Graded Minimal Surface Periodic Structures for Multiphysics Metamaterial Applications

Abstract The continuous progress of additive manufacturing techniques has enabled engineers and designers to build complex geometries at various length scales with minimal setup time, reduced need for skilled labor, and minimal material waste. One important subset of structures endowed with complex geometrical features is formed by periodic and non-periodic metamaterials that enable engineering applications where certain combinations of performance features are desirable. For example, these structures could be used in naval engineering applications where light-weight, large surface area, energy absorption, heat dissipation, and acoustic bandgaps are critical. Nevertheless, to deploy these complex geometry structures, their multiphysics response must be well understood and characterized. The current effort aims to describe an initial approach for designing and deploying graded triply periodic minimal surface (TPMS) architectures. The work focuses on three TPMS systems: (a) Neovius, (b) Schoen’s gyroid, and (c) Schoen’s F-RD made of Ti-6Al-4V alloy. These three geometries are enhanced using variable wall thickness to obtain the so-called graded TPMS. Three problems are explored: (1) evaluation of the elastic equivalent material properties of various unit cells with graded thickness; (2) investigation of acoustics dispersion properties of three cells and (3) a thermo-structural response of a complex geometry made of twelve graded representative volume elements (RVE). Finite element results of the relevant thermo-structural partial differential equations for the case of a gyroid triply periodic cylindrical sandwich structure are presented.