## Key findings

- Primitive structures with 15 mm and 20 mm unit cell sizes showed 1.5–2 times higher shear modulus and 1.5–3 times higher shear yield stress than 10 mm unit cells.
- Shear modulus and shear yield stress increased with relative density for Diamond and Gyroid structures but decreased for Primitive structures with larger unit cells.
- Unit cell size had a significant effect on Primitive structures but not on Diamond or Gyroid structures.

## Abstract

This work examines the simulation-based torsion properties of TPMS structures. Although TPMS structures are gaining more interest in research and potential practical applications, their torsion properties are not widely studied. In this work, sheet-based Diamond, Gyroid, and Primitive TPMS structures are analyzed numerically using the finite element method. The samples have a diameter of 20 mm and a length of 40 mm. Relative densities are 30%, 50%, and 70%, while unit cell sizes are 10 mm, 15 mm, and 20 mm. Cell geometry did not significantly affect the properties for samples with a 10 mm unit cell size. For other unit cell sizes, the shear modulus and shear yield stress were 1.5–4 times higher for the Primitive structure than for other geometries. With increasing relative density, the shear modulus and shear yield stress increased by 1.5–2 times for the Diamond and Gyroid structures, as well as for the Primitive structure with a 10 mm unit cell size. The Primitive structure with 15 mm and 20 mm unit cell sizes showed a decrease in properties with increasing relative density. Regarding the effect of unit cell size, the shear modulus and shear yield stress showed insignificant differences for the Diamond and Gyroid structures, while the Primitive structure showed dependence on unit cell size. Samples with a 15 mm unit cell size had 1.5–2 times higher shear modulus and 1.5–3 times higher shear yield stress than samples with a 10 mm unit cell size. Samples with a 20 mm unit cell size exhibited slightly lower shear modulus and shear yield stress than those with 15 mm unit cells.