Abnormal nonlocal scale effect on static bending of single-layer MoS 2 .

The nonlocal scale parameter of nonlocal Euler-Bernoulli beam theory is evaluated for the static bending of single-layer molybdenum disulfide (SLMoS2 ) without predetermined bending rigidity. The evaluation is performed by matching the fitted curve between the maximum deflection and the beam length obtained from molecular mechanics simulations. It was observed that the fitted curves have an abnormal sign in the second-order term of the maximum deflection for SLMoS2 , opposite to that for graphene and regardless of the interatomic interaction potentials used. Based on the nature of 'nonlocal' and the phenomenological point of view, a modified nonlocal constitutive relation with a positive sign in front of the higher-order term is suggested for SLMoS2 . The nonlocal parameter and the bending rigidity of SLMoS2 are finally extracted, and the effect of the nonlocal scale parameter on the bending response for SLMoS2 is found to be significant for beam length less than a critical length, depending on both the interatomic interaction potentials and the boundary conditions. Our new perspective should be useful for researchers who are interested in the engineering application of graphene-like quasi-two-dimensional nanostructures using nonlocal beam theories.