A note on tensile instabilities and loss of ellipticity for a fiber-reinforced nonlinearly elastic solid

• Autorzy: Merodio J. , Neff P.
• Języki publikacji: EN

Abstrakty

EN

In this paper we examine the loss of ellipticity and the associated failure of fiber-reinforced compressible nonlinearly elastic solids under deformations leading to fiber extension. In particular, the analysis concerns a material model that consists of an isotropic base material augmented by a reinforcement depending on the fiber direction and referred to as a reinforcing model. We examine a reinforcement that introduces additional stiffness under simple shear deformations in the fiber direction. In previous contributions it was shown for this material that loss of ellipticity under uniaxial tensile loading in the fiber direction requires a non-convex reinforcing model. Here we generalize this result and show that loss of ellipticity under plane deformations not associated with uniaxial loading in the fiber direction but also creating fiber extension may occur for convex reinforcing models.

Słowa kluczowe

EN

nonlinear elasticity; loss of ellipticity; fibre reinforcement; reinforcing models; transverse isotropy

PL

nieliniowa sprężystość; utrata eliptyczności; wzmocnienie włóknem; modele wzmocnienia; izotropia poprzeczna

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2006
• Tom: Vol. 58, nr 3
• Strony: 293--303
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Merodio J.

autor

Neff P.

• Department of Continuum Mechanics and Structures E. T. S. Ing. Caminos, Canales y Puertos, Universidad Politecnica de Madrid 28040, Madrid, Spain

Bibliografia

• 1. S. HARTMANN, P. NEFF Polyconvexity of generalized polynomial type hyperelastic strain energy functions for near incompressibility, Int. J. Solids Struct., 40, 2767-2791, 2003.
• 2. J. SCHRODER, P. NEFF, Invariant formulation of hyperelastic transverse isotropy based on poly convex free energy functions, Int. J. Solids Struct., 40, 401-445, 2003.
• 3. J. SCHRODER, P. NEFF, D. BALZANI, A variational approach for materially stable anisotropic hyperelasticity, Int. J. Solids Struct., 42, 4352-4371, 2004.
• 4. J.C. CRISCIONE, A.S. DOUGLAS, W.C. HUNTER, Physically based strain invariant set for materials exhibiting transversely isotropic behavior, J. Mech. Phys. Solids, 49, 871-897, 2001.
• 5. J. MERODIO, R.W. OGDEN, Mechanical response of fiber-reinforced incompressible non-linearly elastic solids. Int. J. Nonlinear Mech., 40, 213-227, 2005.
• 6. 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.
• 7. J. MERODIO and G. SACCOMANDI, Remarks on cavity formation in fiber-reinforced incompressible nonlinearly elastic materials, Eur. J. Mech., Solids/A, to appear 2006.
• 8. J. MERODIO, R.W. OGDEN, Material instabilities in fiber-reinforced nonlinearly elastic solids under plane deformation, Arch. Mech., 54, 525-552, 2002.
• 9. J. MERODIO, R.W. OGDEN, Instabilities and loss of ellipticity in fiber-reinforced compressible non-linearly elastic solids under plane deformation. Int. J. Solids Structures 40, 4707-4727, 2003.
• 10. J. MERODIO, R.W. OGDEN A note on strong ellipticity for transversely isotropic linearly elastic solids. Q. J. Mech. Appl. Math.. 56, 589-591, 2003.
• 11. J. MERODIO, R.W. OGDEN On tensile instabilities and ellipticity loss in fiber-reinforced incompressible nonlinearly elastic solids, Mech. Res. Comm., 32, 290-299, 2005.
• 12. J. MERODIO, R.W. OGDEN, Tensile instabilities and ellipticity in fiber-reinforced compressible nonlinearly elastic solids, Int. J. Engng Sci., 43, 697-706, 2005.
• 13. J. MERODIO, R.W. OGDEN, Remarks on tensile instabilities and ellipticity for a compressible reinforced nonlinearly elastic solids, Q. Appl. Math., 63, 325-333, 2005.