Mechanics of Composite Materials

, Volume 41, Issue 4, pp 291–302 | Cite as

Stress Distribution in an Infinite Elastic Body with a Locally Curved Fiber in a Geometrically Nonlinear Statement

  • S. D. Akbarov
  • R. Kosker
  • K. Simsek


Within the framework of a piecewise homogeneous body model, with the use of three-dimensional geometrically nonlinear exact equations of elasticity theory, a method for determining the stress—strain state in unidirectional fibrous composites with locally curved fibers is developed for the case where the interaction between the fibers is neglected. All the investigations are carried out for an infinite elastic body containing a single locally curved fiber. Numerical results illustrating the effect of geometrical nonlinearity on the distribution of the self-balanced normal and shear stresses acting on the interface and arising as a result of local curving of the fiber are presented.


fibrous composites local curving geometrical nonlinearity stress distribution 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Yu. M. Tarnopol’skii, V. I. Zhigun, and V. A. Polyakov, Spatially Reinforced Composite Materials, Handbook [in Russian], Mashinostroenie, Moscow (1987).Google Scholar
  2. 2.
    A. N. Guz’, Failure Mechanics of Composite Materials in Compression [in Russian], Naukova Dumka, Kiev (1990).Google Scholar
  3. 3.
    A. Kelly, “Composite materials: impediments to wider use and some suggestions to overcome them,” in: Proceedings of ECCM-8, 3–6 June, Napoles, Italy. Vol. I (1998), pp. 15–18.Google Scholar
  4. 4.
    S. D. Akbarov and A. N. Guz’, Mechanics of Curved Composites, Kluwer Academic Publ. (2000).Google Scholar
  5. 5.
    A. N. Guz’, “A two-level model in the mesomechanics of compression fracture of cracked composites,” Int. Appl. Mech., 39, No.3, 274–285 (2003).CrossRefGoogle Scholar
  6. 6.
    S. D. Akbarov and A. N. Guz’, “Method of solving problem in the mechanics of fiber composites with curved structures,” Sov. Appl. Mech., No. 3, 777–785 (March, 1985).Google Scholar
  7. 7.
    S. D. Akbarov and A. N. Guz’, “Mechanics of curved composites (piecewise homogeneous body model),” Int. Appl. Mech., 38, No.12, 1415–1439 (2002).CrossRefGoogle Scholar
  8. 8.
    R. Kosker and S. D. Akbarov, “Influence of the interaction between two neighboring periodically curved fibers on the stress distribution in a composite material,” Mech. Compos. Mater., 39, No.2, 165–176 (2003).CrossRefGoogle Scholar
  9. 9.
    S. D. Akbarov and R. Kosker, “On a stress analysis for an infinite elastic body with two neighboring curved fibers,” Composites, Pt. B: Eng., 34, No.2, 143–150 (2003).Google Scholar
  10. 10.
    E. K. Dzhafarova, “Solution method for stress-strain state problems in fibrous composites with locally curved structures,” in: Proceedings of Young Scientists’ Conference, Pt. I [in Russian], Institute of Mechanics of the Ukrainian Academy of Sciences, Kiev (1992), pp. 39–44.Google Scholar
  11. 11.
    E. K. Dzhafarova, “Distribution of self-equilibrated stresses in fibrous composite materials with local curvings in their structures,” Dep. in VINITI 07.09.94, No. 2166-B94 [in Russian] (1994).Google Scholar
  12. 12.
    E. K. Dzhafarova, Stress State in Composite Materials with Locally Curved Fibers, Candidate’s Dissertation [in Russian], Institute of Mathematics and Mechanics of the National Academy of Sciences of Azerbaijan, Baku (1995).Google Scholar
  13. 13.
    A. N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies, Springer (1999).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • S. D. Akbarov
    • 1
    • 2
  • R. Kosker
    • 1
  • K. Simsek
    • 3
  1. 1.Faculty of Chemistry and MetallurgyYildiz Technical UniversityIstanbulTurkey
  2. 2.Institute of Mathematics and MechanicsNational Academy of Sciences of AzerbaijanBakuAzerbaijan
  3. 3.Faculty of Art and SciencesYildiz Technical UniversityIstanbulTurkey

Personalised recommendations