Matematika i Matematičeskoe Modelirovanie (May 2019)
Transversely Isotropic Rod for Modeling Elastic Characteristics of Single-Walled Carbon Nanotube
Abstract
Single-walled carbon nanotubes (SWCNT) are a seamless cylindrical structure formed by folding a single-walled graphene sheet. Nanotubes are of great interest due to their unique thermo-mechanical characteristics. Such objects can be applied in the energy, rocket and aerospace engineering as a filler of advanced structural composite materials.One of the most important SWCNT characteristics is a complex of its elastic properties. The most reliable way to determine the elastic characteristics of a nanotube is to conduct an experiment. However, due to high cost and lengthy time of the experiment completion, it is more preferable to use mathematical modeling of these properties of SWCNT with which the paper deals.The paper proposes a mathematical model that is constructed by methods of generalized continuum mechanics. To use these methods, the nanotube, on the assumption of its transverse isotropy, is presented simultaneously as a cylindrical shell and a continuous circular rod.As a result of consideration of various stress-strain states of the shell and rod, are obtained relations to establish a quantitative relation between the elements of the matrix of compliance coefficients of a rod that simulates a single-walled carbon nanotube, and the elastic characteristics of graphene taken as its basis in the isotropy plane. Also, the constructed mathematical model allows us to define the influence of the nanotube configuration (chiral indices) on its elastic characteristics.The paper presents the application results of the model proposed, using as an example, a SWCNT with chirality indices (7, 0), for which were constructed mutually inverse matrices of compliance and elasticity coefficients that completely describe the elastic properties of the nanotube.Using the proposed mathematical model significantly reduces the time and cost for estimation of the elastic characteristics of the SWCNT, that is especially important at the design stage of new materials based on them.
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