Modeling Mechanical Properties of Graphene-Based and Diamond-Like Nanostructures

Carbon demonstrates a great variety of polymorphs with different mechanical and physical properties. In this chapter, recent developments in modeling the mechanical properties of graphene-based (sp ²-bonded) and diamond-like (sp ³-bonded) nanostructures are discussed. Among the sp ²-bonded structures, crumpled graphene, fullerite, and a regular array of short carbon nanotubes are introduced. For these structures, stress components as the functions of mass density are calculated for uniaxial, biaxial, and hydrostatic compressions. Phenomenological constitutive relations are offered to describe their mechanical response. For a number of bulk sp ³-bonded structures composed of polymerized fullerene-like molecules (fulleranes), graphene sheets (graphanes), or carbon nanotubes (tubulanes), their equilibrium structures are first identified by relaxing the corresponding idealized structures. Afterward, the elastic constants are computed for those structures that are stable. Some of the structures are found to demonstrate partial auxeticity (i.e., they have a negative Poisson’s ratio for a particular choice of the uniaxial loading direction and the direction of the lateral strain measurement).