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Keywords: composite, hyperelasticity, fibre reinforced composite, neo-Hookean, constitutive modelling, transverse isotropy, fibre-matrix shear interaction.

Summary

In this paper, the mechanical behaviour of an incompressible neo-Hookean material directionally reinforced with a generalised neo-Hookean fibre is investigated both theoretically and numerically in the finite deformation regime.

By using appropriate rigid body rotation and choosing appropriate coordinate axes, a multiplicative decomposition scheme of deformation is introduced [1] so that any isochoric deformation can be decomposed into two steps: the uniaxial deformation along the fibre direction, and the remaining shear deformation, including the along fibre shear, and transverse shear. Based on this decomposition, the strain energy associated with the uniaxial deformation along the fibre direction can be obtained analytically. The strain energy associated with shear deformation is estimated by extending the traditional composite theory in infinitesimal elasticity to the finite deformation regime. The Halpin-Tsai equations [2] are adopted to obtain the effective shear stiffness. The strain energy function for the fibre-reinforced composite can then be developed for general deformation state.

To verify the proposed theoretical model, a unit cell model is developed to simulate the macroscopic mechanical responses of the fibre reinforced composite. Periodic boundary conditions are applied to the unit cell model. Eight types of single or combined deformation are simulated for general deformation state. The strain energy stored in the unit cell for each case is compared with the energy predicted by the proposed theoretical model and excellent agreement is reported.

References

1: Z.Y. Guo, X.Q. Peng, B. Moran, "A composites-based hyperelastic constitutive model for soft tissue with application to the human annulus fibrosus", Journal of the Mechanics and Physics of Solids, 54 (9), 1952-1971, 2006. doi:10.1016/j.jmps.2006.02.006
2: J.C. Halpin, K.M. Finlayson, Primer on composite materials analysis, 2nd Edition, Technomic Pub. Co., Lancaster, Pa., 1992.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 85 PROCEEDINGS OF THE FIFTEENTH UK CONFERENCE OF THE ASSOCIATION OF COMPUTATIONAL MECHANICS IN ENGINEERING Edited by: B.H.V. Topping Paper 64 Numerical Simulation of Large Deformation Response of Hyperelastic Fibre Reinforced Composites Z.Y. Guo¹, X.Q. Peng² and B. Moran³ ¹Departments of Mechanical and Civil Engineering, University of Glasgow, United Kingdom ²Department of Mechanical Engineering, Northwestern Polytechnical University, Xi'an, Shaanxi, P.R. China ³Department of Civil and Environmental Engineering, Northwestern University, Evanston IL, United States of America doi:10.4203/ccp.85.64 purchase the full-text of this paper Full Bibliographic Reference for this paper Z.Y. Guo, X.Q. Peng, B. Moran, "Numerical Simulation of Large Deformation Response of Hyperelastic Fibre Reinforced Composites", in B.H.V. Topping, (Editor), "Proceedings of the Fifteenth UK Conference of the Association of Computational Mechanics in Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 64, 2007. doi:10.4203/ccp.85.64 Keywords: composite, hyperelasticity, fibre reinforced composite, neo-Hookean, constitutive modelling, transverse isotropy, fibre-matrix shear interaction. Summary In this paper, the mechanical behaviour of an incompressible neo-Hookean material directionally reinforced with a generalised neo-Hookean fibre is investigated both theoretically and numerically in the finite deformation regime. By using appropriate rigid body rotation and choosing appropriate coordinate axes, a multiplicative decomposition scheme of deformation is introduced [1] so that any isochoric deformation can be decomposed into two steps: the uniaxial deformation along the fibre direction, and the remaining shear deformation, including the along fibre shear, and transverse shear. Based on this decomposition, the strain energy associated with the uniaxial deformation along the fibre direction can be obtained analytically. The strain energy associated with shear deformation is estimated by extending the traditional composite theory in infinitesimal elasticity to the finite deformation regime. The Halpin-Tsai equations [2] are adopted to obtain the effective shear stiffness. The strain energy function for the fibre-reinforced composite can then be developed for general deformation state. To verify the proposed theoretical model, a unit cell model is developed to simulate the macroscopic mechanical responses of the fibre reinforced composite. Periodic boundary conditions are applied to the unit cell model. Eight types of single or combined deformation are simulated for general deformation state. The strain energy stored in the unit cell for each case is compared with the energy predicted by the proposed theoretical model and excellent agreement is reported. References 1 Z.Y. Guo, X.Q. Peng, B. Moran, "A composites-based hyperelastic constitutive model for soft tissue with application to the human annulus fibrosus", Journal of the Mechanics and Physics of Solids, 54 (9), 1952-1971, 2006. doi:10.1016/j.jmps.2006.02.006 2 J.C. Halpin, K.M. Finlayson, Primer on composite materials analysis, 2nd Edition, Technomic Pub. Co., Lancaster, Pa., 1992. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £75 +P&P)
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