Discussion On Bridging Multiple Scale Simulation For Coupling Atom And Continuum

As one of the most popular research fields in mechanics, the multiple scale simulation isattracting more and more attention of scientific researchers and makes a lot of achievementswith the development of computer technology and experiment instrument. Among thesimulation methods, the bridging scale is widely studied due to its good properties that iteliminates wave fluctuation and avoids huge computations. As a method coupling atomistic andcontinuum simulation, the bridging scale has simulated mechanics properties of two or threedimensions and carbon nano tube models. The theory’s derivation and programming of bridgingscale method are the main part of this thesis.The current research status of finite element method (FEM) and molecular dynamics (MD) wasreviewed firstly. Then the basic conceptions of molecular dynamic and three common numericalmethods of differential equation were introduced as basic knowledge of multiple scalesimulation. The MAAD approach and Cauchy-Born rule and their numerical examples werepresented. MAAD is the pioneering multiple scale simulation method coupling tight binding,molecular dynamics and finite elements together first. The example shows that MAAD wouldcause reflection of energy when finite element size is bigger than atom space. As the basis ofquasi-continuum method, the Cauchy-Born rule is aimed to link the energy of atomistic andcontinuum models. Examples are shown to illustrate the applications of both theories.To solve the problem of energy fluctuation, the theory and formulas of bridging scale wasderived in detail. The generalized Langevin equation and its application in bridging scalemethod were introduced. Then the method was programmed using C++language with thedevelopment of pre-processing and post-preprocessing as the basis of extension towards two orthree dimensions problem. The simulation result was analyzed to demonstrate the advantage ofthe bridging scale that this method could be better at spreading the energy compared with othermethods. Since multiple scale simulation belongs to the frontier science, wish this thesis couldprovide some references and help for future researchers.