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Constitutive Prediction for a Non-Linear Orthotropic Media

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Mechanical Identification of Composites

Abstract

Linearly elastic behaviour of paper is described by four independent in — plane constants. Elastic constants depend on probability density functions for length and orientation and also on a coupling network parameter between fibers. It is shown here that the ratio of machine to cross direction Young’s moduli determines the fibre orientation parameter. All constants then simply depend on one network parameter and one orientation parameter.

We can describe the behaviour of a thin non-linear orthotropic plate using an asymptotic expansion method. We apply in this paper the theory proposed by Johnson to an assumed form of the elastic strain energy function. Linear or non-linear biaxial behaviour of such a material is then obtained from ordinary tests.

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References

  1. Jones, R. M., Mechanics of Composite Materials, Mc Graw-Hill, New York, 1975.

    Google Scholar 

  2. Schulgasser, K., Fiber Science and technology, 1975, 15, pp.257–270.

    Article  Google Scholar 

  3. Campbell, J.G., J. Appl. Sci., 1961, 12, p. 356.

    Google Scholar 

  4. Horio M., Onogi S., J. Appl. Phys. 22, 7, p.971, July 1951.

    Article  CAS  Google Scholar 

  5. Gunderson D., ESPRA Conf., Wisconsin Rapids, Wisconsin, May 1984.

    Google Scholar 

  6. Jones A.R., Tappi, vol. 51, n° 5, May 1968.

    Google Scholar 

  7. Van den Akker J.A., The Formation and Structure of Paper, 1962, Clowes and Sons, London, pp.205–209.

    Google Scholar 

  8. Cox H.L., Brit, J. of Appl. Phys. 3, p.72, 1952.

    Article  Google Scholar 

  9. Perkins R.W. and Mark R.E., Proc. The Role of Fundamental Research in papermaking. Mech. Eng. Publ. Ltd, London, 1983.

    Google Scholar 

  10. Perkins R.W., Proc. of the Conf. of Paper Science and Technology. The cutting edge, Institute of Paper Chemistry, Appleton, p.89, 1980.

    Google Scholar 

  11. Perkins R.W., International Paper Physics Conference, p. 83, 1983.

    Google Scholar 

  12. Eusufzai A., Sheet structure in relation to internal network geometry and fiber orientation distribution, Thesis Univ. of New-York, Syracuse, March 1982.

    Google Scholar 

  13. Schulgasser K., J. of Materials Science, 20, p.859, 1985.

    Article  Google Scholar 

  14. Prud’homme R.E., J. Appl. Polym. Sci., 19, p.2609, 1975.

    Google Scholar 

  15. Silvy J., Doc. FCI E.F.P., Grenoble IRFIP, SE 92 46, 1976.

    Google Scholar 

  16. Jones R.W., Tappi 63, p. 163, 1980.

    Google Scholar 

  17. Rigdhal M., Fibre Science and Technology, 19, p.927, 1983.

    Google Scholar 

  18. Petit, Waddoups, J. of Comp. Mat., vol.14, n°l, pp.2–19, 1969.

    Article  Google Scholar 

  19. Jones R.W., J. of Comp. Mat., vol.9, n°l, pp.10–27, 1975.

    Article  Google Scholar 

  20. Tsai. J. of Comp. Mat., vol.7, n°l, pp.102–118, 1973.

    Google Scholar 

  21. Johnson. J. of Appl. Mech., vol. 51, n°l, pp.146–152, 1984.

    Article  Google Scholar 

  22. Urbanik T. J., Effects of paperboard stress-strain characteristics on strength of singlewall corrugated fiberboard: a theorical approach. USDA Forest Service, Research Paper FPL 401, 1981.

    Google Scholar 

  23. El Hosseiny, The stress-strain curve of fibrous networks. Tappi 62, 10, 127, pp.181–187, 1979.

    Google Scholar 

  24. Ramberg W., Osgood W.R., Description of stress-strain curves by three parameters. Naca Technical Note n° 902, 1975.

    Google Scholar 

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© 1991 Elsevier Science Publishers Ltd

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Huchon, R., Pouyet, J., Silvy, J. (1991). Constitutive Prediction for a Non-Linear Orthotropic Media. In: Vautrin, A., Sol, H. (eds) Mechanical Identification of Composites. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3658-7_18

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  • DOI: https://doi.org/10.1007/978-94-011-3658-7_18

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-85166-694-2

  • Online ISBN: 978-94-011-3658-7

  • eBook Packages: Springer Book Archive

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