Topological Control of Triply Periodic Minimal Surfaces for Thermal Design and Advanced Manufacturing: A Gyroid Case Study

Abstract

Recently, triply periodic minimal surfaces have seen tremendous interest in the design of compact process engineering components. Benefits of high surface area per unit volume, modular form, and inherent periodicity provide a holistic self-supporting network and flow-conducive features. Applications of importance pertain to thermal power management, biomimetic scaffolds and structures, and feasibility of advanced manufacturing. This study presents a novel approach to the manipulation of the characteristic Schwarz-G, or ‘gyroid’ triply periodic minimal surface, for thermal design in the context of advanced manufacturing. The study presents relationships between design parameters and resulting surface area as a target response using the characteristic equation of a gyroid. Through parametric control, an approach to induce asymmetry in a gyroid is presented. Then, the characteristic equation is manipulated to produce a 20-fold increase in achievable area over a baseline design characteristic of 25.4 mm through controlled combinations of design parameters. A second relationship is presented as a function of the maximum area achieved and manipulated design parameters. Through the analysis, the study presents a framework to identify and maximize the achievable area of triply periodic minimal surfaces for advanced manufacturing and thermal management applications.