Atomic Finite Element Simulations For Mechanical Properties Of Carbon, Boron Nitride Nanomaterials

With the development of technology, mankind's understanding of the nano-world has reached an unprecedented height. Various types of nano-materials have sprung up in front of people. The Nano-scale material structures possess some attractive properties, which make them have very broad application prospects. Developing theoretical models that can accurately predict the performance of these nano materials is what many researchers have been working for. In this article, the proper finite element models for graphene sheets and boron nitride nanotubes were constructed. And based on these models, a series of calculations about the vibration and mechanical properties has been carried out for the graphene sheets and boron nitride nanotubes (BNNTs). This article mainly includes the following contents.(1) Atomic-Finite element modeling of graphene. By expanding the beam-spring model for carbon nanotubes, a continuum model of graphene sheets was constructed to simulate the deformation energy of C-C bond in graphene accurately. And a number of linear springs with different stiffness are used to fit the interlayer effects of multi-layer graphene sheets. This model could reflect the mechanical properties at the level of individual atoms in the greatest extent, so it has high accuracy for solving the mechanical problems of graphene sheets. Using the established model of graphene sheets, we calculated the vibration characteristics of graphene sheets systematically, and individually analyzed the factors which may affect the vibration of graphene sheets. The results show that its size and boundary conditions may produce great impact to its vibration modes. For the multi-layer graphene sheets, the layer number and the interlayer distance will make some changes to the modes which are perpendicular to the surface, but have little effects to the in-plane vibration modes at the higher frequency.(2) Atomic_Finite element modeling and simulations of BNNTs. A new binary nanotube model was proposed for the BNNTs. This model adopts the variable cross-section beam to simulate the polar B-N bond, which could not only describe the various deformation energies of BN bond, but also effectively distinguish the deformation difference between boron atoms and nitrogen atoms in BNNTs. At the same time, this model could be directly compiled in the standard commercial finite element software, so this model also has gratifying accuracy and excellent applicability. Based on the continuum model of BNNTs, we calculate the low-frequency vibration modes and radial breathing modes of boron nitride nanotubes by using the eigenvalue extraction method. The calculation results show that boron nitride nanotubes have lower natural frequencies compared with the carbon nanotubes and its bending modes are more easily to appear in the low frequency period. At the same time, we find that its radial breathing modes almost depend only on its radius, and we fit this relationship with power series which could be used to predict its radial breathing modes accurately.