Advertisement

Initial Deformations On Behaviour Of Elastic Composites

  • Eduard Marius Craciun
Part of the Solid Mechanics And Its Applications book series (SMIA, volume 154)

Mathematical modelling of the incremental fields in a pre-stressed elastic composite in plane and antiplane states is done using complex variable theory. We formulate and solve the crack problem in all three classical modes by using complex potentials. Following Guz, and using the theory of Riemann-Hilbert problem, Cauchy's integral, Plemelj's functions we obtain the asymptotic behavior of the incremental fields in the vicinity of the crack tip. We obtain the critical values of the incremental stresses which produce crack propagation.

Keyword

pre-stressed elastic composite crack Riemann-Hilbert problem complex potentials resonance 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Cristescu N., Craciun E., Soós E. (2003): Mechanics of Elastic Composites. CRC Press, Chapmann&HallGoogle Scholar
  2. 2.
    Eringen A., Maugin G. (1990): Electrodynamics of Continua, vol. I, Foundations and Solid Media. Springer, New YorkGoogle Scholar
  3. 3.
    Guz A. (1971): Stability of Three-Dimensional Deformable Bodies. Naukova Dumka, Kiev, in RussianGoogle Scholar
  4. 4.
    Guz A. (1983): Mechanics of Brittle Fracture of Materials, with Initial Stresses. Naukova Dumka, Kiev, in RussianGoogle Scholar
  5. 5.
    Guz A. (1983): Mechanics of Brittle Fracture of Prestressed Materials. Visha Schola, Kiev, in RussianGoogle Scholar
  6. 6.
    Guz A. (1986): Fundamentals of Three-Dimensional Theory of Stability of Deformable Bodies. Visha Schola, Kiev, in RussianGoogle Scholar
  7. 7.
    Guz A. (1991): Brittle fracture of materials with initial stress. In: A. Guz (red.) Non-Classical Problems of Fracture Mechanics, tom II, Naukova Dumka, Kiev, in Russian, 27–74Google Scholar
  8. 8.
    Lekhnitski S. (1963): Theory of Elasticity of Aniosotropic Elastic Body. Holden Day, San FranciscoGoogle Scholar
  9. 9.
    Ogden R. (1984): Non-Linear Elastic Deformations. Wiley, New YorkGoogle Scholar
  10. 10.
    Sih G., Leibowitz H. (1968): Mathematical theories of brittle fracture. W: H. Lebowitz (red.) Fracture — An Advanced Treatise, Vol. II. Mathematical Fundamentals, str. 68–191, Academic Press, New YorkGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Faculty of Mathematics and InformaticsOvidius University ConstantaRomania

Personalised recommendations