Mesh-free and Multiscale Methods for Predicting the Mechanical Properties of Carbon Nanotubes

Due to their outstanding physical, mechanical, and electrical properties, carbon nanotubes (CNTs) have attracted a great deal of attention for their various potential applications. In addition to a large amount of experimental work, theoretical modeling also plays an important role in understanding the properties of nanostructures. However, the development of effective and efficient computational methods for the analysis of nanostructures is still an ongoing and challenging process.CNTs are generally modeled and studied through atomistic simulation. However, the fastest supercomputer today may be able to handle up to a billion atoms, but that only corresponds only to a small cube of 1 μm in size. Due to this limitation, continuum methods have become a useful alternative in comprehending the properties of CNTs. These methods, however, are unable to capture the microscale physical laws of nanostructures. The multiscale method is emerging as a feasible and efficient approach for large-size problems. The multiscale method couples the continuum method and atomistic simulations, and makes use of the advantages of both atomistic and continuum simulations. An efficient multiscale method first requires a reasonably accurate continuum model. Therefore, the exploration of an efficient and rational continuum technique is very important and significant to the study of nanostructures.The present researchers recently proposed a higher order Cauchy-Born rule for the continuum analysis of CNTs. Some primary theoretical studies have revealed that this rule is more accurate and efficient than other previous models. This project will explore the application of this rule in the continuum numerical simulation of CNTs. Due to the distinctly different characteristics of the higher order Cauchy-Born rule, the advantages of the mesh-free method will be utilized, and it is expected that a mesh-free computational framework will be developed to investigate the numerical implementation of the continuum constitutive based on the rule. The mechanical response of CNTs under the axial and radial compressing, twisting, and bending loads will be modeled, and the buckling and failure mechanism will be explored in the scheme of higher order gradient continuum.Another important purpose of this study is to investigate the coupling of the developed mesh-free method with atomistic simulation. In most of the work on multiscale computations, the research has been focused on the approach to bridging two different scales. In fact, the rationality and accuracy of the continuum model have a large effect on the computational efficiency of the multiscale method. Based on the characteristics of the higher order Cauchy-Born rule and the advantages of the mesh-free method, the researchers aim to develop a suitable multiscale method for the analysis of nanostructures. Certain localized problems of CNTs, e.g., CNT defects and fracture, will be studied using the developed multiscale method.