Computers and Concrete

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Investigation of continuous and discontinuous contact cases in the contact mechanics of graded materials using analytical method and FEM

  • Yaylaci, Murat (Department of Civil Engineering, Recep Tayyip Erdogan University) ;
  • Adiyaman, Gokhan (Department of Civil Engineering, Karadeniz Technical University) ;
  • Oner, Erdal (Department of Civil Engineering, Bayburt University) ;
  • Birinci, Ahmet (Department of Civil Engineering, Karadeniz Technical University)
  • Received : 2020.07.29
  • Accepted : 2021.01.21
  • Published : 2021.03.25
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Abstract

The aim of this paper was to examine the continuous and discontinuous contact problems between the functionally graded (FG) layer pressed with a uniformly distributed load and homogeneous half plane using an analytical method and FEM. The FG layer is made of non-homogeneous material with an isotropic stress-strain law with exponentially varying properties. It is assumed that the contact at the FG layer-half plane interface is frictionless, and only the normal tractions can be transmitted along the contacted regions. The body force of the FG layer is considered in the study. The FG layer was positioned on the homogeneous half plane without any bonds. Thus, if the external load was smaller than a certain critical value, the contact between the FG layer and half plane would be continuous. However, when the external load exceeded the critical value, there was a separation between the FG layer and half plane on the finite region, as discontinuous contact. Therefore, there have been some steps taken in this study. Firstly, an analytical solution for continuous and discontinuous contact cases of the problem has been realized using the theory of elasticity and Fourier integral transform techniques. Then, the problem modeled and two-dimensional analysis was carried out by using ANSYS package program based on FEM. Numerical results for initial separation distance and contact stress distributions between the FG layer and homogeneous half plane for continuous contact case; the start and end points of separation and contact stress distributions between the FG layer and homogeneous half plane for discontinuous contact case were provided for various dimensionless quantities including material inhomogeneity, distributed load width, the shear module ratio and load factor for both methods. The results obtained using FEM were compared with the results found using analytical formulation. It was found that the results obtained from analytical formulation were in perfect agreement with the FEM study.

Keywords

References

  1. Abhilash, M.N. and Murthy, H. (2014), "Finite element analysis of 2-D elastic contacts Involving FGMs", Int. J. Comput. Meth. Eng. Sci. Mech., 15(3), 253-257. https://doi.org/10.1080/15502287.2014.882445.
  2. Adiyaman, G., Oner, E. and Birinci, A. (2017), "Continuous and discontinuous contact problem of a functionally graded layer resting on a rigid foundation", Acta Mechanica, 228(9), 3003-3017. https://doi.org/10.1007/s00707-017-1871-y.
  3. Aizikovich, S., Vasil'ev, A., Krenev, L., Trubchik, I. and Seleznev, N. (2011), "Contact problems for functionally graded materials of complicated structure", Mech. Compos. Mater., 47(5), 539-548. https://doi.org/10.1007/s11029-011-9232-8.
  4. Alinia, Y., Beheshti, A., Guler, M.A., El-Borgi, S. and Polycarpou, A.A. (2016), "Sliding contact analysis of functionally graded coating/substrate system", Mech. Mater., 94, 142-155. https://doi.org/10.1080/15502287.2014.882445.
  5. ANSYS (2013), Swanson Analysis Systems Inc., Houston, PA, USA.
  6. Arslan, O. (2020), "Plane contact problem between a rigid punch and a bidirectional functionally graded medium", Eur. J. Mech.-A/Solid., 80, 103925. https://doi.org/10.1016/j.euromechsol.2019.103925.
  7. Balci, M.N. and Dag, S. (2019), "Solution of the dynamic frictional contact problem between a functionally graded coating and a moving cylindrical punch", Int. J. Solid. Struct., 161, 267-281. https://doi.org/10.1016/j.ijsolstr.2018.11.020.
  8. Balci, M.N. and Dag, S. (2020), "Moving contact problems involving a rigid punch and a functionally graded coating", Appl. Math. Model., 81, 855-886. https://doi.org/10.1016/j.apm.2020.01.004.
  9. Birinci, A. and Erdol, R. (2001), "Continuous and discontinuous contact problem for a layered composite resting on simple supports", Struct. Eng. Mech., 12(1), 17-34. https://doi.org/10.12989/sem.2001.12.1.017.
  10. Cakiroglu, E., Comez, I. and Erdol, R. (2005), "Application of artificial neural networks to a double receding contact problem with a rigid stamp", Struct. Eng. Mech., 21(2), 205-220. https://doi.org/10.12989/sem.2005.21.2.205.
  11. Chen, X.W. and Yue, Z.Q. (2019), "Contact mechanics of two elastic spheres reinforced by functionally graded materials (FGM) thin coatings", Eng. Anal. Bound. Elem., 109, 57-69. https://doi.org/10.1016/j.enganabound.2019.09.009.
  12. Chidlow, S.J., Chong, W.W.F. and Teodorescu, M. (2013), "On the two-dimensional solution of both adhesive and non-adhesive contact problems involving functionally graded materials", Eur. J. Mech.-A/Solid., 39, 86-103. https://doi.org/10.1016/j.euromechsol.2012.10.008.
  13. Choi, H.J. (2009), "On the plane contact problem of a functionally graded elastic layer loaded by a frictional sliding flat punch", J. Mech. Sci. Technol., 23(10), 2703-2713. https://doi.org/10.1007/s12206-009-0734-4.
  14. Comez, I. (2015), "Contact problem for a functionally graded layer indented by a moving punch", Int. J. Mech. Sci., 100, 339-344. https://doi.org/10.1016/j.ijmecsci.2015.07.006.
  15. Comez, I. (2020), "Contact mechanics of the functionally graded monoclinic layer", Eur. J. Mech.-A/Solid., 83, 104018. https://doi.org/10.1016/j.euromechsol.2020.104018.
  16. Comez, I. and El-Borgi, S. (2018), "Contact problem of a graded layer supported by two rigid punches", Arch. Appl. Mech., 88(10), 1893-1903. https://doi.org/10.1007/s00419-018-1416-4.
  17. Comez, I., Kahya, V. and Erdol, R. (2018), "Plane receding contact problem for a functionally graded layer supported by two quarter-planes", Arch. Mech., 70(6), 485-504. https://doi.org/10.24423/aom.2846.
  18. El-Borgi, S. and Comez, I. (2017), "A receding frictional contact problem between a graded layer and a homogeneous substrate pressed by a rigid punch", Mech. Mater., 114, 201-214. https://doi.org/10.1016/j.mechmat.2017.08.003.
  19. Elloumi, R., El-Borgi, S., Guler, M.A. and Kallel-Kamoun, I. (2016), "The contact problem of a rigid stamp with friction on a functionally graded magneto-electro-elastic half-plane", Acta Mechanica, 227(4), 1123-1156. https://doi.org/10.1007/s00707-015-1504-2.
  20. Elloumi, R., Kallel-Kamoun, I. and El-Borgi, S. (2010), "A fully coupled partial slip contact problem in a graded half-plane", Mech. Mater., 42(4), 417-428. https://doi.org/10.1016/j.mechmat.2010.01.002.
  21. Guler, M.A., Alinia, Y. and Adibnazari, S. (2012), "On the rolling contact problem of two elastic solids with graded coatings", Int. J. Mech. Sci., 64(1), 62-81. https://doi.org/10.1016/j.ijmecsci.2012.08.001.
  22. Guler, M.A., Gulver, Y.F. and Nart, E. (2012), "Contact analysis of thin films bonded to graded coatings", Int. J. Mech. Sci., 55(1), 50-64. https://doi.org/10.1016/j.ijmecsci.2011.12.003.
  23. 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. https://doi.org/10.1016/j.ijmecsci.2016.11.004.
  24. Gun, H. and Gao, X.W. (2014), "Analysis of frictional contact problems for functionally graded materials using BEM", Eng. Anal. Bound. Elem., 38, 1-7. https://doi.org/10.1016/j.enganabound.2013.10.004.
  25. Karabulut, P.M., Adiyaman, G. and Birinci, A. (2017), "A receding contact problem of a layer resting on a half plane", Struct. Eng. Mech., 64(4), 505-513. https://doi.org/10.12989/sem.2017.64.4.505.
  26. Li, M., Lei, M., Munjiza, A. and Wen, P.H. (2015), "Frictional contact analysis of functionally graded materials with Lagrange finite block method", Int. J. Numer. Meth. Eng., 103(6), 391-412. https://doi.org/10.1002/nme.4894.
  27. Liu, C., Cheng, I., Tsai, A.C., Wang, L.J. and Hsu, J. (2010), "Using multiple point constraints in finite element analysis of two dimensional contact problems", Struct. Eng. Mech., 36(1), 95-110. https://doi.org/10.12989/sem.2010.36.1.095.
  28. Liu, J., Ke, L.L. and Wang, Y.S. (2011), "Two-dimensional thermoelastic contact problem of functionally graded materials involving frictional heating", Int. J. Solid. Struct., 48(18), 2536-2548. https://doi.org/10.1016/j.ijsolstr.2011.05.003.
  29. Liu, T.J., Li, P. and Zhang, C. (2017), "On contact problem with finite friction for a graded piezoelectric coating under an insulating spherical indenter", Int. J. Eng. Sci., 121, 1-13. https://doi.org/10.1016/j.ijengsci.2017.08.001.
  30. Liu, T.J., Wang, Y.S. and Xing, Y.M. (2012), "The axisymmetric partial slip contact problem of a graded coating", Meccanica, 47(7), 1673-1693. https://doi.org/10.1007/s11012-012-9547-0.
  31. Ma, J., El-Borgi, S., Ke, L.L. and Wang, Y.S. (2016), "Frictional contact problem between a functionally graded magnetoelectroelastic layer and a rigid conducting flat punch with frictional heat generation", J. Therm. Stress., 39(3), 245-277. https://doi.org/10.1080/01495739.2015.1124648.
  32. Mohamed, S., Helal, M. and Mahmoud, F. (2006), "An incremental convex programming model of the elastic frictional contact problems", Struct. Eng. Mech., 23(4), 431-447. https://doi.org/10.12989/sem.2006.23.4.431.
  33. Nikbakht, A., Arezoodar, A.F., Sadighi, M., Zucchelli, A. and Lari, A.T. (2013), "Frictionless elastic contact analysis of a functionally graded vitreous enameled low carbon steel plate and a rigid spherical indenter", Compos. Struct., 96, 484-501. https://doi.org/10.1016/j.compstruct.2012.08.044.
  34. Nikbakht, A., Fallahi Arezoodar, A., Sadighi, M. and Talezadeh, A. (2014), "Analyzing contact problem between a functionally graded plate of finite dimensions and a rigid spherical indenter", Eur. J. Mech.-A/Solid., 47, 92-100. https://doi.org/10.1016/j.euromechsol.2014.03.001.
  35. Oner, E., Yaylaci, M. and Birinci, A. (2015), "Analytical solution of a contact problem and comparison with the results from FEM", Struct. Eng. Mech., 54(4), 607-622. http://doi.org/10.12989/sem.2015.54.4.607.
  36. Ozsahin, T.S. (2007), "Frictionless contact problem for a layer on an elastic half plane loaded by means of two dissimilar rigid punches", Struct. Eng. Mech., 25(4), 383-403. https://doi.org/10.12989/sem.2007.25.4.383.
  37. Patra, R., Barik, S.P. and Chaudhuri, P.K. (2018), "Frictionless Contact Between a Rigid Indentor and a Transversely Isotropic Functionally Graded Layer", Int. J. Appl. Mech. Eng., 23(3), 655-671. https://doi.org/10.2478/ijame-2018-0036.
  38. Rhimi, M., El-Borgi, S. and Lajnef, N. (2011), "A double receding contact axisymmetric problem between a functionally graded layer and a homogeneous substrate", Mech. Mater., 43(12), 787-798. https://doi.org/10.1016/j.mechmat.2011.08.013.
  39. Rhimi, M., El-Borgi, S., Ben Said, W. and Ben Jemaa, F. (2009), "A receding contact axisymmetric problem between a functionally graded layer and a homogeneous substrate", Int. J. Solid. Struct., 46(20), 3633-3642. https://doi.org/10.1016/j.ijsolstr.2009.06.008.
  40. Sarfarazi, V., Faridi, H.R., Haeri, H. and Schubert, W. (2015), "A new approach for measurement of anisotropic tensile strength of concrete", Adv. Concrete Constr., 3(4), 269-282. http://doi.org/10.12989/acc.2015.3.4.269.
  41. Sburlati, R. (2012), "Elastic solution in a functionally graded coating subjected to a concentrated force", J. Mech. Mater. Struct., 7(4), 401-412. https://doi.org/10.2140/jomms.2012.7.401
  42. 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.
  43. Trubchik, I.S., Evich, L.N. and Mitrin, B.I. (2011), "The analytical solution of the contact problem for the functionally graded layer of complicate structure", Procedia Eng., 10, 1754-1759. https://doi.org/10.1016/j.proeng.2011.04.292.
  44. Volkov, S., Aizikovich, S., Wang, Y.S. and Fedotov, I. (2013), "Analytical solution of axisymmetric contact problem about indentation of a circular indenter into a soft functionally graded elastic layer", Acta Mechanica Sinica, 29(2), 196-201. https://doi.org/10.1007/s10409-013-0022-5.
  45. Yan, J. and Li, X. (2015), "Double receding contact plane problem between a functionally graded layer and an elastic layer", Eur. J. Mech.-A/Solid., 53, 143-150. https://doi.org/10.1016/j.euromechsol.2015.04.001.
  46. Yaylaci, E.U., Yaylaci, M., Olmez, H. and Birinci, A. (2020), "Artificial neural network calculations for a receding contact problem", Comput. Concrete, 25(6), 551-563. https://doi.org/10.12989/cac.2020.25.6.551.
  47. Yaylaci, M. and Birinci, A. (2013), "The receding contact problem of two elastic layers supported by two elastic quarter planes", Struct. Eng. Mech., 48(2), 241-255. http://doi.org/10.12989/sem.2013.48.2.241.
  48. Yaylaci, M., Terzi, C. and Avcar, M. (2019), "Numerical analysis of the receding contact problem of two bonded layers resting on an elastic half plane", Struct. Eng. Mech., 72(6), https://doi.org/10.12989/sem.2019.72.6.775.
  49. Yilmaz, K.B., Comez, I., Yildirim, B., Guler, M.A. and El-Borgi, S. (2018), "Frictional receding contact problem for a graded bilayer system indented by a rigid punch", Int. J. Mech. Sci., 141, 127-142. https://doi.org/10.1016/j.ijmecsci.2018.03.041.
  50. Zhang, H., Wang, W., Liu, Y. and Zhao, Z. (2019), "Semi-analytic modelling of transversely isotropic magneto-electro-elastic materials under frictional sliding contact", Appl. Math. Model., 75, 116-140. https://doi.org/10.1016/j.apm.2019.05.018.
  51. Zhang, Y.F., Yue, J.H., Li, M. and Niu, R.P. (2020), "Contact analysis of functionally graded materials using smoothed finite element methods", Int. J. Comput. Meth., 17(05), 1940012. https://doi.org/10.1142/S0219876219400127.

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