Soap film inspired mechanical metamaterials approaching theoretical bound of stiffness across full density range

Structural mechanical metamaterials, with their mass-efficient architectures and unprecedented mechanical properties, are in critical demand for high-performance applications. However, finding the optimal 3D geometries towards a particular property, such as reaching the stiffness upper bound, usually demands high volume of calculations or numerical optimizations. Here we generate structured mechanical metamaterials by imitating the natural occupation of periodic volume by inflated soap films. Our strategy of occupying volume between two periodic constant mean curvature (CMC) surfaces generates a series of mechanical metamaterials of varied relative densities ranging from 0 to 1. The mechanically isotropic ISO-CMC structures exhibit bulk moduli over 94% of the theoretical limit. Using finite element models, we reveal the fundamental mechanical behaviors of the structures that lead to ideal performances. These phenomena are found to be in close relation to the curvature-driven design of our metamaterial structures. These structures are compared to other reported mechanical metamaterials, such as closed-cell plate structures and triply periodic minimal surface (TPMS) structures. The unique curvature-driven thickening strategy of our method renders structures that outperform their peers in terms of bulk moduli and relative density coverage. The CMC structures present a new class of easily 3D printable, permeable and stiff mechanical metamaterials. The design methodology also could serve in future development of novel mechanical metamaterials powered by advanced computational tools.