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# A New Multiscale Computational Method for Mechanical Analysis of Closed Liquid Cell Materials

H.W. Zhang1,2, J. Lv1, Y.G. Zheng1

State Key Laboratory for Structural Analysis of Industrial Equipment, Department of Engineering Mechanics, Faculty of Vehicle Engineering and Mechanic, Dalian University of Technology, Dalian 116024, P R China
Corresponding author. E_mail: zhanghw@dlut.edu.cn

Computer Modeling in Engineering & Sciences 2010, 68(1), 55-94. https://doi.org/10.3970/cmes.2010.068.055

## Abstract

A new multiscale computational method named as extended multiscale finite element method is proposed for the mechanical analysis of closed liquid cell materials. The numerical base functions for both the displacement field and the pressure of the incompressible fluid within the closed cells are employed to establish the relationship between the macroscopic deformation and the microscopic variables such as deformation, stress, strain and fluid pressure. The results show that the extended multiscale finite element method constructed with the conventional four-node quadrilateral coarse-grid elements sometimes will have strong boundary effects and cannot predict well the fluid pressure in the closed cells. Thus more reasonable higher order coarse-grid elements which can characterize more accurately the structural deformation of the closed cells are introduced. Furthermore, inspired by the periodic boundary conditions used in the homogenization method, the generalized periodic boundary conditions are proposed for the construction of the numerical base functions of the higher order elements. Numerical results indicate that the extended multiscale finite element method with higher order elements can be successfully used for the mechanical analysis of closed liquid cell materials. Particularly, combining with the periodic boundary conditions, the extended multiscale finite element method with higher order elements can give more accurate results.

## Keywords

APA Style
Zhang, H., Lv, J., Zheng, Y. (2010). A new multiscale computational method for mechanical analysis of closed liquid cell materials. Computer Modeling in Engineering & Sciences, 68(1), 55-94. https://doi.org/10.3970/cmes.2010.068.055
Vancouver Style
Zhang H, Lv J, Zheng Y. A new multiscale computational method for mechanical analysis of closed liquid cell materials. Comput Model Eng Sci. 2010;68(1):55-94 https://doi.org/10.3970/cmes.2010.068.055
IEEE Style
H. Zhang, J. Lv, and Y. Zheng "A New Multiscale Computational Method for Mechanical Analysis of Closed Liquid Cell Materials," Comput. Model. Eng. Sci., vol. 68, no. 1, pp. 55-94. 2010. https://doi.org/10.3970/cmes.2010.068.055

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