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.2013005712
pages 369-387

## A NEW MULTISCALE FINITE ELEMENT METHOD FOR MECHANICAL ANALYSIS OF PERIODIC HETEROGENEOUS COSSERAT MATERIALS

Zhaoqian Xie
State Key Laboratory for Structural Analysis of Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian 116024, P. R. China
Hongwu Zhang
Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanics, State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, P. R. China

### ABSTRACT

A new multiscale finite element method is developed for mechanical analysis of periodic heterogeneous Cosserat materials. The main idea of the method is to numerically construct the multiscale base functions to capture the small-scale features of the coarse elements. Considering the existence of rotation in the Cosserat materials, specified boundary conditions of the base functions for extended multiscale finite element method (EMsFEM) are developed based on the relationship between transverse displacement and rotation (slope) of the two-node beam element, and the corresponding periodic boundary conditions are developed. By adopting both kinds of boundary conditions, the numerical base functions for displacement and rotation fields of Cosserat materials are constructed, respectively, to establish the relationship between the macroscopic deformation and the microscopic stress and strain. It is shown that the proposed method does not require the estimation of the overall material parameters of the heterogeneous Cosserat materials as the general homogenization methods. Numerical examples are carried out to verify the validity and efficiency of the developed multiscale finite element method.

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