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

doi:10.1007/s10483-022-2910-7

Applied Mathematics and Mechanics (English Edition) ›› 2022, Vol. 43 ›› Issue (10): 1515-1530.doi: https://doi.org/10.1007/s10483-022-2910-7

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

M. H. B. M. SHARIFF¹, J. MERODIO², R. BUSTAMANTE³

1. Department of Mathematics, Khalifa University of Science and Technology, Abu Dhabi 127788, United Arab Emirates;
2. Departamento de Matemática Aplicada a las TIC, ETS de Ingeniería de Sistemas Informaticos, Universidad Politecnica de Madrid, Madrid 28031, Spain;
3. Departamento de Ingeniería Mecánica, Universidad de Chile, Beauchef 851, Santiago Centro, Santiago 8370448, Chile

收稿日期:2022-04-20 修回日期:2022-08-08 发布日期:2022-10-25
通讯作者: M. H. B. M. SHARIFF, E-mail: mohd.shariff@ku.ac.ae

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

M. H. B. M. SHARIFF¹, J. MERODIO², R. BUSTAMANTE³

1. Department of Mathematics, Khalifa University of Science and Technology, Abu Dhabi 127788, United Arab Emirates;
2. Departamento de Matemática Aplicada a las TIC, ETS de Ingeniería de Sistemas Informaticos, Universidad Politecnica de Madrid, Madrid 28031, Spain;
3. Departamento de Ingeniería Mecánica, Universidad de Chile, Beauchef 851, Santiago Centro, Santiago 8370448, Chile

Received:2022-04-20 Revised:2022-08-08 Published:2022-10-25
Contact: M. H. B. M. SHARIFF, E-mail: mohd.shariff@ku.ac.ae

摘要/Abstract

摘要： 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

Abstract: 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.

Key words: fibre-reinforced solid, residual stress, bending stiffness, spectral invariant, second gradient, finite elasticity

中图分类号:

M. H. B. M. SHARIFF, J. MERODIO, R. BUSTAMANTE. Nonlinear elastic constitutive relations of residually stressed composites with stiff curved fibres[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(10): 1515-1530.

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

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

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