Analysis of thermoelastic contact interaction of bodies with a nonlinear winkler layer and a groove

Keywords

thermo-elasticity, contact interaction, nonlinear Winkler layer, surface groove, variational equations, domain decomposition method.

Cite as

Prokopyshyn I. I. and Serednytska Kh. I. Analysis of thermoelastic contact interaction of bodies with a nonlinear winkler layer and a groove. Physicochemical Mechanics of Materials. 2026. 62(3), 154-161.

Abstract

A plane thermo-elasticity problem of the contact of two bodies with a nonlinear Winkler layer and a surface groove is considered. During contact interaction, the nonlinear inter¬layer resists the deformation of bodies and heat transfer. The presence of a groove leads to the formation of a gap, the height and width of which changes during loading. It is assumed that the gap is filled with a heat-conducting substance, which does not resist the deformation of the bodies. The problem is reduced to a system of linear and nonlinear variational equations, which is solved using a domain decomposition method with finite element approximations. The temperature and stresses in each of the bodies are determined, and their change at the contact surface is analyzed depending on the thermo-elastic characteristics of the layer.

References

1. M.M. Yovanovich, J. DeVaal, and A.H. Hegazy, “A statistical model to predict thermal gap conductance between conforming rough surfaces,” AIAA Paper No. 82-0888 (1982). https://doi.org/10.2514/6.1982-888
2. S. Zilberman, and B.N.J. Persson, “Adhesion between elastic bodies with rough surfaces,” Solid State Commun., 123, Iss. 3-4, 173-177 (2002). https://doi.org/10.1016/S0038-1098(02)00179-5
3. R.M. Martinyak, and R.M. Shvets’, “A mathematical model of mechanical contact of bodies across a thin inhomogeneous layer,” J. Math. Sci., 90, Is. 2, 2000-2002 (1998). https://doi.org/10.1007/BF02432319
4. A.N. Podgorny, P.P. Gontarovsky, B.N. Kyrkach, Yu.I. Matyukhin, and G.L. Khavin, Problems of Contact Interaction of Structural Elements [in Russian], Naukova Dumka, Kyiv (1989).
5. I.I. Dyyak, and Ya.H. Savula, “D-adaptive mathematical model of solid body with thin coating,” Matematychni Studii [in Ukrainian], 7, Is. 1, 103-109 (1997).
6. Kh.I. Serednytska, “Heat transfer through an interfacial gap of variable height with a heat-conducting filler,” Phyziko-Matematycne Modelyuvannia i Informatsijni Tekhnologii [in Ukrainian], 24, 80-87 (2016).
7. R. Martynyak, and K. Chumak, “Effect of heat-conductive filler of interface gap on thermoelastic contact of solids,” Int. J. Heat Mass Transfer., 55, Is. 4, 1170-1178 (2012). https://doi.org/10.1016/j.ijheatmasstransfer.2011.09.053
8. O.O. (Jr.) Bobylev, and V.V. Loboda, “Axisymmetric contact problem of thermoelasticity for a three-layer elastic cylinder with rigid nonuniformly heated core,” J. Math. Sci., 208, Is. 4, 448-459 (2015). https://doi.org/10.1007/s10958-015-2459-5
9. I.I. Prokopyshyn, “Domain decomposition algorithms for problems of thermomechanical contact of many elastic bodies,” Fizyko-Matematycne Modelyuvannia i Informatsijni Tekhnologii [in Ukrainian], 26, 63-82 (2017). https://doi.org/10.15407/fmmit2017.26.063
10. I.S. Skorodyns’kyi, “Iterative algorithms for the solution of quasistatic unilateral problems of thermal friction,” Mater. Sci. 36, Is. 6, 870-877 (2000). https://doi.org/10.1023/A:1011338822063
11. L. Johansson, and A. Klarbring, “Thermoelastic frictional contact problems: Modelling, finite element approximation and numerical realization,” Comput. Meth. Appl. Mech. Eng., 105, Is. 2, 181-210 (1993). https://doi.org/10.1016/0045-7825(93)90122-E
12. G. Zavarise, P. Wriggers, and B.A. Schrefler, “On augmented Lagrangian algorithms for thermomechanical contact problems with friction,” Int. J. Numer. Methods Eng., 38, 2929-2949 (1995). https://doi.org/10.1002/nme.1620381706
13. I.A. Prokopyshyn, and D.G. Khlebnikov, “Asymptotic analysis of the solution of the theory of elasticity for a transversely isotropic layer and the construction of refined plate theories for contact problems,” Issledovaniya po Teorii Plastin i Obolochek [in Russin], 24, 108-113 (1992).
14. P.M. Suquet, “Discontinuities and plasticity,” in J. J. Moreau, P. D. Panagiotopoulos (editors), Nonsmooth Mechanics and Applications, Wien-New York, Springer (1988). CISM Courses and Lectures, No. 302.
15. N.M. Dyachenko, I.A. Stolyarchuk, D.G. Rezvina, and T.M. Smolyankova, “Exponential-power law of roughness deformation in a plane problem of stamp indentation,”, Dopovidi Zaporizhskogo Natsionalnogo Universytetu, Phizyko-Matematyvchni Nauky, Is 2, 42-55 (2014).
16. N.N. Tkachuk, N.B. Skrypchenko, N.A. Tkachuk, and A.V. Grabovsky, Contact Interaction of Complex Profile Parts of Machinebuilding Constructions Taking into Account Local Compliance of the Surface Layer, A.N. Panov Publ. House, Kharkiv (2017).
17. R.M. Martynyak, I.A. Prokopyshyn, and I.I. Prokopyshyn, “Contact of elastic bodies with nonlinear Winkler surface layers,” J. Math. Sci., 205, Is. 4, 535-553 (2015). https://doi.org/10.1007/s10958-015-2265-0
18. I.I. Prokopyshyn, and A.O. Styahar, “Investigation of contact between elastic bodies one of which has a thin coating connected with the body through a nonlinear Winkler layer by the domain decomposition methods,” J. Math. Sci., 258, Is. 4, 477-506 (2021). https://doi.org/10.1007/s10958-021-05562-5
19. D. Bresch, and J. Koko, “An optimization-based domain decomposition method for nonlinear wall laws in coupled systems,” Math. Models Methods Appl. Sci., 14, Is. 7, 1085-1101 (2004). https://doi.org/10.1142/S0218202504003556
20. J. Koko, “Convergence analysis of optimization-based domain decomposition methods for a bonded structure,” Appl. Numer. Math., 58, Is. 1, 69-87 (2008). https://doi.org/10.1016/j.apnum.2006.10.005
21. I.I. Prokopyshyn, “Thermomechanical contact of elastic bodies with nonlinear Winkler surface layers,” J. Math. Sci., 265, Is. 3, 512-538 (2022). https://doi.org/10.1007/s10958-022-06068-4
22. T.R. Thomas, and S.D. Probert, “Thermal contact resistance: the directional effect and other problems,” Int. J. Heat Mass Transf., 13, Is. 5, 789-807 (1970). https://doi.org/10.1016/0017-9310(70)90126-2