Evaluation of Cellular Solids Derived from Triply Periodic Minimal Surfaces

Abstract

Cellular solids are a class of materials that have many interesting engineering applications, including ultralight structural materials. The traditional method for analyzing these solids uses convex uniform polyhedral honeycombs to represent the geometry of the material, and this approach has carried over into the design of digital cellular solids. However, the use of such honeycomb-derived lattices makes the problem of decomposing a three-dimensional lattice into a library of two-dimensional parts non-trivial. We introduce a method for generating periodic frameworks from triply periodic minimal surfaces, which result in geometries that are easier to decompose into digital parts. Additionally, we perform finite element modelling of two cellular solids generated from two TPMS, the P- and D-Schwarz, and two cellular solids, the Kelvin and Octet honeycombs. We show that the simulated behavior of these TMPS-derived structures shows the expected modulus of the cellular solid scaling linearly with relative density, which matches the behavior of the highest-coordination honeycomb structure, the octet truss.