Analysis of Linear and Non-Linear Stress-Strain Properties for Graphene and Single Walled Carbon Nanotubes

Carbon Nanotube (CNT) has revolutionized the world of nanotechnology with several novel applications in the field of sensors and actuators. Such popularity of CNT is due to its excellent mechanical and electrical properties. There are several studies done on understanding the modeling of mechanical and electrical properties using different approaches ranging from molecular to continuum based method. In this thesis, we focus on estimating the mechanical properties of single walled carbon nanotube (SWCNT) mainly based on stress-strain relationship.\ud There are several approaches such as molecular mechanics, molecular dynamics, coupled molecular-structural mechanics, exponential Cauchy born based continuum method, etc, for estimating the linear and nonlinear stress-strain relationship in order to find elastic modulus of SWCNT. In this thesis, we first find the analytical model using molecular mechanics approach to study the variation of elasticity with the diameter of SWNT under different configurations. It is found that the elasticity becomes size independent if the diameter is above 1 nm. Moreover this approach does not help us to get accurate nonlinear stress-strain relationship. Therefore, we used coupled molecular-structural approach to study the nonlinear variation of stress-strain relationship for different configurations. Then, we come up with compact formulas in order to predict the nonlinear stress-strain relationship. Capitalizing on this approach, we find the equivalent mechanical properties of a beam element for the corresponding C-C bond that exists in CNT. Thereafter, we use these properties to do structural modeling in ANSYS which drastically reduces the modeling effort as compared to molecular dynamics approach. In order to standardize this approach, we do several comparisons and tests with existing results based on other methods. It is found that the results are in good agreement with the literature. After validating the stress-strain properties of SWCNT under different configurations, we do modal analysis to find the first few frequencies for fixed-fixed and cantilever kinds of support. On comparing the results with analytical model based from continuum theory, we get relatively good match for cantilever under\ud vii\ud wider range of aspect ratio- a ratio of length to diameter of SWNT. However, analytical result for the fixed-fixed condition matches well only for larger length to diameter ratio. Furthermore, we investigate different modes of graphene and SWCNT under different configurations to demonstrate the capabilities of this method