Stability Loss in the Structure of Unidirected Fibrous Elastic and Viscoelastic Composites

  • Surkay Akbarov


Internal and near surface stability loss of unidirected fibrous elastic and viscoelastic composites are studied within the scope of the piecewise homogeneous body model using the approach based on the investigation of the evolution of the fibers’ initial infinitesimal imperfections with compressed forces or with time. For this purpose, as in the previous chapters, 3D geometrically nonlinear field equations for viscoelastic bodies are employed.


Contact Condition Laplace Transformation Infinite System Middle Line Zeroth Approximation 
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  1. Akbarov SD, Babazade MB (1987) On the methods of problem solving in mechanics of fibrous composite materials with curved fibers. Deposited in VINITI, CI, ONT. No 4993-B87, 67p (in Russian)Google Scholar
  2. Akbarov SD, Guz AN (1985) Stability of two fibers in an elastic matrix with small strains. Int Appl Mech 21:1–7Google Scholar
  3. Akbarov SD, Guz AN (2000) Mechanics of curved composites. Kluwer Academic Publishers, DortrechtCrossRefzbMATHGoogle Scholar
  4. Akbarov SD, Guz AN (2004) Mechanics of curved composites and some related problems for structural members. Mech Advan Mater Struct 11(6):445–515Google Scholar
  5. Akbarov SD, Kosker R (2001) Fiber buckling in a viscoelastic matrix. Mech Comp Mater 37(4):299–306CrossRefGoogle Scholar
  6. Akbarov SD, Kosker R (2004) Internal stability loss of two neighboring fibers in a viscoelastic matrix. Int J Eng Sci 42 (17/18):1847–1873CrossRefGoogle Scholar
  7. Akbarov SD, Mamedov AR (2009) On the solution method for problems related to the micro-mechanics of a periodically curved fiber near a convex cylindrical surface. CMES: Comput Model Eng Sci 42(3):257–296Google Scholar
  8. Akbarov SD, Mamedov AR (2011) Stability loss of the micro-fiber in the elastic and viscoelastic matrix near the free convex cylindrical surface. Eur J Mech A/Solids 22(2):167–182CrossRefMathSciNetGoogle Scholar
  9. Babaev MS, Guz AN, Cherevko MA (1985) Stability of a series of fibers in an elastic matrix at small subcritical deformations. Int Appl Mech 21(5):443-450zbMATHGoogle Scholar
  10. Babich IYu (1973) On the stability loss of a fiber in a matrix under small deformations. Int Appl Mech 9(4):370–373Google Scholar
  11. Biot MA. (1965) Mechanics of incremental deformations. Wiley, New YorkGoogle Scholar
  12. Guz AN (1990) Fracture mechanics of composites under compression. Naukova Dumka, Kiev (in Russian)Google Scholar
  13. Guz AN (1999) Fundamentals of the Three-dimensional theory of stability of deformable bodies. Springer, Berlin CrossRefzbMATHGoogle Scholar
  14. Guz AN (2008a) Fundamentals of the compressive fracture mechanics of composites: fracture in structure of materials. vol 1 Litera, Kiev (in Russian)Google Scholar
  15. Guz AN (2008b) Fundamentals of the compressive fracture mechanics of composites: related mechanics of fracture. vol 2 Litera, Kiev (in Russian)Google Scholar
  16. Guz AN, Lapusta YuN (1986) Stability of a fiber near a free surface. Int Appl Mech 22 (8):711–719zbMATHGoogle Scholar
  17. Guz AN, Lapusta YuN (1988) Stability of fibers near a free cylindrical surface. Int Appl Mech 24(10):939–944zbMATHGoogle Scholar
  18. Guz AN, Lapusta YuN (1999) Three-dimensional problems of the near-surface instability of fiber composites in compression (Model of a piecewise- uniform medium) (survey). Int Appl Mech 35(7):641–670CrossRefGoogle Scholar
  19. Guz AN, Rushchitsky JJ, Guz IA (2008) Comparative computer modeling of carbon-polimer composites with carbon or graphite microfibers or carbon nanofibers. CMES: Comput Model Eng Sci 26(3):139–156Google Scholar
  20. Kantarovich LV, Krilov VI (1962) Approximate methods in advanced calculus. Moscow, Fizmatgiz, (in Russian).Google Scholar
  21. Lapusta YuN (1988) Stability of fibers near the free surface of a cavity during finite precritical strains. Int Appl Mech 24(5):453–458zbMATHGoogle Scholar
  22. Maligino AR, Warrior NA, Long AC (2009) Effect of inter-fibre spacing on damage evolution in unidirectional (UD) fibre-reinforced composites. Eur J Mech A/Solids 28:768–776CrossRefGoogle Scholar
  23. Qian D, Dickey EC, Andrews R, Rantell T (2000) Load transfer and deformation mechanisms of carbon nanotube-plytyrene composites. Appl Phys Lett 76(20):2868–2870CrossRefGoogle Scholar
  24. Rabotnov YuN (1977) Elements of hereditary mechanics of solid bodies, Nauka, Moscow (in Russian)Google Scholar
  25. Schapery RA (1962) Approximate method of transform inversion for viscoelastic stress analysis. In: Proceeding 4th US National Congress Applied Mechanics ASME : 1075–1085Google Scholar
  26. Schapery RA. (1978) A viscoelastic behaviour of composite materials, in Composite materials, Vol. 1-7, In: Broutman LJ, Krock RH (Eds.) Mir Moscow, translated from English), vol. 2. Mechanics of composite materials, 102–195(in Ruıssion, translated from English)Google Scholar
  27. Schwartz MM (Editor in Chief) (1992) Composite materials handbook, Second edition, Mc Graw-Hill, Inc. New YorkGoogle Scholar
  28. Watson GM (1958) Theory of Bessel functions. Cambridge at the University PressGoogle Scholar
  29. Zhuk YuA, Guz IA (2007) Features of plane wave propagation along the layers of a pre-strained nanocomposites. Int Appl Mech 43(4):361–379CrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Faculty of MechanicsYildiz Technical UniversityBarbaros BulvariTurkey

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