Advertisement

Mechanics of Solids

, Volume 53, Issue 3, pp 277–283 | Cite as

Influence of Medium Nonlocality on Distribution of Temperature and Stresses in Elastic Body under Pulsed Heating

  • I. Yu. SavelievaEmail author
Article
  • 6 Downloads

Abstract

An approach to constructing mathematical models of thermomechanical processes in a deformable body is considered by the rational thermodynamic relations of irreversible processes for a continuous medium with intrinsicstate parameters as well as the Eringen model for nonlocal theory of elasticity. The models take into account the effects of temporal and spatial nonlocality of a continuous medium. The temperature and stresses for the problem of pulsed heating in one-dimensional case are calculated.

Keywords

thermomechanics nonlocal deformation thermal conductivity dynamic stresses pulsed heating 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. A. Andrievskii, and A. V. Ragulya, Nanostructural Materials (Akademiya,Moscow, 2005) [in Russian].Google Scholar
  2. 2.
    A. N. Gusev, Nanomaterials, Nanostructures, and Nanotechnologies (Fizmatlit, Moscow, 2005) [in Russian].Google Scholar
  3. 3.
    H. Kobayashi, Introduction to Nanotechnology (BINOM,Moscow, 2005) [in Russian].Google Scholar
  4. 4.
    Ch. Poole Jr., and F. J. Owens, Introduction to Nanotechnology (Wiley, 2003; Tekhnosfera,Moscow, 2006).Google Scholar
  5. 5.
    R.W. Kelsall (Editor), Nanoscale Science and Technology (Wiley, 2005).CrossRefGoogle Scholar
  6. 6.
    J. Peddieson, G. R. Buchanon, and R. P. McNitt, “Application of Nonlocal Continuum Medium Models to Nanotechnology,” Int. J. Engng Sci. 41, 305–312 (2003).CrossRefGoogle Scholar
  7. 7.
    A. M. Krivtsov, Deformation and Failure of Rigid Bodies with Microstructure (Fizmatlit,Moscow, 2007) [in Russian].Google Scholar
  8. 8.
    I. A. Kunin, Theory of Elastic Media with Microstructure. Nonlocal Theory of Elasticity (Nauka, Moscow, 1975) [in Russian].Google Scholar
  9. 9.
    M.Onemi, S. Iwasimidzu, K. Genka, et al., Introduction toMicromechanics (Metallurgiya,Moscow, 1987) [in Russian].Google Scholar
  10. 10.
    G. N. Kuvyrkin, A. V. Zhuravskii, and I. Yu. Savel’eva, “Mathematical Modeling of Chemical Vapor Deposition ofMaterial on a Curvilinear Surface,” J. Engng Phys. Therm. 89 (6), 1374–1379 (2016).CrossRefGoogle Scholar
  11. 11.
    V. S. Zarubin and G. N. Kuvyrkin, MathematicalModels of ContinuumMechanics and Electrodynamics (Izdat. MGTU im. Baumana, Moscow, 2008) [in Russian].Google Scholar
  12. 12.
    V. S. Zarubin and G. N. Kuvyrkin, “Mathematical Modeling of Thermomechanical Processes under Intense Thermal Effect,” Teplofiz. Vysokikh Temp. 41 (2), 300–309 (2003) [High Tempr. (Engl. Transl.) 41 (2), 257–265 (2003)].Google Scholar
  13. 13.
    V. S. Zarubin, G. N. Kuvyrkin, and I. Yu. Savelieva, “Mathematical Model of a Nonlocal Medium with Internal State Parameters,” Inzh.-Fiz. Zh. 86 (4), 768–773 (2013) [J. Engng Phys. Thermophys. (Engl. Transl.) 86 (4), 820–826 (2013)].Google Scholar
  14. 14.
    G. N. Kuvyrkin and I. Yu. Savelieva, “MathematicalModel ofHeatConduction ofNew StructuralMaterials,” VestnikMGTU im. Baumana. Ser. Estestv. Nauki, No 3, 72–85 (2010).Google Scholar
  15. 15.
    A. C. Eringen, Nonlocal Continuum Field Theories (Springer, New York–Berlin–Heidelberg, 2002).zbMATHGoogle Scholar
  16. 16.
    A. A. Pisano, and P. Fuschi, “Closed Form Solution for a Nonlocal Elastic Bar in Tension [J],“ Int. J. Solids Struct. 40 (2), 13–23 (2003).MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    C. Polizzotto, “Nonlocal Elasticity and Related Variational Principles,” Int. J. Solids Struct. 38 (2), 7359–7380 (2001).MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    G. N. Kuvyrkin, and I. Y. Savelieva, “Thermomechanical Model of Nonlocal Deformation of a Solid,” Izv. Akad. Nauk.Mekh. Tverd. Tela, No. 3, 20–27 (2016) [Mech. Solids (Engl. Transl.) 51 (3), 256–262 (2016)].Google Scholar

Copyright information

© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.Bauman Moscow State Technical UniversityMoscowRussia

Personalised recommendations