Mechanical stabilities of silicene

The mechanical stabilities of planar (g) and low-buckled (b) honeycomb monolayer structures of silicon under various large strains are investigated using density functional theory (DFT). The mechanical properties, including the ultimate stresses, ultimate strains, and high order elastic constants of silicene are predicted, as well as the structure evolutions. Both g-Si and b-Si can sustain large strains (eta >= 0.15) for armchair, zigzag, and biaxial deformation. The third, fourth, and fifth order elastic constants are indispensable for accurate modeling of the mechanical properties under strains larger than 0.03, 0.06, and 0.08 respectively. The second order elastic constants, including in-plane stiffness, are predicted to monotonically increase with pressure while the Poisson ratio monotonically decreases with increasing pressure. Our results on the positive ultimate strengths and strains, second order elastic constants, and the in-plane Young's modulus indicate that both g-Si and b-Si are mechanically stable.