Skip to main content
Have a personal or library account? Click to login
Effective Elastic Moduli of Thin Films with Rough Surfaces: A Modeling Approach Cover

Effective Elastic Moduli of Thin Films with Rough Surfaces: A Modeling Approach

Open Access
|Jul 2026

References

  1. Abadias G, Chason E, Keckes J, Sebastiani M, Thompson GB, Barthel E, Martinu L. Review Article: Stress in thin films and coatings: current status, challenges, and prospects. J Vac Sci Technol A. 2018;36(2): 020801. https://doi.org/10.1116/1.5011790
  2. Bull SJ, Chalker PR, Johnston C, Moore V. The effect of roughness on the friction and wear of diamond thin films. Surf Coat Technol. 1994; 68:603–610. https://doi.org/10.1016/0257-8972(94)90224-0
  3. Elanjeitsenni VP, Vadivu KS, Prasanth BM. A review on thin films, conducting polymers as sensor devices. Mater Res Express. 2022;9(2):022001. https://doi.org/10.1088/2053-1591/ac4aa1
  4. Pang X, Zhang L, Yang H, Gao K, Volinsky AA. Residual stress and surface energy of sputtered TiN films. J Mater Eng Perform. 2015;24:1185–1191. https://doi.org/10.1007/s11665-015-1393-5
  5. Fahs A, Mi S, Nicolazzi W, Molnár G, Bousseksou A. Disentangling surface energy and surface/interface stress effects in spin crossover nanomaterials. Adv Phys Res. 2023;2(10):2200055. https://doi.org/10.1002/apxr.202200055
  6. Goudarzi T., Avazmohammadi R, Naghdabadi R. Surface energy effects on the yield strength of nanoporous materials containing nanoscale cylindrical voids. Mech Mater. 2010;42(9):852-862. https://doi.org/10.1016/j.mechmat.2010.07.006
  7. Ling FF, Lai WM, Lucca DA. Fundamentals of Surface Mechanics. New York: Springer; 2002. https://doi.org/10.1007/978-0-387-21776-5
  8. Nasr Esfahani M, Jabbari M. Influence of the surface stress on the size-dependent elastic behavior of silicon nanowires. J Appl Phys. 2020;127(19):195106. https://doi.org/10.1063/5.0006989
  9. Povstenko Y. Mathematical modeling of phenomena caused by surface stresses in solids. In: Altenbach H, Morozov N, editors. Surface Effects in Solid Mechanics. Berlin Heidelberg: Springer. Adv Struc Mater. 2013; 30. https://doi.org/10.1007/978-3-642-35783-1_11
  10. Johnson KL. Contact Mechanics. Cambridge: Cambridge University Press; 1985. https://doi.org/10.1017/CBO9781139171731
  11. Kragelsky IV, Demkin NB. Contact area of rough surfaces. Wear. 1960;3(3):170–187. https://doi.org/10.1016/0043-1648(60)90136-8
  12. Sedlaček M, Podgornik B, Vižintin J. Correlation between standard roughness parameters skewness and kurtosis and tribological behaviour of contact surfaces. Tribol Int. 2012;48:102–112. https://doi.org/10.1016/j.triboint.2011.11.008
  13. Zhu S, Huang P. Influence mechanism of morphological parameters on tribological behaviors based on bearing ratio curve. Tribol Int. 2017;109:10–18. https://doi.org/10.1016/j.triboint.2016.12.014
  14. Nahirnyj T, Tchervinka K. Mathematical modeling of structural and nearsurface non-homogeneities in thermoelastic thin films. Int J Eng Sci. 2015;91:49–62. https://doi.org/10.1016/j.ijengsci.2015.02.001
  15. Nahirnyj T, Tchervinka K. Functional kinetic equations in mathematical modeling of coupled processes in solids. Contin Mech Thermodyn. 2020;32:1727–1743. https://doi.org/10.1007/s00161-020-00877-1
  16. Nahirnyj T, Tchervinka K. Mathematical modeling of the coupled processes in nanoporous bodies. Acta Mech Autom. 2018;12(3):196–203. https://doi.org/10.2478/ama-2018-0030
  17. Nahirnyj T, Sąsiadek M, Tchervinka K. Modeling the effect of surface roughness on mechanical fields in an elastic solid bounded by nominally flat surfaces. Int J Solids Struct. 2024;302:112979. https://doi.org/10.1016/j.ijsolstr.2024.112979
  18. Asmani M, Kermel C, Leriche A, Ourak M. Influence of porosity on Young’s modulus and Poisson’s ratio in alumina ceramics. J Eur Ceram Soc. 2001;21(8):1081–1086. https://doi.org/10.1016/S0955-2219(00)00314-9
  19. Kováčik J. Correlation between Young’s modulus and porosity in porous materials. J Mater Sci Lett. 1999;18(13):1007–1010. https://doi.org/10.1023/A:1006669914946
  20. Lam DC, Lange FF, Evans AG. Mechanical properties of partially dense alumina produced from powder compacts. J Am Cer Soc. 1994;77(8):2113–2117. https://doi.org/10.1111/j.1151-2916.1994.tb07105.x
  21. Altenbach H. An alternative determination of transverse shear stiffnesses for sandwich and laminated plates. Int J Solids Struct. 2000;37(25):3503–3520. https://doi.org/10.1016/S0020-7683(99)00057-8
  22. Jankowski P. On the nonlocal interaction range for stability of nanobeams with nonlinear distribution of material properties. Acta Mech Autom. 2022;16(2): 151-161. https://doi.org/10.2478/ama-2022-0019
  23. Bîrsan M, Sadowski T, Marsavina L, Linul E, Pietras D. Mechanical behavior of sandwich composite beams made of foams and functionally graded materials. Int J Solids Struct. 2013;50(3-4):519–530. https://doi.org/10.1016/j.ijsolstr.2012.10.011
  24. Nahirnyj T, Tchervinka K. Near-surface mass defect in models of locally heterogeneous solid mechanics. Acta Mech Autom. 2019;13(3):205-210. https://doi.org/10.2478/ama-2019-0027
  25. Gibson LJ, Ashby MF. Cellular Solids: Structure and Properties. Cambridge: Cambridge University Press; 1999. https://doi.org/10.1017/CBO9781139878326
  26. Niyogi S, Gupta BS. Mechanical properties and pore size distribution in athermal shear-strained porous glasses. arXiv [Preprint] arXiv:2106.03473. 2021. https://doi.org/10.48550/arXiv.2106.03473
  27. Altenbach H, Bruno G, Eremeyev VA, Gutkin MY, Müller WH, editors. Mechanics of Heterogeneous Materials. Cham: Springer International Publishing; 2023. https://doi.org/10.1007/978-3-031-28744-2
DOI: https://doi.org/10.65731/ama/2026-0038 | Journal eISSN: 2300-5319 | Journal ISSN: 1898-4088
Language: English
Page range: 380 - 388
Submitted on: Feb 24, 2026
Accepted on: Apr 11, 2026
Published on: Jul 16, 2026
In partnership with: Paradigm Publishing Services

© 2026 Taras Nahirnyj, Michał Sąsiadek, Kostiantyn Tchervinka, published by Bialystok University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.