Size-dependent non-linear mechanical properties of graphene nanoribbons

An atomistic, spring-based, non-linear finite element method is implemented in order to predict the non-linear mechanical behavior of graphene nanoribbons. According this method, appropriate non-linear springs are utilized to simulate each interatomic interaction. Their force–displacement curve follows the relation between the first differentiation of the potential energy of the corresponding interaction-bond deformation. The potential which corresponds to the bond angle variation is simulated by a torsional spring, while the bond stretching is simulated by a uniaxial compression/extension spring. The linear approximation, commonly made in the literature for the bond angle bending interaction, is not followed here and thus the overall non-linear response of the specific interaction is accurately introduced into the model. Following the proposed formulation, the tensile uniaxial stress–strain behavior for various graphene nanoribbons, of zigzag as well as armchair orientation, arise. The results demonstrate that the linear and non-linear mechanical properties are strongly dependent on the structure as well as on the size of the graphene strip tested.