PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Two-parametric analysis of anti-plane shear deformation of a coated elastic half-space

Autorzy
Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The anti-plane shear deformation problem of a half-space coated by a soft or a stiff thin layer is considered. The two-term asymptotic analysis is developed motivated by the scaling for the displacement and stress components obtained from the exact solution of a model problem for a shear harmonic load. It is shown that for a rather high contrast in stiffness of the layer and the half-space Winklertype behaviour appears for a relatively soft coating, while for a relatively stiff one, the equations of plate shear are valid. For low contrast, an alternative approximation is suggested based on the reduced continuity conditions and the fact that the applied load may be transmitted to the interface. In case of a stiff layer, a simpler problem for a homogeneous half-space with effective boundary condition is also formulated, modelling the effect of the coating, while for a relatively soft layer a uniformly valid approximate formula is introduced.
Rocznik
Strony
270--275
Opis fizyczny
Bibliogr. 29 poz., rys., tab., wykr.
Twórcy
autor
  • School of Computing and Mathematics, Keele University, Keele, Staffordshire, ST5 5BG, United Kingdom
Bibliografia
  • 1. Aghalovyan L. (2015), Asymptotic theory of anisotropic plates and shells, Singapore: World Scientific.
  • 2. Ahmad M., Nolde E., Pichugin, A.V. (2011), Explicit asymptotic modelling of transient Love waves propagated along a thin coating, Zeitschrift für angewandte Mathematik und Physik, 62(1), 173-181.
  • 3. Alexandrov V.M. (2010), Contact problems on soft and rigid coatings of an elastic half-plane, Mechanics of Solids, 45(1), 34-40.
  • 4. Argatov I., Mishuris G. (2016), Contact mechanics of articular cartilage layers, Springer.
  • 5. Bose S. (2017), High temperature coatings, Butterworth-Heinemann.
  • 6. Cherdantsev M., Cherednichenko K.D. (2012), Two-scale Гconvergence of integral functionals and its application to homogenisation of nonlinear high-contrast periodic composites, Archive for Rational Mechanics and Analysis, 2014(2), 445-478.
  • 7. Figotin A., Kuchment P. (1998), Spectral properties of classical waves in high-contrast periodic media, SIAM Journal on Applied Mathematics, 58(2), 683-702.
  • 8. Goldenveizer A.L., Kaplunov J.D., Nolde E.V. (1993), On Timoshenko-Reissner type theories of plates and shells, International Journal of Solids and Structures, 30(5), 675-694.
  • 9. Goryacheva I.G., Torskaya E.V. (2010), Modeling of fatigue wear of a two-layered elastic half-space in contact with periodic system of indenters, Wear, 268(11-12), 1417-1422.
  • 10. Holmberg K., Ronkainen H., Laukkanen A., Wallin K., Hogmark S., Jacobson S., Wiklund U., Souza R.M., Ståhle P. (2009). Residual stresses in TiN, DLC and MoS2 coated surfaces with regard to their tribological fracture behaviour. Wear, 267(12), 2142-2156.
  • 11. Horgan C.O. (1995), Anti-plane shear deformations in linear and nonlinear solid mechanics, SIAM review, 37(1), 53-81.
  • 12. Jiang H., Browning R., Whitcomb J.D., Ito M., Shimouse M., Chang T.A., Sue H.J. (2010). Mechanical modeling of scratch behavior of polymeric coatings on hard and soft substrates, Tribology letters, 37(2), 159-167.
  • 13. Kaplunov J., Nobili A. (2017), Multi‐parametric analysis of strongly inhomogeneous periodic waveguideswith internal cutoff frequencies, Mathematical Methods in the Applied Sciences, 40(9), 3381-3392.
  • 14. Kaplunov J., Prikazchikov D., Sergushova O. (2016), Multiparametric analysis of the lowest natural frequencies of strongly inhomogeneous elastic rods, Journal of Sound and Vibration, 366, 264-276.
  • 15. Kaplunov J., Prikazchikov D., Sultanova L. (2018), Justification and refinement of Winkler-Fuss hypothesis, Zeitschrift für Angewandte Mathematik und Physik, 69(3), 80.
  • 16. Kaplunov J., Prikazchikov D.A. (2017), Asymptotic theory for Rayleigh and Rayleigh-type waves, Advances in Applied Mechanics, 50, 1-106, Elsevier.
  • 17. Kaplunov J., Prikazchikov D.A., Prikazchikova, L.A. (2017), Dispersion of elastic waves in a strongly inhomogeneous threelayered plate, International Journal of Solids and Structures, 113, 169-179.
  • 18. Li M., Liu Q., Jia Z., Xu X., Cheng Y., Zheng Y., Xi T., Wei S. (2014), Graphene oxide/hydroxyapatite composite coatings fabricated by electrophoretic nanotechnology for biological applications, Carbon, 67, 185-197.
  • 19. Mishuris G. (2001), Interface crack and nonideal interface concept (Mode III), International Journal of Fracture, 107(3), 279–296.
  • 20. Mishuris G. (2003), Mode III interface crack lying at thin nonhomogeneous anisotropic interface. Asymptotics near the crack tip, IUTAM Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics, 251-260.
  • 21. Mishuris G. (2004), Imperfect transmission conditions for a thin weakly compressible interface. 2D problems, Archives of Mechanics, 56(2), 103-115. 22. Mishuris G. and Öchsner A. (2005), Transmission conditions for a soft elasto-plastic interphase between two elastic materials. Plane strain state, Archives of Mechanics, 57(2-3), 157-169.
  • 23. Mishuris G. and Öchsner A. (2007), 2D modelling of a thin elastoplastic interphase between two different materials: plane strain case, Composite Structures, 80(3), 361-372.
  • 24. Mishuris G., Öchsner A. and Kuhn G. (2005), FEM-Analysis of nonclassical transmission conditions between elastic structures part 1: soft imperfect interface, CMC-TECH SCIENCE PRESS, 2(4), 227.
  • 25. Mishuris G.S. (1999), Stress singularity at a crack tip for various intermediate zones in bimaterial structures (Mode III), International Journal of Solids and Structures, 36(7), 999-1015.
  • 26. Pawlowski L. (2008), The science and engineering of thermal spray coatings, John Wiley & Sons.
  • 27. Prikazchikova L., Ece Aydın Y., Erbaş B., Kaplunov J. (2018), Asymptotic analysis of an anti-plane dynamic problem for a threelayered strongly inhomogeneous laminate, Mathematics and Mechanics of Solids, 1081286518790804.
  • 28. Smyshlyaev V.P. (2009), Propagation and localization of elastic waves in highly anisotropic periodic composites via two-scale homogenization, Mechanics of Materials, 41(4), 434-447.
  • 29. Yang F. (2006), Asymptotic solution to axisymmetric indentation of a compressible elastic thin film, Thin Solid Films, 515(4), 2274-2283.
Uwagi
The study was supported by ACORN Scholarship from Keele University. Fruitful discussions with J. Kaplunov and D. A. Prikazchikov and valuable suggestions of the referees are gratefully acknowledged. The author was also supported during her visit to Russia by grant 14.Z50.31.0036 awarded to R.E. Alexeev from Nizhny Novgorod Technical University by the Department of Education and Science of the Russian Federation.
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-06ba0ccb-e070-4ad6-be56-b92dc9ebe133
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.