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Nonlinear elastic constitutive relations of residually stressed composites with stiff curved fibres

Applied Mathematics and Mechanics(English Edition) 2022年第10期43卷 1515-1530页

作者： M.H.B.M.Shariff J.Merodio R.Bustamante Department of Mathematics Khalifa University of Science and TechnologyAbu Dhabi127788United Arab Emirates Departamento de Matemática Aplicada a las TIC ETS de Ingeniería de Sistemas InformaticosUniversidad Politecnica de MadridMadrid28031Spain Departamento de Ingeniería Mecánica Universidad de ChileBeauchef 851Santiago CentroSantiago8370448Chile

Mechanical models of residually stressed fibre-reinforced solids,which do not resist bending,have been developed in the literature.However,in some residually stressed fibre-reinforced elastic solids,resistance to fibre bending is significant,and the mechanical behavior of such solids should be investigated.Hence,in this paper,we model the mechanical aspect of residually stressed elastic solids with bending stiffness due to fibre curvature,which up to the authors’knowledge has not been mechanically modeled in the past.The proposed constitutive equation involves a nonsymmetric stress and a couple-stress tensor.Spectral invariants are used in the constitutive equation,where each spectral invariant has an intelligible physical meaning,and hence they are useful in experiment and analysis.A prototype strain energy function is proposed.Moreover,we use this prototype to give results for some cylindrical boundary value problems.

关键词： fibre-reinforced solid residual stress bending stiffness spectral invariant second gradient finite elasticity

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ANALYTICAL AND NUMERICAL INVESTIGATIONS OF TWO SPECIAL CLASSES OF GENERALIZED CONTINUUM MEDIA

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Acta Mechanica Solida Sinica 2011年第4期24卷 326-339页

作者： Zhaohui Zhang Zhanli Liu Yuan Gao Junfang Nie Zhuo Zhuang Department of Engineering Mechanics School of AerospaceTsinghua UniversityBeijing 100084China Institute of Nuclear and New Energy Technology Tsinghua UniversityBeijing 100084China Naval Academy of Armament Beijing 100073China

In this paper,the micromorphic theory and the second gradient theory are proposedwhere 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.

关键词： micromorphic second gradient boundary layer size effect finite element

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