A first-principles study of the mechanical properties of g-GeC

•First time to predict the nonlinear elastic properties of g-GeC.•Up to fifth order elastic constants for a rigorous continuum description.•Prediction of the pressure-dependent second order elastic constants.•Pressure effect on velocities of sound waves and promising applications.

We investigate the mechanical properties of graphene-like hexagonal germanium carbide monolayers (g-GeC) using first-principles calculations based on density-functional theory. Compared to graphene, g-GeC is much softer, with 41% in-plane stiffness, 44%, 42% and 37% ultimate strengths in armchair, zigzag, and biaxial strains respectively, as well as smaller ultimate strains. However, g-GeC has a larger Poisson’s ratio, 0.28, about 1.5 times that of graphene. We obtained the second, third, fourth, and fifth order elastic constants for a rigorous continuum description of the elastic response of g-GeC. The second order elastic constants, including in-plane stiffness, are predicted to monotonically increase with pressure while the Poisson’s ratio monotonically decreases with increasing pressure. The sound velocity of a compressional wave has a minima at an in-plane pressure of −7 GPa while that of a shear wave monotonically with pressure.