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This paper compares simple interatomic potentials for carbon nanostructures with hexagonal lattice, by investigating the in-plane and the out-of-plane tensile behaviour of single-layer graphene sheets. Attention is given both to potentials already considered in the literature and to a new one, which we call the damped DREIDING potential, in which damping functions are added to the DREIDING potential. For each potential, a calibration of its parameters and a focus on its performance are carried out in the in-plane context, by comparison with ab initio results of the rigidities and of the tensile limit properties, under periodic conditions. In addition, the damped DREIDING potential is used to perform in-plane tensile tests on both pristine and perforated single-layer graphene sheets of finite size. In the out-of-plane context, the calibration from ab initio results is only possible with reference to the rigidity. For the damped DREIDING potential, a sensitivity analysis, applied to a nanoindentation problem, on a pristine single-layer graphene sheet of finite size is provided. In doing so, a narrow range of value of the force needed to remove an atom from a sheet is given.

This paper deals with a numerical model for the buckling and post-buckling analysis of single-wall carbon nanotubes. Reasons of efficiency lead to the choice of a simple molecular statics model, wherein binary, ternary and quaternary atomic interactions are accounted for and described using Morse and cosine potential functions. The equations of the model are discussed in depth and the parameters of the potential functions are justified in the light of a comparison with ab-initio results. Several case studies regarding zigzag and armchair tubes of different aspect ratios, under compression, bending and torsion, are addressed with the aim of investigating the efficacy of the model and the role of the quaternary interactions, in contexts of both global and local behaviours.

The paper presents a study of defect-free achiral single-wall CNTs starting from a simple and effective molecular mechanics model (stick-and-spring), accounting for binary and ternary interactions at the atomic scale. The analytical expressions of the elastic constants related to the membrane behaviour of a Donnell thin shell are derived exploiting proper discrete homogenization tools and the results are compared with those of numerical analyses of the tubes under tensile, radial and torsional loads. By the analysis of the results, size and small scale effects are clearly highlighted and a discussion about their relevance is carried out.

The tensile behaviour and the pure shear behaviour of pristine and perforated single-layer graphene sheets are numerically investigated through a stick-and-spring model including both material and geometric non-linearities. The model is formulated in finite kinematics and the atomic interactions are modelled through the modified Morse potential, tuned with an improved set of parameters. The progression of the failure process of the sheets is numerically reconstructed using the arc-length strategy. The failure profiles are displayed and discussed. A continualization of the obtained results is made. The engineering strains and stresses and the second Piola and Green–Lagrange tensors are computed and compared with results given in the literature.

The paper presents a nonlinear buckling analysis of single-layer graphene sheets using a molecular mechanics model which accounts for binary, ternary and quaternary interactions between the atoms. They are described using a geometrically exact setting and by the introduction of Morse and cosine potential functions, equipped with an appropriate set of parameters. We examine the critical and post-critical behaviours of graphene, under compression in the zigzag and in the armchair directions, and shear. Our findings show the suitability of standard thin-plates theory for the prediction of simple critical behaviours under various edge constraint conditions.

The paper presents a numerical study of defect-free single-wall carbon, boron nitride and silicon carbide armchair and zigzag nanotubes, through a simple stick-and-spring model, based on Morse and cosine potential functions. The study investigates the relaxed configuration of the tubes and gives a comprehensive evaluation of their elastic constants, which is performed by framing tensile, torsional and radial tests within the membrane behaviour of a Donnell thin shell model. Extensive comparisons with reference ab-initio results are given and used to refine some parameters of the potential functions for hexagonal silicon carbide nanomaterials.

The force constants related to the bond stretching and angular variation of boron nitride, silicon carbide, aluminium nitride and gallium nitride nanosheets are directly evaluated from ab-initio reference solutions of the Young’s modulus and the Poisson’s ratio. To this end, the analytical expressions of the elastic constants of a generic monolayer hexagonal diatomic sheet are derived, starting from its sticks-and-springs molecular mechanics model, through proper tools of the homogenization of periodic discrete media. Numerical benchmark assessments are given.

Several nanomechanics formulations based on common two and three-body bonding potentials are compared. Numerical simulations and analytical approaches are used to investigate the not negligible differences among the predictions of the in-plane elastic constants of graphene sheets in the literature, separately exploring the role of the potentials and that of the structural descriptions (beams and trusses) of the original molecular mechanics (MM) model. The energetic differences between the structural models and the MM model are highlighted through exact discrete homogenization procedures. In so doing, some theoretical expressions of the graphene elastic constants available in the literature are recovered and supported by the numerical experimentation. The results provide also an assessment of the accuracy of some potentials largely employed in the literature with respect to several ab-initio reference solutions and the experimental measurements available. Some suggestions towards a reparametrization of the modified Morse potential are consequently formulated.