A Multiscale Asymptotic Method by Transmitting Some Quantities from Quantum Mechanics to Continuum Mechanics

摘要

In this talk, we will propose a multiscale asymptotic method by the transmission of some physical quantities such as some elastic constants and some energy for the dynamic elasticity of composite structures and interfaces. This lecture consists of the following parts: 1. The setting of dynamic elasticity for composite structures and interfaces; 2. TB method for calculating the elastic constants on the interfaces and the mathematical proof of some crucial conclusions ; 3. Homogenization method for evaluating the macroscopic effective elastic constants; 4. The multiscale calculations of some macroscopic stresses, strains and energies; 5. TB-MD simulation on the interfaces under the influence of external force fields. 6. Some numerical results and discussion.This work is supported by National Natural Science Foundation of China (grant No. 10372108) and Special Funds for Major State Basic Research Projects(grant No. TG2000067102).