Graphene characterization: A fully non-linear spring-based finite element prediction

In the present study, a spring-based finite element model is formulated and utilized to predict the stress–strain behavior of single-layer graphene. Generalized force–generalized displacement behavior of the developed nonlinear springs follows the relation between the first derivative of the potential energy and the corresponding bond deformation, describing interatomic interactions. A number of different loading cases are examined in order to predict mechanical properties and characterize the graphene sheet. Predicted Young's and shear moduli, tensile and shear strength, tensile and shear failure strain, etc., under tension, compression and pure shear, are compared to results found in the literature, which are based on numerical, analytical or experimental methodologies. In all the above loading cases the graphene sheet is examined as a virtually orthotropic material, exhibiting different material properties in the armchair and zigzag directions. Different behaviors in tension and compression, as suggested by the modified Morse atomic bond stretching potential, are illustrated by the predicted stress–strain curves.