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http://dx.doi.org/10.12989/cac.2021.27.3.199

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)
Publication Information
Computers and Concrete / v.27, no.3, 2021 , pp. 199-210 More about this Journal
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
contact mechanics; functionally graded layer; finite element method; contact area; contact stress;
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1 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.   DOI
2 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   DOI
3 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.   DOI
4 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.   DOI
5 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.   DOI
6 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.   DOI
7 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.   DOI
8 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.   DOI
9 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.   DOI
10 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.   DOI
11 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.   DOI
12 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.   DOI
13 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.   DOI
14 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.   DOI
15 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.   DOI
16 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.   DOI
17 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.   DOI
18 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.   DOI
19 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.   DOI
20 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.   DOI
21 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.   DOI
22 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.   DOI
23 ANSYS (2013), Swanson Analysis Systems Inc., Houston, PA, USA.
24 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.   DOI
25 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.   DOI
26 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.   DOI
27 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.   DOI
28 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.   DOI
29 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.   DOI
30 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.   DOI
31 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.   DOI
32 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.   DOI
33 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.   DOI
34 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.   DOI
35 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.   DOI
36 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.   DOI
37 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.   DOI
38 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.   DOI
39 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.   DOI
40 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.   DOI
41 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.   DOI
42 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.   DOI
43 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.   DOI
44 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.   DOI
45 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.   DOI
46 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.   DOI
47 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.   DOI
48 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.   DOI
49 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.   DOI
50 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.   DOI
51 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.   DOI