International Applied Mechanics

, Volume 42, Issue 7, pp 729–743 | Cite as

Influence of prestress on the velocities of plane waves propagating normally to the layers of nanocomposites

  • Ya. A. Zhuk
  • I. A. Guz
Article
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Abstract

The paper is concerned with longitudinal and transverse waves propagating at a right angle to the layers of a nanocomposite material with initial (process-induced residual) stresses. The composite consists of alternating layers of two dissimilar materials. The materials are assumed nonlinearly elastic and described by the Murnaghan potential. For simulation of wave propagation, a problem is formulated within the framework of the three-dimensional linearized theory of elasticity for finite prestrains. It is established that the relative velocities of waves depend linearly on small prestresses. In some composite materials, however, the thicknesses of the layers may be in a ratio such that the wave velocities are independent of the prestress level

Keywords

composite materials nanocomposites three-dimensional linearized theory of elasticity initial stress longitudinal and transverse waves wave velocities 
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References

  1. 1.
    L. M. Brekhovskikh, Waves in Layered Media [in Russian], Izd. AN SSSR, Moscow (1957).Google Scholar
  2. 2.
    A. N. Guz, Stability of Elastic Bodies with Finite Strains [in Russian], Naukova Dumka, Kyiv (1973).Google Scholar
  3. 3.
    A. N. Guz, Elastic Waves in Prestressed Bodies [in Russian], in 2 vols., Naukova Dumka, Kyiv (1986).Google Scholar
  4. 4.
    A. N. Guz, Elastic Waves in Bodies with Initial (Residual) Stresses [in Russian], A.S.K., Kyiv (2004).Google Scholar
  5. 5.
    A. N. Guz, A. P. Zhuk, and F. G. Makhort, Waves in a Prestressed Layer [in Russian], Naukova Dumka, Kyiv (1976).Google Scholar
  6. 6.
    A. N. Guz and L. M. Han, “Wave propagation in composite layered materials with large initial deformations,” Int. Appl. Mech., 12, No. 1, 1–7 (1976).MATHGoogle Scholar
  7. 7.
    A. N. Guz, F. G. Makhort, O. I. Gushcha, and V. I. Lebedev, Fundamentals of the Ultrasonic Nondestructive Stress Analysis of Solids [in Russian], Naukova Dumka, Kyiv (1974).Google Scholar
  8. 8.
    S. M. Rytov, “Acoustic properties of fine-stratified medium,” Akust. Zh., 2, No. 1 (68), 71–83 (1956).MathSciNetGoogle Scholar
  9. 9.
    S. D. Akbarov and M. Ozisik, “The influence of the third order elastic constants to the generalized Rayleigh wave dispersion in a pre-stressed stratified half-plane,” Int. J. Eng. Sci., 41, 2047–2061 (2003).CrossRefGoogle Scholar
  10. 10.
    M. Arroyo and T. Belytschko, “Finite element methods for the non-linear mechanics of crystalline sheets and nanotubes,” Int. J. Numer. Meth. Eng., 59, 419–456 (2004).MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    G. S. Attard, P. N. Barlett, N. R. B. Coleman, J. M. Elliott, J. R. Owen, and J. H. Wang, “ Mesoporous platinum films from lyotropic liquid crystalline phases,” Science, 278, 838–840 (1997).CrossRefADSGoogle Scholar
  12. 12.
    L. Brillouin and M. Parodi, Wave Propagation in Periodic Structures, Dover, New York (1953).MATHGoogle Scholar
  13. 13.
    P. J. Dobson, “Nanocomposite optoelectronic materials,” in: Proc. Materials Congress 2000 on Materials for the 21st Century, Cirencester, Gloucestershire, UK, April 12–14 (2000), p. 6.Google Scholar
  14. 14.
    E. Drexler, C. Peterson, and G. Pergami, Unbounding the Future, William Morrow & Company, New York (1991).Google Scholar
  15. 15.
    A. S. Edelstein and R. C. Cammarata, Nanomaterials: Synthesis, Properties and Applications, Institute of Physics Publishing, Bristol (1996).Google Scholar
  16. 16.
    H. L. Frisch, J. M. West, C. G. Golter, and G. S. Attard, “Pseudo IPNs and IPNs of porous silicas and polystyrene,” J. Plym. Sci., A Polym. Chem., 34, 1823–1826 (1996).CrossRefGoogle Scholar
  17. 17.
    S. Govindjee and J. L. Sackman, “On the use of continuum mechanics to estimate the properties of nanotubes,” Solid State Communications, 110, 227–230 (1999).CrossRefGoogle Scholar
  18. 18.
    A. N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies, Springer-Verlag, Berlin (1999).MATHGoogle Scholar
  19. 19.
    A. N. Guz, “On foundation of non-destructive method of determination of three-axial stress in solids, ” Int. Appl. Mech., 37, No. 7, 899–905 (2001).MathSciNetCrossRefGoogle Scholar
  20. 20.
    A. N. Guz and J. J. Rushchitsky, “Nanomaterials: On the mechanics of nanomaterials,” Int. Appl. Mech., 39, No. 11, 1271–1293 (2003).CrossRefGoogle Scholar
  21. 21.
    A. N. Guz, A. A. Rodger, and I. A. Guz, “Developing a compressive failure theory for nanocomposites,” Int. Appl. Mech., 41, No. 3, 233–255 (2005).CrossRefGoogle Scholar
  22. 22.
    I. A. Guz and J. J. Rushchitsky, “Comparing the evolution characteristics of waves in nonlinearly elastic micro-and nanocomposites with carbon fillers,” Int. Appl. Mech., 40, No. 7, 785–793 (2004).CrossRefGoogle Scholar
  23. 23.
    I. A. Guz and J. J. Rushchitsky, “Theoretical description of a delamination mechanism in fibrous micro-and nanocomposites,” Int. Appl. Mech., 40, No. 10, 1129–1136 (2004).Google Scholar
  24. 24.
    O. Lefevre, O. V. Kolosov, A. G. Every, G. A. D. Briggs, and Y. Tsukahara, “Elastic measurements of layered nanocomposite materials by Brillouin spectroscopy,” Ultrasonics, 38, 459–465 (2000).CrossRefGoogle Scholar
  25. 25.
    C. Li and T.-W. Chen, “A structural mechanics approach for the analysis of carbon nanotubes,” Int. J. Solids Struct., 40, 2487–2499 (2003).CrossRefMATHGoogle Scholar
  26. 26.
    Y. J. Liu and X. L. Chen, “Evaluation of the effective material properties of carbon nanotube-based components using a nanoscale representative volume element,” Mech. Mater., 35, 69–81 (2003).CrossRefGoogle Scholar
  27. 27.
    M. Zehetbauer and R. S. Valiev, “Nanomaterials by severe plastic deformation,” in: Proc. Conf. on Nanomaterials by Severe Deformation NANOSPD2 (December 9–13, 2002, Vienna, Austria), John Willey & Sons (2004).Google Scholar
  28. 28.
    G. M. Odegard, T. S. Gates, L. M. Nickolson, and K. P. Wise, “Equivalent-continuum modelling of nano-structured materials,” Composite Sci. & Tech., 62, 1869–1880 (2002).CrossRefGoogle Scholar
  29. 29.
    S. L. K. Pang, A. M. Vassallo, and M. A. Wilson, “Fullerenes from coal: A self consistent preparation and purification process,” Energy and Fuels, 6, 176–179 (1992).CrossRefGoogle Scholar
  30. 30.
    J. J. Rushchitsky, C. Cattani, and E. V. Terletskaya, “Wavelet analysis of a single pulse in a linearly elastic composite,” Int. Appl. Mech., 41, No. 4, 374–380 (2005).CrossRefGoogle Scholar
  31. 31.
    G. Smith, G. Davies, and O. Sax, “Counting up the benefits of nanotechnology,” Materials World, 8, No. 1, 10–12 (2000).Google Scholar
  32. 32.
    B. Bhushan (ed.), Springer Handbook on Nanotechnology, Springer-Verlag, Berlin-Heidelberg (2004).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Ya. A. Zhuk
    • 1
  • I. A. Guz
    • 2
  1. 1.S. P. Timoshenko Institute of MechanicsNational Academy of Sciences of UkraineKyiv
  2. 2.Centre for Micro-and NanomechanicsUniversity of AberdeenScotland

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