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A note on finite elastic deformations of fiber-reinforced non-linearly elastic tubes

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A fibre-reinforced non-linearly elastic tube subject to a finite radially symmetric deformation given by the combination of axial stretch, radial deformation and torsion is analysed. The deformation is supported by axial load, internal pressure and end moment. The materials at hand are neo-Hookean models augmented with a function that accounts for the existence of a unidirectional reinforcement. This function endows the material with its anisotropic character and is referred to as a reinforcing model. The nature of the considered anisotropy has a particular influence on the shear response of the material, in contrast to previous analyses in which the reinforcing model was taken to depend only on the stretch in the fibre direction. Furthermore, the ellipticity analysis of the deformations at hand has been carried out. It is shown that most of the deformations are non-elliptic, which opens the possibility to discontinuous solutions.
Rocznik
Strony
95--109
Opis fizyczny
Bibliogr. 14 poz., rys.
Twórcy
  • Department of Continuum Mechanics and Structures Universidad Politécnica de Madrid 28040, Madrid, Spain
autor
  • Department of Continuum Mechanics and Structures Universidad Politécnica de Madrid 28040, Madrid, Spain
Bibliografia
  • 1. M. El Hamdaoui, J. Merodio, R.W. Ogden, J. Rodríguez, Finite elastic deformations of transversely isotropic circular cylindrical tubes, International Journal of Solids and Structures, 51, 5, 1188–1196, 2014.
  • 2. J. Merodio, R.W. Ogden, Remarks on instabilities and ellipticity for a fiber-reinforced compressible nonlinearly elastic solid under plane deformation, Quarterly of Applied Mathematics, 63, 2, 325–333, 2005.
  • 3. J. Merodio, P. Neff, A note on tensile instabilities and loss of ellipticity for a fiber reinforced nonlinearly elastic solid, Archives of Mechanics, 58, 3, 293–303, 2006.
  • 4. J. Merodio, R.W. Ogden, Tensile instabilities and ellipticity in fiber-reinforced compressible non-linearly elastic solids, International Journal of Engineering Science, 43, 89, 697–706, 2005.
  • 5. S.H Lee, C.S. Yerramalli, A.M Waas, Compressive splitting response of glass-fiber reinforced unidirectional composites Composites Science and Technology, 60, 16, 2957–2966, 2000.
  • 6. R.S. Rivlin, D.W. Saunders, Large elastic deformations of isotropic materials. VII: experiments on the deformation of rubber, 243, 865, 251–288, 1951.
  • 7. A.N. Gent, R.S. Rivlin, Experiments on the mechanics of rubber, II: The torsion, inflation and extension of a tube, Proceedings of the Physical Society. Section B, 65, 7, 487, 1952.
  • 8. L. Kanner, C. Horgan, On extension and torsion of strain-stiffening rubber-like elastic circular cylinders, Journal of Elasticity, 93, 1, 39–61, 2008.
  • 9. C. Horgan, D. Polignone, A note on the pure torsion of a circular cylinder for a compressible nonlinearly elastic material with nonconvex strain-energy, Journal of Elasticity, 37, 2, 167–178, 1994.
  • 10. D.M. Haughton, R.W. Ogden, Bifurcation of inflated circular cylinders of elastic material under axial loading. Mmbrane theory for thin-walled tubes, Journal of the Mechanics and Physics of Solids, 27, 3, 179–212, 1979.
  • 11. J. Merodio, D.M. Haughton, Bifurcation of thick-walled cylindrical shells and the mechanical response of arterial tissue affected by marfans syndrome, Mechanics Research Communications, 37, 1, 1–6, 2010.
  • 12. J. Rodríguez, J. Merodio, A new derivation of the bifurcation conditions of inflated cylindrical membranes of elastic material under axial loading. Application to aneurysm formation, Mechanics Research Communications, 38, 3, 203–210, 2011.
  • 13. J. Merodio, R.W. Ogden, Mechanical response of fiber-reinforced incompressible nonlinearly elastic solids, International Journal of Non-Linear Mechanics, 40, 23, 213–227, 2005.
  • 14. J.G. Murphy, Transversely isotropic biological, soft tissue must be modelled using both anisotropic invariants, European Journal of Mechanics - A/Solids, 42, 90–96, 2013.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-ecdbf127-9876-4d6d-8f45-cdb85817cf12
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