Mechanical properties of 3D graphene metamaterials with primitive three-period minimal surface

Three-dimensional graphene metamaterials based on triply periodic minimal surfaces (TPMS) can achieve exceptional mechanical properties; however, the P-type Schwarz Primitive surface remains largely underexplored. For the first time, we quantified how unit cell size (30 Å, 45 Å, 60 Å), architectural dimensionality (0D, 1D, 2D), and tensile strain rate govern the uniaxial strength and fracture strain of pure carbon P-type multidimensional structures. Reactive molecular dynamics simulations reveal that both strength and fracture strain increase significantly as the unit cell size decreases. Furthermore, these structures exhibit distinct mechanical responses depending on their dimensionality, demonstrating a pronounced size effect. Additionally, strain rate plays a critical role: moderate strain rates facilitate atomic rearrangement and the formation of truss-like load-bearing networks, thereby enhancing load-bearing capacity. These findings establish clear structure-property relationships for scalable, ultralight carbon nano-architectures.

All atomistic tensile tests were performed with LAMMPS using the AIREBO potential to describe C-C interactions. P-type Schwarz Primitive surfaces were generated with an in-house protocol that hexagonalizes a Delaunay triangulation without Voronoi tessellation. After energy minimization and 50 ps NVT equilibration at 300 K with a Nosé-Hoover thermostat, uniaxial tension was applied in strain-control mode while the lateral cell faces remained traction-free. Stress-strain curves and atomic fracture sequences were analyzed with OVITO.