In the present study, potential of finite element based molecular
structural mechanics (MSM) for evaluating stress concentration factor of
single-layered graphene sheets (SLGSs) with elliptical vacancies is
successfully addressed. The MSM approach mimics the interatomic
forces of the nanostructure by defining an equivalent frame structure
containing beam elements. To obtain the mechanical and cross sectional
properties of the equivalent beam, the potential energies of chemical
bonds between carbon atoms in the hexagonal lattice of SLGSs are
equaled to the strain energies of the beams. This novel proposed
approach accurately predicts the stress concentration in graphene sheets
with significantly less computational effort in comparison to
computational physics methods. Both armchair and zigzag configurations
are considered. Furthermore, a comparison between the results obtained
by presented MSM approach and theory of elasticity for thin infinite
panels having elliptical holes is presented. Influence of chirality, and
geometry of elliptical vacancies are investigated in details. Results reveal
that MSM approach can successfully predicts stress concentration factor
phenomena in nano structures, especially SLGSs. It is seen that chirality
has a significant effect on the stress concentration factor so that armchair
SLGSs show a larger value of stress concentration.