Acta Mechanica Solida Sinica

, Volume 24, Issue 4, pp 326–339

# Analytical and Numerical Investigations of Two Special Classes of Generalized Continuum Media

• Zhaohui Zhang
• Zhanli Liu
• Yuan Gao
• Junfang Nie
• Zhuo Zhuang
Article

## Abstract

In this paper, the micromorphic theory and the second gradient theory are proposed-where the micromorphic model can be reduced to the second gradient model with the vanishing relative deformation between macrodeformation gradient and microdeformation. Analytical solutions for the simple shear problem in the case of a general small strain isotropic elasticity micromorphic model and the second gradient model are presented, respectively. Besides, uniaxial tension of a constrained layer with two different boundary conditions is also analytically solved. Finally, the micromorphic theory is implemented numerically within a two-dimensional plane strain finite element framework by developing two isoparametric elements.

## Key words

micromorphic second gradient boundary layer size effect finite element

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© The Chinese Society of Theoretical and Applied Mechanics and Technology 2011

## Authors and Affiliations

• Zhaohui Zhang
• 1
• 3
• Zhanli Liu
• 1
• Yuan Gao
• 1
• Junfang Nie
• 2
• Zhuo Zhuang
• 1
1. 1.Department of Engineering Mechanics, School of AerospaceTsinghua UniversityBeijingChina
2. 2.Institute of Nuclear and New Energy TechnologyTsinghua UniversityBeijingChina