Discrete-Continuous and Continuous-Moment Models of Graphene under In-Plane Deformation
- PDF / 181,242 Bytes
- 7 Pages / 612 x 792 pts (letter) Page_size
- 38 Downloads / 224 Views
rete-Continuous and Continuous-Moment Models of Graphene under In-Plane Deformation S. H. Sargsyan1* 1
Shirak State University named after M. Nalbandyan, Gyumri, 377501 Armenia * e-mail: [email protected] Received August 15, 2019, revised August 15, 2019, accepted September 02, 2019
Abstract—A model of in-plane graphene deformation is developed by considering a linear chain of atoms with regard to the independent moment interaction and noncentral force interaction between atoms. A discrete and continuous beam models of the linear chain of atoms are constructed. Assuming that each graphene atom interacts only with its nearest neighbors, the atomic system is replaced by a beam system using the obtained continuous beam model of the linear atomic chain. A discrete-continuous and continuous models of graphene are derived. The first one is a special molecular dynamics model, and the second is a plane stress model of the moment theory of elasticity with independent displacement and rotation fields. The elastic constants of the second model are determined through the atomic structure parameters of graphene. It is shown that the problems of in-plane graphene deformation can be solved using both the discrete-continuous model (beam system model) and the continuous model as the plane stress model of the moment theory of elasticity with independent displacement and rotation fields with known elastic constants. Keywords: linear chain of atoms, one-dimensional, discrete, continuous (beam) model, graphene, graphene plane, discrete-continuous, continuous-moment models DOI: 10.1134/S1029959920040049
1. INTRODUCTION The rapid development of nanotechnology has led to the need for mathematical modeling of nanomaterials in order to determine and investigate their elastic and strength properties [1–4]. The derivation of discrete models for such nanomaterials as graphene and carbon nanotubes requires taking into account the independent moment and noncentral force interactions between atoms [5–7]. There were attempts to apply the approach to constructing a beam system (discretecontinuous model) equivalent to the atomic model for nanoscale structures [8–12]. The beam model in the cited works was the classical model of thin elastic beams with and without allowance for bending deformation. Here, a discrete model of a linear atomic chain is developed taking into account the moment and noncentral force interactions between atoms as well as its continuous-moment model. The interaction between graphene atoms (when studying in-plane deformations) in a unit cell of graphene is replaced by the beam model. This is the way of obtaining a discretecontinuous graphene model (the model of the beam
system replacing the atomic system) as well as a continuous-moment model of graphene constructed by passing to the limit under bending deformation. As a result, the elastic constants of the moment theory of elasticity for plane stress are determined. 2. A STRUCTURAL AND CONTINUOUSMOMENT (BEAM) MODELS OF A LINEAR ATOMIC CHAIN Let us consider a linear chain o
Data Loading...
