▎ 摘　　要

The mechanics of triply periodic minimal surfaces (TPMSs) with three-dimensional (3D) graphene foams are systematically studied to understand the effects of structure and size on the mechanical properties, for example, elasticity, strength, and fracture. The design of lightweight open-shell porous solid materials with TPMSs has shown excellent and tunable load-bearing properties. However, fracture properties and their relations with surface topologies are largely unknown. Utilizing reactive molecular dynamics simulations, here we investigate the elastic and fracture properties of three different surface topologies with 3D graphene foams: P (primitive), D (diamond), and G (gyroid), called Schwarzites. Models with different lattice sizes are utilized to derive power laws, which can connect the properties along different sizes to shed light on the multiscale mechanics of TPMSs. Our study provides a systematic understanding of the relation between TPMS topologies and their mechanical properties, including failure mechanisms of graphene foams, opening opportunities to explore designable structures with tailored properties.