Numerical Analysis for Effective Moduli of Micropolar Composites with Periodic Microstructure

• Main Authors: Yu-HsiangPeng, 彭昱翔
• Other Authors: Tung-Yang Chen
• Format: Others
• Language: zh-TW
• Published: 2014
• Online Access: http://ndltd.ncl.edu.tw/handle/74748547586190415231

碩士 === 國立成功大學 === 土木工程學系 === 102 === In the framework of micromechanics, under certain lengthscales, the microstructure effect of materials cannot be ignored, thus classical continuum mechanics could not be adequate for characterizing the media with complex microstructure effects. The Cosserat theory is one of the approaches we can choose to deal with this level of complexity. In Cosserat elasticity the stresses are not only characterized by the translational motion u but also rotational degrees of freedom. In this thesis, we first recall the basic formulations of Cosserat elasticity, and compare the differences between classical elasticity and Cosserat elasticity. Second, we use the average-field theory to calculate the average stresses, average couple, average strain and average curvature for a Cosserat medium. lastly, we employ the proposed average theory to determine the effective moduli of two dimensional model with periodic microstructures. Numerical simulation is also performed by a finite element method. We design a medium with periodic microstructure that is composed of an elastic material to make it effectively resemble an effect of Cosserat elasticity. It is found that the more asymmetric the microstructural configuration is, the more Cosserat effect it behaves with. Using the methodology proposed in this thesis, we can reasonably predict the overall mechanical behavior of periodic micropolar composites.