An atomistic-based finite element progressive fracture model for silicene nanosheets

A progressive finite element method is proposed herein to investigate the fracture of silicene nanosheets. By treating a silicene nanosheet as a buckled frame structure, its mechanical behavior is simulated using the modified Morse potential function. The interatomic force per atom is calculated for all atoms as a set of inharmonic oscillator networks, which are described by the modified Morse potential function, while the nonlinear behavior is defined by these interatomic forces with an iterative solution procedure as strain increases. The nonlinear stress–strain relationships of the armchair and zigzag silicene nanosheets are also obtained for pristine and defective cases including the tensile strength and ultimate strain. For the silicene with both configurations, i.e., armchair and zigzag, a sudden drop is seen in the stress–strain diagram, showing that both of them represent the brittle behavior. Moreover, it is concluded that the tensile strength and ultimate strain of the armchair silicenes are slightly larger than those of the zigzag one. It is also seen that the mechanical properties of the silicene are significantly affected by the single-vacancy and Stone–Wales defects. The computed results reveal that single-vacancy defects can reduce the ultimate strain of silicene by approximately 7.3% with respect to that of pristine silicene, whereas the effect of Stone–Wales defects is less significant.