考虑纤维弯曲刚度的橡胶-帘线复合材料各向异性超弹性本构模型

孙书蕾; 毛建良; 彭雄奇

doi:10.3879/j.issn.1000-0887.2014.05.001

考虑纤维弯曲刚度的橡胶-帘线复合材料各向异性超弹性本构模型

doi: 10.3879/j.issn.1000-0887.2014.05.001

¹西北工业大学机电学院,西安 710072;²中国南方航空股份有限公司,广州 510405;³上海交通大学材料科学与工程学院,上海 200030

基金项目: 国家自然科学基金(11172171)

详细信息

作者简介:
孙书蕾（1980—），男，湖北荆门人，博士生(E-mail: bobsunstuy@gmail.com)

中图分类号: O331;O34;TB332
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- 被引次数: 0
出版历程
- 收稿日期: 2013-12-16
- 修回日期: 2014-04-04
- 刊出日期: 2014-05-15

An Anisotropic Hyperelastic Constitutive Model With Fibre Bending Stiffness for Cord-Rubber Composites

¹School of Mechanical Engineering, Northwestern Polytechnical University, Xi’an 710072, P.R.China;²China Southern Airlines Ltd., Guangzhou 510405, P.R.China;³School of Materials Science and Engineering, Shanghai Jiao Tong University,Shanghai 200030, P.R.China

Funds: The National Natural Science Foundation of China(11172171)

摘要

摘要: 针对纤维增强复合材料的有限变形，基于Spencer的连续介质力学不变量理论，提出了一种考虑纤维弯曲刚度的非线性超弹性本构模型.通过引入变形后纤维方向向量的梯度项，把单位体积的自由应变能分解为便于参数识别的体积变形、等容变形、各向异性变形和弯曲刚度4部分.理论和实验分析均表明传统的基于连续介质力学的纤维增强复合材料有限变形理论不适用于弯曲变形，必须考虑纤维弯曲刚度的影响.数值仿真结果也验证了在应变能函数中增加弯曲刚度项是必要的.
- 复合材料 /
- 本构 /
- 超弹性 /
- 弯曲刚度 /
- 各向异性
Abstract: Based on the invariant theory of continuum mechanics by Spencer, an anisotropic nonlinear hyperelastic constitutive model involving fibre bending effect was developed for cord-reinforced rubber composite materials. Through introduction of the gradient of fiber vector after deformation, the unit-volume strain energy function was decomposed into four parts: volumetric, isochoric, anisotropic and bending deformation energy terms, which were convenient for parameter identification. Both the theoretical analysis and experimental study indicate that the traditional finite deformation theory based on the continuum mechanics for fibre-reinforced composite materials is not suitable for bending deformation. With the fibre bending stiffness taken into consideration, the present constitutive model’s correctness is validated by the numerical bending simulation of a previous test.
- composite /
- constitutive /
- hyperelastic /
- bending stiffness /
- anisotropic

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参考文献(13)

[1]	Adkins J E, Rivlin R S. Large elastic deformations of isotropic materials X: reinforcement by inextensible cords[J]. Philosophical Transactions of the Royal Society of London Series A, Mathematical and Physical Sciences,1955,248(944): 201-223.
[2]	Spencer A J M. Deformations of Fibre Reinforced Materials(Science Research Papers) [M]. Oxford: Clarendon Press, 1972.
[3]	Spencer A J M. Constitutive theory for strongly anisotropic solids[C]//Spencer A J M ed. Continuum Theory of the Mechanics of Fibre-Reinforced Composites. CISM Courses and Lectures No 282. Wien: Springer-Verlag, 1984: 1-32.
[4]	Nam T H, MarvalovB. Deformation analysis of inflated cylindrical membrane of composite material with rubber matrix reinforced by cords[C]// XXI International Congress of Theoretical and Applied Mechanics (ICTAM).Warsaw, Poland, 2004.
[5]	Peng X Q, Guo Z Y, Moran B. An anisotropic hyperelastic constitutive model with fiber-matrix shear interaction for the human annulus fibrosus[J]. Journal of Applied Mechanics,2006,73(5): 815-824.
[6]	Holzapfel G A, Gasser T C, Ogden R W. A new constitutive framework for arterial wall mechanics and a comparative study of material models[J]. Journal of Elasticity and the Physical Science of Solids,2000,61(1/3): 1-48.
[7]	Spencer A J M, Soldatos K P. Finite deformations of fibre-reinforced elastic solids with fibre bending stiffness[J]. International Journal of Non-Linear Mechanics,2007,42(2): 355-368.
[8]	Simo J C, Taylor R L. Quasi-incompressible finite elasticity in principal stretches. continuum basis and numerical algorithms[J]. Computer Methods in Applied Mechanics and Engineering,1991,85(3): 273-310.
[9]	Weiss J A, Maker B N, Govindjee S. Finite element implementation of incompressible, transversely isotropic hyperelasticity[J]. Computer Methods in Applied Mechanics and Engineering,1996,135(1/2): 107-128.
[10]	Kaliske M. A formulation of elasticity and viscoelasticity for fibre reinforced material at small and finite strains[J]. Computer Methods in Applied Mechanics and Engineering,2000,185(2/4): 225-243.
[11]	Ogden R W. Nonlinear Elastic Deformations [M]. Mineola, New York: Dover Publication, 1984.
[12]	Zheng Q S. Theory of representations for tensor functions—a unified invariant approach to constitutive equations[J]. Applied Mechanics Reviews,1994,47(11): 545-587.
[13]	Ishikawa S, Tokuda A, Kotera H. Numerical simulation for fibre reinforced rubber[J].Journal of Computational Science and Technology,2008,2(4): 587-596.