Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Remarks on instabilities and ellipticity for a fiber-reinforced compressible nonlinearly elastic solid under plane deformation

Authors: J. Merodio and R. W. Ogden
Journal: Quart. Appl. Math. 63 (2005), 325-333
MSC (2000): Primary 74B20
DOI: https://doi.org/10.1090/S0033-569X-05-00954-1
Published electronically: February 18, 2005
MathSciNet review: 2150778
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we examine loss of ellipticity and associated failure for fiber-reinforced compressible nonlinearly elastic solids under plane deformation. The analysis concerns a material model that consists of an isotropic base material augmented by a reinforcement dependent on the fiber direction. We examine reinforcement that introduces additional stiffness under shear deformations. It is shown that loss of ellipticity may be associated with, in particular, a weak surface of discontinuity normal to or parallel to the deformed fiber direction or at an intermediate angle. More particularly, under uniaxial loading in the fiber direction loss of ellipticity may be associated with different failure mechanisms. Under compression these include fiber kinking and fiber splitting, while under extension the relevant mechanism is matrix failure.

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  • 1. J. Merodio and R. W. Ogden, Material instabilities in fiber-reinforced nonlinearly elastic solids under plane deformation, Arch. Mech. (Arch. Mech. Stos.) 54 (2002), no. 5-6, 525–552. MR 1964402
  • 2. J. Merodio and R. W. Ogden, Instabilities and loss of ellipticity in fiber-reinforced compressible non-linearly elastic solids under plane deformation, Internat. J. Solids Structures 40 (2003), no. 18, 4707–4727. MR 1994903, https://doi.org/10.1016/S0020-7683(03)00309-3
  • 3. J. Merodio and R. W. Ogden, A note on strong ellipticity for transversely isotropic linearly elastic solids, Quart. J. Mech. Appl. Math. 56 (2003), no. 4, 589–591. MR 2026873, https://doi.org/10.1093/qjmam/56.4.589
  • 4. J. Merodio, R.W. Ogden. On tensile instabilities and ellipticity loss in fiber-reinforced incompressible nonlinearly elastic solids. Mech. Res. Comm., in press (2004).
  • 5. J. Merodio, R.W. Ogden. Mechanical response of fiber-reinforced incompressible nonlinearly elastic solids. Int. J. Nonlinear Mech. 40, 213-227 (2005).
  • 6. J. Merodio, R.W. Ogden. Tensile instabilities and ellipticity in fiber-reinforced compressible nonlinearly elastic solids. Int. J. Engng Sci., submitted (2004).
  • 7. C.S. Yerramalli, A.M. Waas. A nondimensional number to classify composite compressive failure. J. Appl. Mech. 71, 402-408 (2004).
  • 8. Ogden, R.W., 1984. Non-linear Elastic Deformations. Ellis Horwood, Chichester.MR 0770388 (86h:73011)
  • 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).

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Additional Information

J. Merodio
Affiliation: Department of Structural and Mechanical Engineering, E.T.S. de Ingenieros Industriales y de Telecomunicación, University of Cantabria, 39005, Santander, Spain
Email: merodioj@unican.es

R. W. Ogden
Affiliation: Department of Mathematics, University of Glasgow, Glasgow G12 8QW, United Kingdom
Email: rwo@maths.gla.ac.uk

DOI: https://doi.org/10.1090/S0033-569X-05-00954-1
Keywords: Nonlinear elasticity, loss of ellipticity, fiber reinforcement, reinforcing models, transverse isotropy
Received by editor(s): June 18, 2004
Published electronically: February 18, 2005
Article copyright: © Copyright 2005 Brown University

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