Recent progress of simulations/modeling at the atomic level has led to a better understanding of the mechanical behaviors of graphene, which include the linear elastic modulus E, the nonlinear elastic modulus D, the Poisson’s ratio ν, the intrinsic strength σ_int and the corresponding strain ε_int as well as the ultimate strain ε_max (the fracture strain beyond which the graphene lattice will be unstable). Due to the two-dimensional geometric characteristic, the in-plane tensile response and the free-standing indentation response of graphene are the focal points in this review. The studies are based on multiscale levels: including quantum mechanical and classical molecular dynamics simulations, and parallel continuum models. The numerical studies offer useful links between scientific research with engineering application, which may help to fulfill graphene potential applications such as nano sensors, nanotransistors, and other nanodevices.

Using molecular dynamics (MD) simulations, a new approach based on the behavior of pressurized water out of a nanopore (1.3–2.7 nm) in a flat plate is developed to calculate the relationship between the water surface curvature and the pressure difference across water surface. It is found that the water surface curvature is inversely proportional to the pressure difference across surface at nanoscale and this relationship will be effective for different pore size, temperature and even for electrolyte solutions. Based on the present results, we cannot only effectively determine the surface tension of water and the effects of temperature or electrolyte ions on the surface tension, but also show that the Young-Laplace (Y-L) equation is valid at nanoscale. In addition, the contact angle of water with the hydrophilic material can be further calculated by the relationship between the critical instable pressure of water surface (burst pressure) and nanopore size. Combining with the infiltration behavior of water into hydrophobic microchannels, the contact angle of water at nanoscale can be more accurately determined by measuring the critical pressure causing the instability of water surface, based on which the uncertainty of measuring the contact angle of water at nanoscale is highly reduced.

The bending buckling behaviors of single-walled carbon nanotubes (SWCNTs) are systematically investigated by using both molecular dynamics (MD) simulation and finite element method (FEM), to analyze the relationships between critical bending buckling curvature, critical buckling strain and nanotube geometry parameters (e.g., tube diameter, length and chirality). The postbuckling shape of SWCNT and the effect of loading boundary conditions are also discussed. The comparison between MD and FEM simulations shows that the continuum shell model provides some useful insights into the bending buckling mechanisms, yet it cannot quantitatively reproduce the bending buckling behavior of SWCNTs, since the continuum model does not account for the geometrical imperfections in the atomic system that are critical to the onset of buckling. Improvements of continuum models are suggested based on the findings.

Based on the benchmark created by the first principle calculations, the effectiveness of different empirical potential functions, including CVFF1, CVFF2, SW and REBO potentials, on describing the mechanical behavior of single layer MoS ₂ (SLMoS ₂ ) are evaluated. The mechanical properties including the elastic modulus E , Poisson’s ratio ν , nonlinear elastic modulus D , failure stress and ultimate strain are considered. It is found that under a small deformation, the REBO and CVFF2 potentials can provide an effective description of the elastic behavior of SLMoS ₂ ; whereas under a large deformation, the SW potential gives a more accurate stress value and the CVFF2 potential can only predict the right value under biaxial tension. After modifying the cut-off distances in the REBO potential, the failure strain can be reasonably predicted by the REBO potential; whereas the failure stress will be overestimated by about 20–40% for biaxial and uniaxial tension. The present study can provide help on accurately understanding the mechanical behavior of SLMoS ₂ .