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A new micromechanical approach of micropolar continuum modeling for 2-D periodic cellular material

A new micromechanical approach of micropolar continuum modeling for 2-D periodic cellular material Abstract In this paper, we present a new united approach to formulate the equivalent micropolar constitutive relation of two-dimensional (2-D) periodic cellular material to capture its non-local properties and to explain the size effects in its structural analysis. The new united approach takes both the displacement compatibility and the equilibrium of forces and moments into consideration, where Taylor series expansion of the displacement and rotation fields and the extended averaging procedure with an explicit enforcement of equilibrium are adopted in the micromechanical analysis of a unit cell. In numerical examples, the effective micropolar constants obtained in this paper and others derived in the literature are used for the equivalent micropolar continuum simulation of cellular solids. The solutions from the equivalent analysis are compared with the discrete simulation solutions of the cellular solids. It is found that the micropolar constants developed in this paper give satisfying results of equivalent analysis for the periodic cellular material. Graphic abstract http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Acta Mechanica Sinica" Springer Journals

A new micromechanical approach of micropolar continuum modeling for 2-D periodic cellular material

Niu, Bin; Yan, Jun
"Acta Mechanica Sinica" , Volume 32 (3): 13 – Jun 1, 2016
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References (61)

Publisher
Springer Journals
Copyright
2015 The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
ISSN
0567-7718
eISSN
1614-3116
DOI
10.1007/s10409-015-0492-8
Publisher site
See Article on Publisher Site

Abstract

Abstract In this paper, we present a new united approach to formulate the equivalent micropolar constitutive relation of two-dimensional (2-D) periodic cellular material to capture its non-local properties and to explain the size effects in its structural analysis. The new united approach takes both the displacement compatibility and the equilibrium of forces and moments into consideration, where Taylor series expansion of the displacement and rotation fields and the extended averaging procedure with an explicit enforcement of equilibrium are adopted in the micromechanical analysis of a unit cell. In numerical examples, the effective micropolar constants obtained in this paper and others derived in the literature are used for the equivalent micropolar continuum simulation of cellular solids. The solutions from the equivalent analysis are compared with the discrete simulation solutions of the cellular solids. It is found that the micropolar constants developed in this paper give satisfying results of equivalent analysis for the periodic cellular material. Graphic abstract

Journal

"Acta Mechanica Sinica" – Springer Journals

Published: Jun 1, 2016

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