Strength of Materials

, Volume 16, Issue 6, pp 779–784 | Cite as

Mathematical description of transient creep

  • É. I. Blinov
Scientific-Technical Section
Received:
  • 18 Downloads

Conclusions

  1. 1.

    We observed a qualitative agreement between results obtained by extending a simplified variant of the kinetic strain theory to the class of generalized functions on the one hand and data from [3] on viscoelastic media based on completely different premises on the other hand.

     
  2. 2.

    By replacing the first-order time derivatives by fractional derivatives in the governing equations of any variant of viscoelasticity or viscoplasticity, it is possible to obtain Volterra-type integral equations with kernels retaining a singularity of type found in an Abel kernel for the purpose of describing the initial stage of relaxation and creep of materials.

     

Keywords

Generalize Function Integral Equation Governing Equation Time Derivative Fractional Derivative 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Literature Cited

  1. 1.
    Yu. N. Rabotnov and S. T. Mileiko, Short-Term Creep [in Russian], Nauka, Moscow (1970).Google Scholar
  2. 2.
    K. N. Rusinko and É. I. Blinov, “Analytical description of the thermoelastoplastic deformation of a solid,” Prikl. Mekh.,17, No. 11, 48–53 (1981).Google Scholar
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    Yu. N. Rabotnov, Creep Problems in Structural Members, Elsevier (1972).Google Scholar
  4. 4.
    S. I. Meshkov, Viscoelastic Properties of Metals [in Russian], Nauka, Moscow (1974).Google Scholar
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    G. A. Korn and T. M. Korn, Manual of Mathematics, McGraw-Hill (1967).Google Scholar
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    I. M. Gel'fand and G. E. Shilov, Generalized Functions: Properties and Operations, Academic Press (1964).Google Scholar
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    A. M. Borzdyka and L. B. Getsov, Stress Relaxation in Metals and Alloys [in Russian], Metallurgiya, Moscow (1978).Google Scholar
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    Yu. N. Rabotnov, L. Kh. Panernik, and E. N. Zvonov, Tables of Rational-Exponential Functions of Negative Parameters and Their Integrals [in Russian], Nauka, Moscow (1969).Google Scholar

Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • É. I. Blinov

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