Decoupling minimal surface metamaterial properties through multi-material hyperbolic tilings.

Rapid advances in additive manufacturing over the past decade have kindled widespread interest in the rational design of metamaterials with unique properties. However, many applications require multi-physics metamaterials, where multiple properties are simultaneously optimized. This is challenging, since different properties, such as mechanical and mass transport properties, typically impose competing requirements on the nano-/micro-/meso-architecture of metamaterials. Here, we propose a parametric metamaterial design strategy that enables independent tuning of the effective permeability and elastic properties. We apply hyperbolic tiling theory to devise simple templates based on which triply periodic minimal surfaces (TPMS) are partitioned into hard and soft regions. Through computational analyses, we demonstrate how the decoration of hard, soft, and void phases within the TPMS substantially enhances their permeability-elasticity property space and offers high tunability in the elastic properties and anisotropy, at constant permeability. We also show that this permeability-elasticity balance is well captured using simple scaling laws. We then proceed to demonstrate the proposed concept through multi-material additive manufacturing of representative specimens. Our approach, which is generalizable to other designs, offers a route towards multi-physics metamaterials that need to simultaneously carry a load and enable mass transport, such as load-bearing heat exchangers or architected tissue-substituting meta-biomaterials.