Prediction of the nonlocal scaling parameter for graphene sheet

A nonlocal model considering the nonlocal stress as the weighted average stress, which incorporates information about small size scale, is presented. With this model, the explicit expression of the nonlocal scaling parameter is derived and the implication of the nonlocal scaling parameter is revealed. Moreover, exact closed form solutions for the nonlocal scaling parameter for zigzag and armchair graphene sheets are obtained and verified by molecular dynamics simulations. Nonlocal scaling parameter is not a constant but a scale-related variable dependent on the size of the structures and independent of the value of the loads.