Skip to main content
SpringerLink
Log in

Strength of a Conducting Nonferromagnetic Layer. Size Effect

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

We present the results of investigations of the steady state of a conducting nonferromagnetic layer performed with the use of the local gradient approach in thermomechanics with regard for the geometric inhomogeneity of its surface. It is shown that the surface stresses and strength are characterized by the multiscale size effect and that the characteristic sizes of the subsurface inhomogeneity are connected with the structural heterogeneity of the material, geometric inhomogeneity of the actual surface of the body, and the forces of Coulomb interaction. The values of the thermodynamic electric potential and charge set on the surface are uniquely determined by the physical and geometric characteristics of the body. The influence of the parameters of geometric inhomogeneity of the actual surface of the body on the size effects of the surface stresses and strength are analyzed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. T. S. Nahirnyj and K. A. Tchervinka, Foundations of the Mechanics of Locally Nonhomogeneous Deformable Solids [in Ukrainian], Rastr-7, Lviv (2018).

    MATH  Google Scholar 

  2. T. Nahirnyj, Yu. Senyk, and K. Tchervinka, “Modeling of the stationary state of a locally inhomogeneous conducting nonferromagnetic thermoelastic body,” Fiz.-Mat. Model. Inform. Tekhnol., Issue 19, 127–135 (2014).

    Google Scholar 

  3. T. Nahirnyj and K. Tchervinka, “Structural and near-surface inhomogeneities in conducting half spaces and conducting layers,” Fiz.-Mat. Model. Inform. Tekhnol., Issue 25, 100–112 (2017).

    Google Scholar 

  4. V. V. Panasyuk, A. E. Andreikiv, and V. Z. Parton, Foundations of the Fracture Mechanics of Materials, in: V. V. Panasyuk (editor), Fracture Mechanics and Strength of Materials [in Russian], Vol. 1, Naukova Dumka, Kiev (1988).

  5. Ya. Burak, T. Nahirnyj, and K. Tchervinka, “Local gradient thermomechanics,” in: R. B. Hetnarski (editor), Encyclopedia of Thermal Stresses, Vol. 6, Springer, Dordrecht (2014), pp. 2794–2801; https://doi.org/10.1007/978-94-007-2739-7_833.

    Chapter  Google Scholar 

  6. H. Hirakata, S. Matsumoto, M. Takemura, M. Suzuki, and T. Kitamura, “Anisotropic deformation of thin films comprised of helical nanosprings,” Int. J. Solids Struct., 44, Nos. 11-12, 4030–4038 (2007); https://doi.org/10.1016/j.ijsolstr.2006.11.005.

    Article  Google Scholar 

  7. M. Mohammadi, G. C. Saha, and A. H. Akbarzadeh, “Elastic field in composite cylinders made of functionally graded coatings,” Int. J. Eng. Sci., 101, 156–170 (2016); https://doi.org/10.1016/j.ijengsci.2015.12.011.

  8. T. Nahirnyj and K. Tchervinka, “Interface phenomena and interaction energy at the surface of electroconductive solids,” Comput. Meth. Sci. Technol., 14, No. 2, 105–110 (2008); 10.12921/cmst.2008.14.02.105-110.

  9. T. Nahirnyj and K. Tchervinka, “Mathematical modeling of structural and near-surface non-homogeneities in thermoelastic thin films,” Int. J. Eng. Sci., 91, 49–62 (2015); https://doi.org/10.1016/j.ijengsci.2015.02.001.

  10. T. Nahirnyj and K. Tchervinka, “Mathematical modeling of the coupled processes in nanoporous bodies,” Acta Mech. Autom., 12, No. 3, 196–203 (2018); https://doi.org/10.2478/ama-2018-0030.

    Article  Google Scholar 

  11. H. N. Pishkenari, B. Afsharmanesh, and F. Tajaddodianfar, “Continuum models calibrated with atomistic simulations for the transverse vibrations of silicon nanowires,” Int. J. Eng. Sci., 100, 8–24 (2016); https://doi.org/10.1016/j.ijengsci.2015.11.005.

  12. J. L. Plawsky, J. K. Kim, and E. F. Schubert, “Engineered nanoporous and nanostructured films,” Mater. Today, 12, No. 6, 36–45 (2009).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, National Academy of Sciences of Ukraine, Lviv, Ukraine

    Т. S. Nahirnyi, K. А. Tchervinka & Yu. А. Senyk

Authors
  1. Т. S. Nahirnyi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. А. Tchervinka
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yu. А. Senyk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yu. А. Senyk.

Additional information

Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 62, No. 4, pp. 124–130, October–December, 2019.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nahirnyi, Т.S., Tchervinka, K.А. & Senyk, Y.А. Strength of a Conducting Nonferromagnetic Layer. Size Effect. J Math Sci 265, 489–497 (2022). https://doi.org/10.1007/s10958-022-06066-6

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-022-06066-6

Keywords

Search

Navigation