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Thermoelastic influence of convective and conduction interstitial conditions on the size of the contact zone in three-dimensional receding thermoelastic contact problem

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Abstract

The temperature variation within two elastic bodies in perfect thermoelastic contact may cause the contact area to become convex and hence lead to a reduction in the size of the contacting surface. In receding thermoelastic contact problems, the final size of the contact zone is independent of the applied loads, being only affected by the thermomechanical properties of the solids. However, the final size of the contact zone can also be affected by the conductive and convective boundary conditions at the separation zones of the contacting surfaces. In those regions, the heat flux is a function of the separation between the solids, so the thermal and the thermoelastic problems are highly coupled. For this reason, this work studies the three-dimensional receding thermomechanical contact problem under conductive and convective boundary conditions at the interstitial zones of the contact area. After the validation of the numerical scheme presented to solve this problem, several examples are presented and discussed in detail. The results reveal that conductive and convective interstitial boundary conditions have a significant effect not only on the size of the contact zone, but also on the resulting tractions, temperature and heat flux distributions.

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References

  1. Dundurs, J.: Distorsion of a body caused by free thermal expansion. Mech. Res. Commun. 1(3), 121–124 (1974). https://doi.org/10.1016/0093-6413(74)90001-9

    Google Scholar 

  2. Comninou, M., Dundurs, J.: On the barber boundary conditions for thermoelastic contact. J. Appl. Mech. 46, 849–853 (1979)

    MATH  Google Scholar 

  3. Barber, J.R.: Indentation of the semi-infinite elastic solid by a hot sphere. Int. J. Mech. Sci. 15, 813–819 (1973)

    Google Scholar 

  4. Dundurs, J., Stippes, M.: Role of elastic constants in certain contact problems. J. Appl. Mech. 37, 965–970 (1970)

    Google Scholar 

  5. Comez, I., Birinci, A., Erdol, R.: Double receding contact problem for a rigid stamp and two elastic layers. Eur. J. Mech. A Solids 23, 301–309 (2004)

    MATH  Google Scholar 

  6. Kahya, V., Ozsahin, T.S., Birinci, A., Erdol, R.: A receding contact problem for an anisotropic elastic medium consisting of a layer and a half plane. Int. J. Solids Struct. 44, 5695–5710 (2007)

    MATH  Google Scholar 

  7. Ahn, Y.J., Barber, J.R.: Response of frictional receding contact problems to cyclic loading. Int. J. Mech. Sci. 50, 1519–1528 (2008)

    MATH  Google Scholar 

  8. Rhimi, M., El-Borgi, S., Ben Said, W., Ben Jemaa, F.: A receding contact axisymmetric problem between a functionally graded layer and a homogeneous substrate. Int. J. Solids Struct. 46(20), 3633–3642 (2009). https://doi.org/10.1016/j.ijsolstr.2009.06.008

    MATH  Google Scholar 

  9. Yan, J., Li, X.: Double receding contact plane problem between a functionally graded layer and an elastic layer. Eur. J. Mech. A Solids 53, 143–150 (2015). https://doi.org/10.1016/j.euromechsol.2015.04.001

    MathSciNet  MATH  Google Scholar 

  10. Parel, K.S., Hills, D.A.: Frictional receding contact analysis of a layer on a half-plane subjected to semi-infinite surface pressure. Int. J. Mech. Sci. 108–109, 137–143 (2016)

    Google Scholar 

  11. Yilmaz, K.B., Comez, I., Yildirim, B., Güler, M.A., El-Borgi, S.: Frictional receding contact problem for a graded bilayer system indented by a rigid punch. Int. J. Mech. Sci. 141, 127–142 (2018)

    Google Scholar 

  12. Lopes, J.P., Hills, D.A.: The axisymmetric frictional receding contact of a layer pressed against a half-space by pressure outside a disk. Eur. J. Mech. A Solids 77, 103787 (2019)

    MathSciNet  MATH  Google Scholar 

  13. Lopes, J.P., Hills, D.A.: The axisymmetric frictional receding contact of a layer pressed against a half-space by a point force. Int. J. Solids Struct. 171, 47–53 (2019)

    MATH  Google Scholar 

  14. Wriggers, P., Zavarise, G.: Thermomechanical contact—a rigorous but simple numerical approach. Comput. Struct. 46(1), 47–53 (1993)

    Google Scholar 

  15. Johansson, L., Klarbring, A.: Thermoelastic frictional contact problems: modelling, finite element aproximantion and numerical realization. Comput. Methods Appl. Mech. Eng. 105, 181–210 (1993)

    MATH  Google Scholar 

  16. Strömberg, N.: Finite element treatment of two-dimensioanl thermoelastic wear problems. Comput. Methods Appl. Mech. Eng. 177, 441–455 (1999)

    MATH  Google Scholar 

  17. Ireman, P., Klarbring, A., Strömberg, N.: Finite element algorithms for thermoelastic wear problems. Eur. J. Mech. A Solids 21, 423–440 (2002)

    MathSciNet  MATH  Google Scholar 

  18. Strömberg, N.: An Eulerian approach for simulating frictional heating in disc-pad systems. Eur. J. Mech. A Solids 30, 673–683 (2011)

    MATH  Google Scholar 

  19. Bouzinov, P.A., Patunso, D., Bathe, K.-J.: A finite element procedure for the analysis of thermomechanical solids in contact. Comput. Struct. 75, 551–573 (2000)

    Google Scholar 

  20. Hüeber, S., Wohlmut, B.I.: Thermo-mechanical contact problems on non-matching meshes. Comput. Methods Appl. Mech. Eng. 198, 1338–1350 (2009)

    MATH  Google Scholar 

  21. Ovcharenko, A., Yang, M., Chun, K., Talke, F.E.: Transient therm-mechanical contact of an impacting sphere on a moving flat. J. Tribol. 133, 031404 (2011)

    Google Scholar 

  22. Seitz, A., Wall, W.A., Popp, A.: Nitsche’s method for finite deformation thermomechanical contact problems. Comput. Mech. 63, 1091–1110 (2019)

    MathSciNet  MATH  Google Scholar 

  23. Chan, S.K., Tuba, I.S.: A finite element method for contact problems of solid bodies—1: theory and validation. Int. J. Mech. Sci. 13, 615–625 (1971)

    MATH  Google Scholar 

  24. Francavilla, A., Zienkiewicz, O.C.: A note on numerical computation of elastic contact problems. Int. J. Numer. Methods Eng. 19, 913–924 (1975)

    Google Scholar 

  25. Jing, H.S., Liao, M.L.: An improved finite element scheme for elastic contact problems with friction. Comput. Struct. 35(5), 571–578 (1990)

    Google Scholar 

  26. Aliabadi, F.M.H.: The Boundary Element Method: Applications in Solids and Structures, vol. 2. Wiley, Chichester (2002)

    MATH  Google Scholar 

  27. Man, K.W., Aliabadi, M.H.: BEM frictional contact analysis: modelling considerations. Eng. Anal. Bound. Elem. 11, 77–85 (1993)

    Google Scholar 

  28. Rodríguez-Tembleque, L., Abascal, R.: A FEM-BEM fast methodology for 3D frictional contact problems. Comput. Struct. 88, 924–937 (2010)

    MATH  Google Scholar 

  29. Rodríguez-Tembleque, L., Abascal, R., Aliabadi, M.H.: A boundary element formulation for wear modeling on 3d contact and rolling-contact problems. Int. J. Solids Struct. 47, 2600–2612 (2010)

    MATH  Google Scholar 

  30. Rodríguez-Tembleque, L., Buroni, F.C., Sáez, A.: 3d bem for orthotropic frictional contact of piezoelectric bodies. Comput. Mech. 56, 491–502 (2015)

    MathSciNet  MATH  Google Scholar 

  31. Alonso, P., Garrido García, J.A.: BEM applied to 2D thermoelastic contact problems including conduction and forced convection in interstitial zones. Eng. Anal. Bound. Elem. 15(3), 249–259 (1995)

    Google Scholar 

  32. Espinosa, J.V., Mediavilla, A.F.: Boundary element method applied to three dimensional thermoelastic contact. Eng. Anal. Bound. Elem. 36(6), 928–933 (2012)

    MATH  Google Scholar 

  33. Vallepuga-Espinosa, J., Ubero-Martínez, I., Sánchez, L., Cifuentes-Rodríguez, J.: An incremental-iterative bem methodology to solve 3d thermoelastic contact problem including variable thermal resistance in the contact zone. Contin. Mech. Thermodyn. 31(5), 1543–1558 (2019)

    MathSciNet  Google Scholar 

  34. Ubero-Martinez, I., Vallepuga-Espinosa, J., Rodríguez-Tembleque, L., Cifuentes-Rodríguez, J.: The effect of conduction and convective conditions at interstitial regions on 3d thermoelastic contact problems. Eng. Anal. Bound. Elem. 107, 243–256 (2019)

    MathSciNet  MATH  Google Scholar 

  35. Andersson, T.: The boundary element method applied to two-dimensional contact problems with friction. In: Brebbia, C.A. (ed.) Boundary Element Methods. Springer, Berlin (1981)

    MATH  Google Scholar 

  36. Garrido, J.A., Foces, A.: BEM applied to receding contact problems with friction. Math. Comput. Model. 133(3—-5), 143–153 (1991)

    MATH  Google Scholar 

  37. Garrido, J.A., Lorenzana, A.: Receding contact problem involving large displacements using the BEM. Eng. Anal. Boun. Elem. 21, 295–303 (1998)

    MATH  Google Scholar 

  38. París, F., Antonio, F., Garrido, J.A.: Application of boundary element method to solve three-dimensional elastic contact problems without friction. Comput. Struct. 43, 19–30 (1992)

    MATH  Google Scholar 

  39. Alonso, P.: Thermoelastic Contact Problem Using BEM. PhD thesis, Universidad de Valladolid, Spain (1995)

  40. Brebbia, C.A., Telles, J.C.F., Wrobel, L.C.: Boundary Element Techniques, pp. 177–236. Springer, Berlin (1984)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Departamento de Tecnología Minera, Topográfica y de Estructuras, Universidad de León, Campus de Vegazana s/n, 24071, León, Spain

    J. Vallepuga-Espinosa, I. Ubero-Martínez & J. Cifuentes-Rodríguez

  2. Escuela Técnica Superior de Ingeniería, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092, Seville, Spain

    L. Rodríguez-Tembleque

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  1. J. Vallepuga-Espinosa
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  2. I. Ubero-Martínez
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  3. J. Cifuentes-Rodríguez
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  4. L. Rodríguez-Tembleque
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Correspondence to I. Ubero-Martínez.

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Vallepuga-Espinosa, J., Ubero-Martínez, I., Cifuentes-Rodríguez, J. et al. Thermoelastic influence of convective and conduction interstitial conditions on the size of the contact zone in three-dimensional receding thermoelastic contact problem. Acta Mech 231, 3065–3084 (2020). https://doi.org/10.1007/s00707-020-02694-8

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  • DOI: https://doi.org/10.1007/s00707-020-02694-8

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