List of basie abbreviations and symbols Overview of graphene and carbon nanotubes Graphene and CNT basie inforniation, production methods, properties and potential applications Production methods Properties Applications Atomie structure and morphology of graphene and carbon nanotubes Modelling techniques of graphene, CNTs and their composites – overview Atomistic dynamie methods Static methods Objectives and scope of this research A novel atomistic-based structural approach for modelling the mechanics of graphene and carbon nanotubes Interatomic potentials used in the analysis of graphene-based structures Modified Morse potential Tersoff-Brenner potential Derivation of a new atomistic-based structural model Nonlinear truss element modelling pairwise interactions Connector element modelling multibody interactions Detailed formulas for the modified Morse potential Remarks conceming the applicability of the proposed model for the Tersoff-Brenner potential Comparison of the proposed truss-connector model with other models based on structural mechanics Beam model Spring model Numerical examples Stretching of a graphene monolayer Stretching of single-walled carbon nanotubes Critical discussion of the obtained results Atomic-scale finite element method (AFEM) Derivation of the atomic-scale finite element formulas Atomic-scale finite element based on considered interatomic potential Comparison of the atomic-scale finite element and the truss-connector model for the Tersoff-Brenner potential Range of applicability of AFEM Numerical simulations of graphene and SWCNTs Size-dependent elastic properties of achiral SWCNTs under axial tension Chirality dependent elastic properties of SWCNTs under axial tension Bending and torsion of SWCNTs Strength and elastic properties of defected graphene and SWCNTs Defected Graphene Defected SWCNT Conclusions A cohesive contact law for graphene and CNTs Contact formułation Numerical examples Deformation of SWCNTs by van der Waals forces Graphene membranę indentation simulation - analysis of elastic properties and intrinsic strength The continuum hypoelastic model for graphene and CNTs Overview ofexisting continuum methods Analysis of elastic in-plane properties of graphene based S-on the modified Cauchy-Born hypothesis under the assumption of large displacements and smali strains Kinematics and potential energy of the graphene unit celi in planar deformation Elasticity matrices for the considered potentials Hypoelastic continuous model for graphene monolayer Resultant initial planar elasticity matrices Thickness of graphene layer Hypoelastic anisotropy Hypoelastic isotropy Numerical model verification Graphene deformation analysis Analysis of a single-walled carbon nanotube under different loads Conclusions Final remarks Original contribution Areas of future work