Computers and Concrete

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Frictionless contact mechanics of an orthotropic coating/isotropic substrate system

  • Oner, Erdal (Department of Civil Engineering, Bayburt University)
  • Received : 2020.09.26
  • Accepted : 2021.07.12
  • Published : 2021.08.25
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Abstract

This study has been performed to investigate the receding contact problem of a homogeneous orthotropic coating that is not bonded to a homogeneous isotropic substrate without any interfacial defects. The isotropic substrate is supported on a Winkler foundation. The problem is solved assuming that the contact between the rigid punch and orthotropic coating, and that between the orthotropic coating and isotropic substrate, are frictionless. Additionally, the effect of the body forces is neglected, and only compressive normal tractions can be transmitted through the interfaces. The contact analysis of the orthotropic coating, which is subjected to a contact load using a rigid cylindrical punch, is performed under plane strain conditions. The governing equations are analytically found using the theory of elasticity and Fourier integral transformation techniques. Subsequently, the governing equations are reduced to a system of two singular equations, wherein the unknowns are the contact stresses and contact widths. To numerically solve the resulting singular integral equations, Gauss-Chebyshev integration formulas are employed. It is analyzed the influence of the following parameters on the contact stresses and contact widths: orthotropic-material properties, punch radius, load ratio, Winkler foundation stiffness.

Keywords

References

  1. Aleksandrov, V.M. (2006), "Two problems with mixed boundary conditions for an elastic orthotropic strip", J. Appl. Math. Mech., 70(1), 128-138. http://doi.org/10.1016/j.jappmathmech.2006.03.003.
  2. Alinia, Y. and Guler, M.A. (2017), "On the fully coupled partial slip contact problems of orthotropic materials loaded by flat and cylindrical indenters", Mech. Mater., 114, 119-133. http://doi.org/10.1016/j.mechmat.2017.08.005.
  3. Alinia, Y., Hosseini-nasab, M. and Guler, M.A. (2018), "The sliding contact problem for an orthotropic coating bonded to an isotropic substrate", Eur. J. Mech. A-Solid., 70, 156-171. http://doi.org/10.1016/j.euromechsol.2018.02.010.
  4. Alinia, Y., Zakerhaghighi, H., Adibnazari, S. and Guler, M.A. (2017), "Rolling contact problem for an orthotropic medium", Acta Mech., 228(2), 447-464. http://doi.org/10.1007/s00707-016-1718-y.
  5. Arslan, O. (2020), "Frictional contact problem of an anisotropic laterally graded layer loaded by a sliding rigid stamp", P. I. Mech. Eng. C-J. Mech., 234(10), 2024-2041. http://doi.org/10.1177/0954406220916486.
  6. Arslan, O. and Dag, S. (2018), "Contact mechanics problem between an orthotropic graded coating and a rigid punch of an arbitrary profile", Int. J. Mech. Sci., 135, 541-554. http://doi.org/10.1016/j.ijmecsci.2017.12.017.
  7. Binienda, W.K. and Pindera, M.-J. (1994), "Frictionless contact of layered metal-matrix and polymer-matrix composite half planes", Compos. Sci. Technol., 50(1), 119-128. https://doi.org/10.1016/0266-3538(94)90131-7.
  8. Birinci, A. and Erdol, R. (2003), "A frictionless contact problem for two elastic layers supported by a Winkler foundation", Struct. Eng. Mech., 15(3), 331-344. https://doi.org/10.12989/sem.2003.15.3.331.
  9. Buczkowski, R. and Kleiber, M. (1997), "Elasto-plastic interface model for 3D-frictional orthotropic contact problems", Int. J. Numer. Meth. Eng., 40(4), 599-619. https://doi.org/10.1002/(SICI)1097-0207(19970228).
  10. Comez, I. (2003), "Rijit bir panc ile bastirilmis ve tabanda tam olarak bagli agirliksiz cift serit problemi (Double strip problem entirely supperted on bottom and compressed with a rigid punch)", Master Thesis, Karadeniz Technical University, Graduate Institute of Natural and Applied Sciences, Civil Engineering Department, Trabzon, Turkey. (in Turkish)
  11. Comez, I. (2019), "Frictional moving contact problem of an orthotropic layer indented by a rigid cylindrical punch", Mech. Mater., 133, 120-127. http://doi.org/10.1016/j.mechmat.2019.02.012.
  12. Comez, I. and Guler, M.A. (2020), "On the contact problem of a moving rigid cylindrical punch sliding over an orthotropic layer bonded to an isotropic half plane", Math. Mech. Solid., 25(10), 1924-1942. http://doi.org/10.1177/1081286520915272.
  13. Comez, I. and Yilmaz, K.B. (2019), "Mechanics of frictional contact for an arbitrary oriented orthotropic material", Z Angew Math Mech., 99(3), e201800084. https://doi.org/10.1002/zamm.201800084.
  14. Comez, I., Yilmaz, K.B., Guler, M.A. and Yildirim, B. (2019), "On the plane frictional contact problem of a homogeneous orthotropic layer loaded by a rigid cylindrical stamp", Arch. Appl. Mech., 89(7), 1403-1419. https://doi.org/10.1007/s00419-019-01511-6.
  15. Eck, C. and Jarusek, J. (2008), "Solvability of static contact problems with coulomb friction for orthotropic material", J. Elast., 93(1), 93-104. http://doi.org/10.1007/s10659-008-9168-y.
  16. Erbas, B., Yusufoglu, E. and Kaplunov, J. (2011), "A plane contact problem for an elastic orthotropic strip", J. Eng. Math., 70(4), 399-409. http://doi.org/10.1007/s10665-010-9422-8.
  17. Erdogan, F. and Gupta, G. (1972), "On the numerical solutions of singular integral equations", Q. J. Appl. Math., 29, 525-534. https://doi.org/10.1090/qam/408277
  18. Gasmi, A., Joseph, P.F., Rhyne, T.B. and Cron, S.M. (2012), "The effect of transverse normal strain in contact of an orthotropic beam pressed against a circular surface", Int. J. Solid. Struct., 49(18), 2604-2616. http://doi.org/10.1016/j.ijsolstr.2012.05.022.
  19. Guler, M.A. (2014), "Closed-form solution of the two-dimensional sliding frictional contact problem for an orthotropic medium", Int. J. Mech. Sci., 87, 72-88. http://doi.org/10.1016/j.ijmecsci.2014.05.033.
  20. Guler, M.A., Kucuksucu, A., Yilmaz, K.B. and Yildirim, B. (2017), "On the analytical and finite element solution of plane contact problem of a rigid cylindrical punch sliding over a functionally graded orthotropic medium", Int. J. Mech. Sci., 120, 12-29. http://doi.org/10.1016/j.ijmecsci.2016.11.004.
  21. Hakobyan, V.N. and Dashtoyan, L.L. (2013), "Contact problem for an orthotropic plane with a slit", Mech. Compos. Mater., 49(5), 507-518. http://doi.org/10.1007/s11029-013-9367-x.
  22. Hayashi, T. and Koguchi, H. (2015), "Adhesive contact analysis for anisotropic materials considering surface stress and surface elasticity", Int. J. Solid. Struct., 53, 138-147. http://doi.org/10.1016/j.ijsolstr.2014.10.006.
  23. Kagadii, T.S. and Pavlenko, A.V. (2003), "Contact problem for an elastic orthotropic half-strip", Int. Appl. Mech., 39(10), 1179-1187. http://doi.org/10.1023/B:INAM.0000010369.53309.1d.
  24. Kolahchi, R. and Kolahdouzan, F. (2021), "A numerical method for magneto-hygro-thermal dynamic stability analysis of defective quadrilateral graphene sheets using higher order nonlocal strain gradient theory with different movable boundary conditions", Appl. Math. Model., 91, 458-475. https://doi.org/10.1016/j.apm.2020.09.060.
  25. Kucuksucu, A., Guler, M.A. and Avci, A. (2014), "Closed-form solution of the frictional sliding contact problem for an orthotropic elastic half-plane indented by a wedge-shaped punch", Key Eng. Mater., 618, 203-225. http://doi.org/10.4028/www.scientific.net/KEM.618.203.
  26. Kucuksucu, A., Guler, M.A. and Avci, A. (2015), "Mechanics of sliding frictional contact for a graded orthotropic half-plane", Acta Mech., 226(10), 3333-3374. http://doi.org/10.1007/s00707-015-1374-7.
  27. Li, X.Y. and Wang, M.Z. (2006), "On the anisotropic piezoelastic contact problem for an elliptical punch", Acta Mech., 186(1-4), 87-98. http://doi.org/10.1007/s00707-006-0365-0.
  28. Liu, Z., Yan, J. and Mi, C. (2018), "On the receding contact between a two-layer inhomogeneous laminate and a half-plane", Struct. Eng. Mech., 66(3), 329-341. http://doi.org/10.12989/sem.2018.66.3.329.
  29. Mohamed, S.A., Helal, M.M. and Mahmoud, F.F. (2006), "An incremental convex programming model of the elastic frictional contact problems", Struct. Eng. Mech., 23(4), 431-447. http://doi.org/10.12989/sem.2006.23.4.431.
  30. Motezaker, M., Jamali, M. and Kolahchi, R. (2020), "Application of differential cubature method for nonlocal vibration, buckling and bending response of annular nanoplates integrated by piezoelectric layers based on surface-higher order nonlocal-piezoelasticity theory", J. Comput. Appl. Math., 369, 112625. https://doi.org/10.1016/j.cam.2019.112625.
  31. Pasternak, E.G. (1999), "Stress distribution at the contact of absolutely rigid stamp and elastic orthotropic strip", J. Elast., 56(1), 1-15. http://doi.org/10.1023/A:1007612807691.
  32. Pozharskii, D.A. (2017), "Contact problem for an orthotropic half-space", Mech. Solid.+, 52(3), 315-322. http://doi.org/10.3103/s0025654417030086.
  33. Reddy, J.N. (2003). Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC Press.
  34. Rodriguez-Tembleque, L. and Abascal, R. (2013), "Fast FE-BEM algorithms for orthotropic frictional contact", Int. J. Numer. Meth. Eng., 94(7), 687-707. http://doi.org/10.1002/nme.4479.
  35. Seitz, A., Popp, A. and Wall, W.A. (2015), "A semi-smooth Newton method for orthotropic plasticity and frictional contact at finite strains", Comput. Meth. Appl. M., 285, 228-254. http://doi.org/10.1016/j.cma.2014.11.003.
  36. Shen, J.J., Wu, Y.Y., Lin, J.X., Xu, F.Y. and Li, C.G. (2018), "Partial slip problem in frictional contact of orthotropic elastic half-plane and rigid punch", Int. J. Mech. Sci., 135, 168-175. http://doi.org/10.1016/j.ijmecsci.2017.11.022.
  37. Shi, D., Lin, Y. and Ovaert, T.C. (2003), "Indentation of an orthotropic half-space by a rigid ellipsoidal indenter", J. Tribol-T ASME, 125(2), 223-231. http://doi.org/10.1115/1.1537743.
  38. Swanson, S.R. (2004), "Hertzian contact of orthotropic materials", Int. J. Solid. Struct., 41(7), 1945-1959. http://doi.org/10.1016/j.ijsolstr.2003.11.003.
  39. Taherifar, R., Zareei, S.A., Bidgoli, M.R. and Kolahchi, R. (2021), "Application of differential quadrature and Newmark methods for dynamic response in pad concrete foundation covered by piezoelectric layer", J. Comput. Appl. Math., 382, 113075. https://doi.org/10.1016/j.cam.2020.113075.
  40. Yildirim, B., Yilmaz, K.B., Comez, I. and Guler, M.A. (2019), "Double frictional receding contact problem for an orthotropic layer loaded by normal and tangential forces", Meccanica, 54, 2183-2206. https://doi.org/10.1007/s11012-019-01058-4.
  41. Yilmaz, K.B., Comez, I., Guler, M.A. and Yildirim, B. (2019), "Analytical and finite element solution of the sliding frictional contact problem for a homogeneous orthotropic coating-isotropic substrate system", Z Angew Math Mech., 99(3), https://doi.org/10.1002/zamm.201800117.
  42. Yilmaz, K.B., Comez, I., Guler, M.A. and Yildirim, B. (2019), "The effect of orthotropic material gradation on the plane sliding frictional contact mechanics problem", J. Strain Anal., 54(4), 254-275. http://doi.org/10.1177/0309324719859110.
  43. Zakerhaghighi, H., Adibnazari, S., Guler, M.A. and Faghidian, S.A. (2017), "Two-dimensional analysis of the fully coupled rolling contact problem between a rigid cylinder and an orthotropic medium", Z. Angew. Math. Mech., 97(10), 1283-1304. http://doi.org/10.1002/zamm.201600281.
  44. Zehil, G.P. and Gavin, H.P. (2014), "Two and three-dimensional boundary element formulations of compressible isotropic, transversely isotropic and orthotropic viscoelastic layers of arbitrary thickness, applied to the rolling resistance of rigid cylinders and spheres", Eur. J. Mech. A-Solid., 44, 175-187. http://doi.org/10.1016/j.euromechsol.2013.10.015.
  45. Zhou, S.X. and Li, X.F. (2019), "Interfacial debonding of an orthotropic half-plane bonded to a rigid foundation", Int. J. Solid. Struct., 161, 1-10. http://doi.org/10.1016/j.ijsolstr.2018.11.003.