Multiscale Simulation Of Material

Multiscale simulation, as a coupled method with combining with the differ-ent models, plays a more and more important role in solving the material phe-nomena spanning the length and time scale. The goal is to perform an accurate simulation method for the critical zone and an approximate one for the outer one. Up to now, there are many kinds of multiscale approaches which make great progress, but there are also some problems, such as spurious reflection, ghost force, which cause the difficult implementation for dynamical multiscale simulation. In this thesis, we develop a new multiscale simulation method which involves the atomic-based finite element method(AFEM) for the continuum re-gion and filter method for damping the spurious reflection, and then apply them for the dynamical simulation.This thesis is composed of six chapters. The first chapter gives an introduc-tion to the different multiscale methods, including their coupled principles and applications. The second chapter analyzes the origin of difficult performance in the dynamical multiscale simulation, which comes from spurious reflection induced by mismatch of dispersion relation between the different models. Mean-while we give the location of spurious reflection:the interface of varying mesh size and handshaking region. Finally we introduce some known methods absorbing the reflected waves.In the third chapter, we devotes to the one-dimensional AFEM model in de-tails. Based on Cauchy-Born rule, we obtain the dynamical equation of AFEM model. By the theoretical analysis, when the mesh size is equal to atomic length, AFEM model becomes the atomic model. And while the mesh size approaches the infinity, it turns out the conventional finite element method. Therefore, AFEM model spreads from atomic scale to continuous scale and exhibits the property from non-locality to locality. Meanwhile the AFEM model can auto-matically emerge with molecular dynamics(MD) method of atomistic region so that the total coupled system avoids the unnecessary refleetion at the hand- shaking region. To solve spurious wave reflection induced by varied mesh size, we design a low-pass filter damping method inspired by filter principal. In the one-dimensional multiscale simulation, the result shows that AFEM seamlessly matches with MD method. The reflection and transmission coefficient exhibits that the filter method eliminates the spurious reflection of high-frequency wave and doesn't affect the propagation of low-frequency one.In the fourth chapter, we turn to the two-dimensional case. We carry out the theoretical deduction about two-dimensional dynamical equation of AFEM model by considering the atomic potential with the nearest neighbor and second neighbor interactions. The AFEM model also shows the transition from atomic scale to continuum scale. From the analysis of energy propagation in the total numerical simulation, AFEM model smoothly merge with the atomic model. As for the spurious reflection, the reflection and transmission coefficient is calcu-lated for separately longitudinal and transverse wave and the results show the validation of filter damping method.In the fifth chapter, we employ the above schemes to extend for the finite temperature multiscale simulation for the nanoindentation experiment. We firstly build the dynamical simulation of total system by adding the temperature control to the atomistic region and inserting the filter layers at the handshaking region. By analyzing the nodal and atomic displacement distribution, the dynamical behavior spreads the total system. We also apply the methods to the simulation of temperature, size effect and rate effect in the two-dimensional nanoindentation systems and the simulation results qualitatively coincide with the experiment.In the last chapter, we give a conclusion about the overall thesis and turn to long term goal about the multiscale method.