Parametric design and evaluation of TPMS-like cellular solids

Abstract

Triply periodic minimal surfaces (TPMS) present a starting point for designing infinitely many novel cellular solids, creating the need for a structured approach to their design and evaluation. In this study the design space is formalised using a set of input parameters and evaluation metrics to provide a structured and reproducible approach to designing a TPMS-like cellular solids. Interactions between the design parameters and evaluation metrics are identified using a full-factorial design of experiments. From this the most impactful design parameters are identified as the TPMS equation, type of structure, and volume fraction. It was found that the gyroid-surface structure provided the most flexibility, with near-isotropic mechanical properties across a wide range of volume fractions, allowing the creation of reduced mass/stiffness designs without introducing anisotropy or variation in Poisson’s ratio. The volume fraction at which the connectivity of a structure changes, “pinch-off limits” are presented for six of the most commonly investigated TPMS-like cellular solids. Additionally, the effects of common transformations are presented including: examples of how phase-shift and/or rotation can be used to modify the features which intersect the free-boundary of a design; dimensional analysis which shows the practical effects changing unit cell size; and analysis showing the effect of rotating a cellular structure on both the mechanical properties and surface orientation. These computational studies are supported with a physical case study which demonstrates how several design parameters may be modified to change the manufacturability of a TPMS-like cellular solid.

Keywords

• Triply periodic minimal surfaces (TPMS)
• Cellular solids
• Additive manufacturing