Evaluation of Cellular Solids Derived from Triply Periodic Minimal Surfaces

TL;DR

This paper introduces a new method for generating cellular solids from triply periodic minimal surfaces, simplifying digital decomposition and demonstrating their mechanical properties through finite element analysis.

Contribution

It presents a novel approach to create cellular structures from TPMS that are easier to decompose and analyze, expanding design options beyond traditional honeycombs.

Findings

TPMS-derived structures exhibit linear modulus scaling with relative density

Finite element simulations confirm comparable behavior to octet truss structures

New frameworks facilitate digital decomposition of complex cellular geometries

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.