Analysis of Multi-scale Structures Using the Atomistic-Continuum Mechanics and the Equivalent Methods

• Main Authors: Huang, Chao-Jen, 黃昭荏
• Other Authors: Chiang, Kuo-Ning
• Format: Others
• Language: en_US
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/27209924926863390353

博士 === 國立清華大學 === 動力機械工程學系 === 101 === The continuous development and improvement in the nanotechnology field prompt many researchers to develop various simulation methods to determine the material properties of nanoscale structures. The most common simulation methodologies include Quantum Mechanics, Molecular Dynamics, and Monte Carlo, among others. However, these methods are restricted by the time limitation of the central processing unit (CPU) computer hardware, which cannot estimate larger-scale nanoscale models. Thus, decreasing the CPU processing time and retaining the physical properties of nanoscale structures have become critical issues. To decrease the CPU processing time and complexity of larger nanoscale models, the current study utilized atomistic-continuum mechanics (ACM) to build an equivalent model. ACM consists of atomic mechanics, continuous mechanics, equivalent theory, finite element method, and high-speed computing theory to estimate the mechanical properties of a multi-scale structure. ACM transfers an originally discrete atomic structure into an equilibrium continuum model, and does not require the assumption of the Young’s modulus and the cross-sectional area of each chemical bond. ACM can allow the Young’s modulus to be obtained using the same model for tensile and modal analyses. This study investigates the mechanical properties of silicon (Si)-germanium (Ge), hereafter SiGe, heterostructures and carbon nanotube (CNT) composite materials. In the estimation of the material properties of SiGe heterostructures, different heterostructure volume fractions and thicknesses reflect the different deformations caused by the Si lattice constant that is not equal to that of Ge. This study utilized the ACM method, constraint equation, and local-global theory to establish a conceptual framework that links the lattices of Si and Ge. Therefore, this strategy can describe the strain effect caused by the lattice mismatch in the nanoscale heterostructure. The strain distribution with Si and Ge having different volume fractions and different thicknesses is investigated. The analytical result is also validated with previous studies indicating that the entire top Si layer surface depicts compressor strain when the mesa length is 50 nm. This study establishes a simulation method to obtain the mechanical behavior of nanoscale strained-silicon and serve as a guide for semiconductor devices design. The Young’s modulus of CNTs can be presented using the ACM method. Both tensile and modal analytical results agree with the experimental results in literature indicating that the ACM model can properly describe mechanical properties. Based on this result, this study investigated the equivalent solid, shell, and beam models to generate similar mechanical behaviors with the ACM model. The similar mechanical behavior of the equivalent model includes the model under tensile, torsion, or shear external loading. These equivalent models can significantly reduce the required total element number and CPU processing time to investigate a larger nanoscale structure. This study also adopted three cross-sectional area definitions to explore whether the Young’s modulus of CNT ropes depends on the cross-sectional area definition. The results indicate that the Young’s modulus distribution based on the circumcircle assumptions well agrees with most of the experimental results. Hence, most experimental methods adopted the circumcircle to obtain the Young’s modulus of the CNT ropes. The circumcircle assumption involves the distribution of the tubes and the gap between each tube. The ratio between the gap and tube areas becomes a stable value when the diameter of the CNT ropes is increased. Therefore, a larger diameter of CNT ropes that represents the Young’s modulus becomes a stable value, as mentioned in literature. This study adopted phenolic resin/CNT composite material to discuss local and global technique applications. The representative volume element was utilized to validate the consistency of the Young’s modulus of theoretical and numerical results. The equivalent models simultaneously decrease the CPU processing time and maintain mechanical behavior, making them sufficient, accurate, and acceptable. This equivalent method is feasible from a local to global perspective and vice versa.