Material instabilities in fiber-reinforced nonlinearly elastic solids under plane deformation

• Autorzy: Merodio J. , Ogden R. W.
• Języki publikacji: EN

Abstrakty

EN

Material instabilities in fiber-reinforced nonlinearly elastic solids are examined under plane deformation. In particular, the materials under consideration are isotropic nonlinearly elastic models augmented by a function that accounts for the existence of a unidirectional reinforcing. This function describes the anisotropic (transversely isotropic) character of the material and is referred to as a reinforcing model. The onset of failure is signalled by the loss of ellipticity of the governing differential equations. Previous work has dealt with the analysis of specific reinforcing models and has established that the loss of ellipticity for such augmented isotropic materials requires contraction in the reinforcing direction. The loss of ellipticity was related to fiber kinking. Here we generalize these results and establish sufficient conditions for the ellipticity of the governing equations of equilibrium for more general reinforcing models to be guaranteed. We also establish necessary conditions for failure of ellipticity. The incipient loss of ellipticity is interpreted in terms of fiber kinking, fiber de-bonding, fiber splitting and matrix failure in fiber-reinforced composite materials. Attention is restricted to incompressible materials in this paper.

Słowa kluczowe

EN

fiber failure; fiber kinking; fiber de-bonding; fiber splitting; matrix failure; loss of ellipticity; reinforcing models; anisotropy

PL

uszkodzenie włókna; zaginanie wlókna; rozszczepienie włókna; rozłączenie włókna; uszkodzenie matrycy; anizotropia

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2002
• Tom: Vol. 54, nr 5-6
• Strony: 525--552
• Opis fizyczny: Bibliogr. 23 poz.

Twórcy

autor

Merodio J.

• Department of Structural and Mechanical Engineering, E. T. S. Ing. Industriales y Tel., University of Cantabria, 39005, Santander, Spain

autor

Ogden R. W.

• Department of Mathematics, University of Glasgow Glasgow G12 8QW, UK

Bibliografia

• 1. B. Budiansky and N. A. Fleck, Compressive failure of fiber composites, J. Mech. Phys. Solids, 41, 183 211, 1993.
• 2. B. Budiansky, N. A. Fleck and J. C. Amazigo, On kink-band propagation in fiber composites, J. Mech. Phys. Solids, 9. 1637 1653, 1998.
• 3. P. M. Moran and C. F. Sum, Kink band formation and band broadening in ductile matrix fiber composites: experiments and analysis, Int. J. Solids Structures, 35, 1709 1722, 1998.
• 4. S. Kyriakides, R. Arseculerane, E. Perry and K. M. Liechti, On the compressive failure of fiber reinforced composites, Int. J. Solids Structures, 32, 689-738, 1995.
• 5. T. J. Vogler and S. Kyriakides, Initiation and axial propagation of kink bands in fiber composites, Acta Metall. Mater., 45, 2443-2454, 1997.
• 6. H. M. Jensen and J. Christoffersen, Kink band formation in fiber reinforced materials, J. Mech. Phys. Solids, 45, 1121-1136, 1997.
• 7. J. Merodio and T. J. Pence, Kink surfaces in a directionally reinforced neo-Hookean material under plane deformation: I. Mechanical equilibrium, J. Elasticity, 62, 119-144, 2001.
• 8. J. Merodio and T. J. Pence, Kink surfaces in a directionally reinforced neo-Hookean material under plane deformation: II. Kink band stability and maximally dissipative band broadening, J. Elasticity, 62, 145-170, 2001.
• 9. S. H. Lee, C. S. Yerramalli, A. M. Waas, Compressive splitting response of glass-fiber reinforced unidirectional composites, Composites Science and Technology, 60, 2957-2966, 2000.
• 10. M. R. Piggott, Why interface testing by single-fibre methods can be misleading, Composites Science and Technology, 57, 965-974, 1997.
• 11. T. Okabe, J. Komotori, M. Shimizu, N. Takeda, Mechanical behavior of SiC fiber reinforced brittle-matrix composites, Journal of Material Science, 34, 3405 3412, 1999.
• 12. K. Liao and K. L. Reifsnider, A tensile model for unidirectional fiber-reinforced brittle matrix composite, Int. J. Fracture, 106, 95 115, 2000.
• 13. J. K. Knowles and E. Sternberg, On the ellipticity of the equations of nonlinear elastostatics for a special material, J. Elasticity, 5, 341 361, 1975.
• 14. L. Zee and E. Sternberg, Ordinary and strong ellipticity m the equilibrium theory of incompressible hyperelastic solids, Arch. Rat. Mech. Anal., 83, 50-90, 1983.
• 15. P. Rosakis, Ellipticity and deformations with discontinuous gradients in plane elastostatics of compressible solids, Arch. Rat. Mech. Anal., 109, 1 37, 1990.
• 16. C. O. Horgan, Remarks on ellipticity for the generalized Blatz-Ko constitutive model for a compressible nonlinearly elastic solid, J. Elasticity, 42, 165-176, 1996.
• 17. J. K. Knowles and E. Sternberg, On the failure of ellipticity and the emergence of discontinuous deformation gradients in plane finite elastostatics, J. Elasticity, 8, 329 379, 1978.
• 18. G. Y. Qiu and T. J. Pence, Loss of ellipticity in plane deformations of a simple directionally reinforced incompressible nonlinearly elastic solid, J. Elasticity, 49, 31 63, 1997.
• 19. N. Triantafyllidis and R. C. Abeyaratne, Instability of a finitely deformed fiber- reinforced elastic material, J. Appl. Mech., 50, 149-156, 1983.
• 20. R. C. Abeyaratne, Discontinuous deformation gradients tn plane finite elastostatics of incompressible materials, J. Elasticity, 10, 255 293, 1980.
• 21. A. J. M. Spencer, Deformations of fibre-reinforced materials, Oxford University Press, 1972.
• 22. A. E. H. Love, A treatise on the mathematical theory of elasticity, 4th Edition, Dover Publications, New York 1944.
• 23. R. W. Ogden, Non-linear elastic deformations, Ellis Horwood, Chichester 1984.