ISSN 打印: 1543-1649
ISSN 在线: 1940-4352

# 国际多尺度计算工程期刊

DOI: 10.1615/IntJMultCompEng.v4.i1.50
pages 47-70

## Multiphysical Modeling and a Transscale Computation of Composite Materials and Their Interfaces

Li-Qun Cao
State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Science-Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O.Box 2719, Beijing, 100080, China
Jun-Zhi Cui
State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Science-Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, P.O.Box 2719, Beijing, 100080, China
Chong-Yu Wang
Department of Physics, Tsinghua University, Beijing, 100084, China

### ABSTRACT

In this paper, we shall discuss kinetic equations of composite materials and their interfaces, which is a typical multiphysical problem, due to the existence of very thin interfaces. A multiphysical model and a transscale computational method will be presented. Our method is composed of four parts: the first one is the first-principle calculation (e.g., TB-DFT method) for calculating the total energy and the elastic constants of interfaces ; the second one is the homogenization method for evaluating the effective elastic constants of macroscopic structures of composite materials; the third one is the multiscale method for computing the stress field of macroscopic structures; and the final one is the quantum molecular dynamical method (e.g.,TB-MD) for calculating the local stress field of the interfaces. Some numerical results are reported. The rigorous proofs of some main theoretical results will be given in the Appendixes.

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