Prediction of Thermal Properties of Solid Contact
Russian journal of nonlinear dynamics, Tome 20 (2024) no. 4, pp. 601-617.

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This article provides a review of the literature devoted to methods of modeling contact heat transfer, as well as the author’s method of numerical modeling and its verification on experimental data. Based on the analysis of the literature, we draw a conclusion about the determining effect of the roughness of the contacting surfaces on the heat exchange between them. We introduce the concept of a digital double of touching surfaces, that is, a model that takes into account their roughness and allows simulating joint mechanical and thermal interaction between contacting bodies. We propose a method of numerical simulation of contact heat transfer, the calculation results of which are in good agreement with experimental data.
Keywords: contact heat transfer, contact thermal resistance, roughness, thermal conductivity, heat flow, cryogenic temperatures, digital surface twin
Mots-clés : surface, microcontact
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A. D. Ezhov; L. V. Bykov; V. P. Kiselev; P. I. Talalaeva; I. V. Kotovich; I. M. Platonov. Prediction of Thermal Properties of Solid Contact. Russian journal of nonlinear dynamics, Tome 20 (2024) no. 4, pp. 601-617. http://geodesic.mathdoc.fr/item/ND_2024_20_4_a10/

[1] Cui, T., Li, Q., and Xuan, Y., “Characterization and Application of Engineered Regular Rough Surfaces in Thermal Contact Resistance”, Appl. Therm. Eng., 71:1 (2014), 400–409 | DOI

[2] Demkin, N. B., Contacting of Rough Surfaces, Nauka, Moscow, 1970, 227 pp. (Russian)

[3] Inzh.-Fiz. Zh., 95:3 (2022), 640–650 (Russian) | DOI

[4] Yezhov, A. D., Bykov, L. V., Mesnyankin, S. Yu., Bogachev, E. A., and Razina, A. S., “Improvement and Optimization of Structural Components with Consideration of Thermal Deformation”, Teplov. Prots. v Tekhn., 2015, no. 11, 510–516 (Russian)

[5] Holm, R., Electric Contacts: Theory and Applications, 4th ed., Springer, Berlin, 1967, xv, 484 pp.

[6] Holm, R., “Contact Resistance Especially at Carbon Contact”, Z. für Techn. Phys., 3:9 (1922), 290–294

[7] Murashov, M., Panin, S., and Klimov, S., “Numerical Modeling of Electrical Contact Conductance of Rough Bodies”, Nauka i Obrazov., 2015, no. 1, 189–200 (Russian)

[8] Carrete, J., Gallego, L. J., Varela, L. M., and Mingo, N., “Surface Roughness and Thermal Conductivity of Semiconductor Nanowires: Going below the Casimir Limit”, Phys. Rev. B, 84:7 (2011), Art. 075403, 4 pp. | DOI

[9] Maxwell, J. C., A Treatise on Electricity and Magnetism: Vol. 1, 3rd ed., Dover, New York, 1954, 560 pp. | MR

[10] Pennec, F., Modélisation du contact métal–métal: Application aux micro-commutateurs MEMS RF, PhD Thesis, Université Paul Sabatier, Toulouse, France, 2009, 196 pp.

[11] Novikov, I. I., Theory of Heat Treatment of Metals, Metallurgiya, Moscow, 1978, 392 pp. (Russian)

[12] Ganin, E. A., “Physical Model of Contact Heat Transfer”, Thermotechnical Problems of Energy-Saving Technologies in Engineering and Light Industry, 1989, 6–22 (Russian)

[13] Inzh.-Fiz. Zh., 38:3 (1980), 441–449 (Russian) | DOI

[14] Bahrami, M., Culham, J. R., Yovanovich, M. M., and Schneider, G. E., “Thermal Contact Resistance of Non-Conforming Rough Surfaces: Part 2. Thermal Model”, J. Thermophys. Heat Transf., 18:2 (2004), 218–227 (Russian) | DOI

[15] Barry, G. W. and Goodling, J. S., “A Stefan Problem with Contact Resistance”, ASME J. Heat Transfer, 109:4 (1987), 820–825 | DOI

[16] Burdo, O. G., Viskalova, I. M., and Sokolovskaya, P. B., “Investigation of Contact Heat Transfer by Electrothermal Analogy Method”, Izv. Vyssh. Uchebn. Zaved. Priborostroenie, 1989, no. 20, 86–90 (Russian)

[17] Muzichka, Y. S., Sridhar, M. R., Yovanovich, M. M., and Antonetti, V. W., “Thermal Spreading Resistance in Multilayered Contacts: Applications in Thermal Contact Resistance”, ASME J. Heat Transfer, 13:4 (1999), 489–494

[18] Madhusudana, C. V. and Fletcher, L. S., “Contact Heat Transfer: The Last Decade”, AIAA J., 24:3 (1986), 510–523 | DOI | MR

[19] Zh. Tekh. Fiz., 67:2 (1997), 1–6 (Russian) | DOI

[20] Mishurenko, A. B., Smolyakova, L. A., Potopaeva, O. P., and Kozlovsky, S., “Model of Contact between Two Rough Surfaces to Determine Contact Resistance”, Aktual. Probl. Aviats. i Kosmonavtiki, 1:8 (2012), 97–98 (Russian)

[21] Kiselev, I. G. and Krylov, D. V., “Mathematical Modeling of Contact Heat Transfer under Elastic Deformation of Microridges of Rough Surfaces”, Scientific, Technical and Economic Cooperation of the APR Countries in the XXI Century: Vol. 2, 2012, 92–96 (Russian)

[22] Malkov, V. A., Favorsky, O. N., and Leontiev, V. N., Contact Heat Transfer in Gas Turbine Engines and Power Plants, Mashinostroenie, Moscow, 1978, 144 pp. (Russian)

[23] Shlykov, Yu. P., Ganin, E. A., and Tsarevsky, S. N., Contact Thermal Resistance, Energiya, Moscow, 1977, 328 pp. (Russian)

[24] Baranovsky, E. F. and Sevastyanov, P. V., “Investigation of Contact Heat Transfer during Freezing on Moving Crystalline Jams”, Vestn. Akad. Nauk BSSR. Ser. Fiz.-Tekhn. Nauk, 1983, no. 1, 59–62 (Russian) | MR

[25] Ponomarev, B. P., “The Influence of Quality of Contact Connections on Localization of Temperature Field”, Semiconductor Devices and Converter Devices: Design, Calculation, Modeling and Control, 1986, 4–12, MordovGU, Saransk (Russian)

[26] Inzh.-Fiz. Zh., 27:5 (1974), 811–817 (Russian) | DOI

[27] Alifanov, O. M., Artyukhin, E. A., and Rumyantsev, S. V., Extreme Methods for Solving Ill-Posed Problems with Applications to Inverse Heat Transfer Problems, Begell House, New York, 1995, 306 pp. | MR | Zbl

[28] Meshkov, V. V. and Zorenko, D. A., “SAE Modeling of Friction Surface Temperature Fields with Taking into Account Experimentally Determined Submicrogeometry”, Mechanics and Physics of Processes on the Surface and in Contact of Solid Bodies, Parts of Technological and Power Equipment: Vol. 7, TvGTU, Tver, 2014, 25–29 (Russian)

[29] Yezhov, A. D., “Determination of the Contact Thermal Resistance of a Pair: C-Si-C Composite Material and Titanium Alloy”, Trudy MAI, 2015, no. 82, Art. 20, 15 pp. (Russian)

[30] Mesnyankin, S. Yu. and Dikov, A. V., “Numerical Calculation of Thermal Contact of Solid Bodies: From Models to Real Surfaces”, Teplov. Prots. v Tekhn., 2014, no. 5, 230–235 (Russian)

[31] Mesnyankin, S. Yu., Ezhov, A. D., and Basov, A. A., “Definition of Contact Thermal Resistance on the Basis of Three-Dimensional Modelling of Adjoining Surfaces”, Izv. Ross. Akad. Nauk. Energetika, 2014, no. 5, 65–74 (Russian)

[32] Ezhov, A. D. and Mesnyankin, S. Yu., “Modelling of Rough Surfaces for Contact Problems with Composite Materials”, Mekhanika Kompozit. Mater. i Konstr., 21:2 (2015), 272–281 (Russian)

[33] Thompson, M. K., “Finite Element Modeling of Multi-Scale Thermal Contact Resistance”, Proc. of the 1st ASME Internat. Conf. on Micro/Nanoscale Heat Transfer: Parts A and B (Tainan, Taiwan, Jun 2008), 509–517

[34] Thompson, M. K. and Thompson, J. M., “Considerations for Predicting Thermal Contact Resistance in ANSYS”, Proc. of the 17th Korea ANSYS User's Conf. (Cheongju, South Korea, Nov 2007), 5 pp.

[35] Zhang, X., Chong, P., Fujiwara, S., and Fujii, M., “A New Method for Numerical Simulation of Thermal Contact Resistance in Cylindrical Coordinates”, Int. J. Heat Mass Transf., 47:5 (2004), 1091–1098 | DOI | Zbl

[36] Ayers, G. H., Cylindrical Thermal Contact Conductance, Master's Thesis, Texas A University, College Station, Texas, USA, 2003, 186 pp.

[37] Jackson, R. L., Bhavnani, S. H., and Ferguson, T. P., “A Multiscale Model of Thermal Contact Resistance between Rough Surfaces”, Trans. ASME J. Heat Transf., 130 (2008), Art. 081301, 8 pp. | DOI

[38] Salti, B. and Laraqi, N., “3-D Numerical Modeling of Heat Transfer between Two Sliding Bodies: Temperature and Thermal Contact Resistance”, Int. J. Heat Mass Transf., 42:13 (1999), 2363–2374 | DOI | Zbl

[39] Thompson, M. K., A Multi-Scale Iterative Approach for Finite Element Modeling of Thermal Contact Resistance, PhD Thesis, Massachusetts Institute of Technology, Boston, Mass., USA, 2007, 100 pp.

[40] Zavarise, G., Wriggers, P., Stein, E., and Schrefler, B. A., “Real Contact Mechanisms and Finite Element Formulation: A Coupled Thermomechanical Approach”, Int. J. Numer. Methods Eng., 35:4 (1992), 767–785 | DOI | Zbl

[41] Temizer, I. and Wriggers, P., “Thermal Contact Conductance Characterization via Computational Contact Homogenization: A Finite Deformation Theory Framework”, Int. J. Numer. Methods Eng., 83:1 (2010), 24–58 | DOI | MR

[42] Popov, V. M., Heat Transfer in the Contact Zone of Detachable and Non-Detachable Joints, Energiya, Moscow, 1971, 216 pp. (Russian)

[43] Zh. Tekh. Fiz., 67:2 (1997), 875–883 (Russian) | DOI

[44] Popov, V. M., Lushnikova, E. N., and Chernoukhov, P. A., “Thermal Contact of Metal Surfaces with Oxide Films”, Lesotekhn. Zh., 2012, no. 1, 7–12 (Russian) | MR

[45] Bahrami, M., Yovanovich, M. M., and Marotta, E. E., “Thermal Joint Resistance of Polymer-Metal Rough Interfaces”, J. Electron. Packag., 128 (2006), 23–29 | DOI

[46] Gibbins, J., Thermal Contact Resistance of Polymer Interfaces, PhD Thesis, University of Waterloo, Waterloo, Ontario, Canada, 2006, 157 pp.

[47] Prasher, R., “Thermal Interface Materials: Historical Perspective, Status, and Future Directions”, Proc. IEEE, 94:8 (2006), 1571–1586 | DOI

[48] Prasher, R. S. and Matayabas, J. C., “Thermal Contact Resistance of Cured Gel Polymeric Thermal Interface Material”, IEEE Trans. Comp. Pack. Technolog., 27:4 (2004), 702–709 | DOI

[49] Temizer, I. and Wriggers, P., “A Multiscale Contact Homogenization Technique for the Modeling of Third Bodies in the Contact Interface”, Comput. Methods Appl. Mech. Eng., 198:3–4 (2008), 377–396 | DOI | MR | Zbl

[50] Wriggers, P. and Reinelt, J., “Multi-Scale Approach for Frictional Contact of Elastomers on Rough Rigid Surfaces”, Comput. Methods Appl. Mech. Eng., 198:21–26 (2009), 1996–2008 | DOI | MR | Zbl

[51] Greenwood, J. A., “Constriction Resistance and the Real Area of Contact”, Br. J. Appl. Phys., 17:12 (1966), 1621–1632 | DOI

[52] Koshkin, V. K., Danilov, Yu. I., Mesnyankin, S. Yu., and Mikhailova, T. V., “Analysis of Calculation Models of Thermal Contact. Heat and Mass Transfer during the Interaction of the Flow with the Surface”, Nauchn. Trudy MAI, MAI, Moscow, 1981, 68–75 (Russian)

[53] Martin, K. A., Yovanovich, M. M., and Chow, Y. L., “Method of Moments Formulation of Thermal Constriction Resistance of Arbitrary Contacts”, Proc. of the 19th Thermophys. Conf. (Snowmass, Colo., USA, Jun 1984), AIAA Paper No. 84-1745, 8 pp.

[54] Kennedy, F. E., Cullen, S. C., and Leroy, J. M., “Contact Temperature and Its Effects in an Oscillatory Sliding Contact”, J. Tribol., 111:1 (1989), 63–69 | DOI

[55] Kuhlmann-Wilsdorf, D., “Temperatures at Interfacial Contact Spots: Dependence on Velocity and on Role Reversal of Two Materials in Sliding Contact”, J. Tribol., 109:2 (1987), 321–329 | DOI

[56] Xu, J. and Fisher, T. S., “Enhanced Thermal Contact Conductance Using Carbon Nanotube Arrays”, Proc. of the 9th Intersociety Conf. on Thermal and Thermomechanical Phenomena in Electronic Systems: Vol. 2 (Las Vegas, Nev., USA, 2004), IEEE Cat. No. 04CH37543, 549–555

[57] Fletcher, L. S., “Recent Developments in Contact Conductance Heat Transfer”, J. Heat Transf., 110:4b (1988), 1059–1070 | DOI

[58] Rhoderick, E. H. and Williams, R. H., Metal-Semiconductor Contacts, Monogr. Electric. Electron. Eng., 19, 2nd ed., Oxford, Oxford Univ. Press, 1988, 272 pp.

[59] Vikulov, D. G. and Mesnyankin, S. Yu., “Thermoelectric Interaction in Metal-Semiconductor Contact”, Proc. of the 4th Russian Natl. Conf. on Heat Exchange: In 8 Vols.: Vol. 8 (Moscow, Russia, Oct 2006), 43–44 (Russian)

[60] Eid, J. C. and Antonetti, V. W., “Small Scale Thermal Contact Resistance of Aluminum against Silicon”, Proc. of the 8th Internat. Heat Transfer Conf. (San Francisco, Calif., USA, Aug 1986), 659–664

[61] Mesnyankin, S. Yu., “Contact Thermal Conductivity of Dissimilar Materials”, Proc. of the 2nd Russian Natl. Conf. on Heat Exchange: In 8 Vols.: Vol. 7 (Moscow, Russia, Oct 1998), 165–167 (Russian)

[62] Blondel, C., Roquessalance, R., Testard, O. A., Latimer, F., and Viratelle, D., “Carbon-Carbon Composite: A Strong Material with Low Thermal Conductivity and Thermal Contact for Rigid Optical Assemblies at Low Temperature”, Cryogenics, 29:5 (1989), 569–571 | DOI

[63] Mesnyankin, S. Yu., “A Modern Approach to Accounting for Contact Thermal Resistances in Power Plants”, Proc. of the 5th Minsk Internat. Forum on Heat and Mass Transfer (Minsk, Belarus, May 2004) (Russian) | Zbl

[64] Mesnyankin, S. Yu. and Myasnikov, S. S., “Modern Fundamental Problems of Contact Heat Transfer in Heat-Stressed Installations”, Proc. of the 15th School-Seminar of Young Scientists and Specialists “Problems of Gas Dynamics and Heat and Mass Transfer in Power Plants”: Vol. 2 (Kaluga, Russia, May 2005), MEI, Moscow, 2005, 308–311 (Russian)

[65] Mesnyankin, S. Yu., “Contact Thermal Conductivity and Ways to Increase It”, Proc. of the 4th Minsk Internat. Forum on Heat and Mass Transfer: Vol. 3. Thermal Conductivity and Heat Transfer Optimization Problems (Minsk, Belarus, May 2000), 363–366 (Russian)

[66] Demkin, N. B., Contacting of Rough Surfaces, Nauka, Moscow, 1970, 227 pp. (Russian)

[67] Thomas, T. R. and Probert, S. D., “Thermal Contact Resistance: The Directional Effect and Other Problems”, Int. J. Heat Mass Transf., 13:5 (1970), 789–807 | DOI

[68] Kumar, S. S. and Ramamurthi, K., “Prediction of Thermal Contact Conductance in Vacuum Using Monte Carlo Simulation”, J. Thermophys. Heat Transfer., 15:1 (2001), 27–33 | DOI

[69] Kumar, S. S. and Ramamurthi, K., “Thermal Contact Conductance of Pressed Contacts at Low Temperatures”, Cryogenics, 44:10 (2004), 727–734 | DOI

[70] Xiao, Y., Sun, H., Xu, L., Feng, H., and Zhu, H., “Thermal Contact Conductance between Solid Interfaces under Low Temperature and Vacuum”, Rev. Sci. Instrum., 75:9 (2004), 3074–3076 | DOI

[71] Xu, R. and Xu, L., “An Experimental Investigation of Thermal Contact Conductance of Stainless Steel at Low Temperatures”, Cryogenics, 45:10–11 (2005), 694–704

[72] Wahid, S. M. S., Madhusudana, C., and Leonardi, E., “Solid Spot Conductance at Low Contact Pressure”, Exp. Therm. Fluid Sci., 28:6 (2004), 489–494 | DOI

[73] Kimura, Y., “Estimation of the Number and the Mean Area of Real Contact Points on the Basis of Surface Profiles”, Wear, 15:1 (1970), 47–55 | DOI

[74] Xu, R., Feng, H., Zhao, L., and Xu, L., “Experimental Investigation of Thermal Contact Conductance at Low Temperature Based on Fractal Description”, Int. Commun. Heat Mass Transf., 33:7 (2006), 811–818 | DOI

[75] Maddren, J. and Marschall, E., “Predicting Thermal Contact Resistance at Cryogenic Temperatures for Spacecraft Applications”, J. Spacecraft Rockets, 32:3 (1995), 469–474 | DOI

[76] Uspekhi Fiz. Nauk, 179:9 (2009), 945–970 (Russian) | DOI | DOI

[77] Zheng, J., Li, Y., Chen, P., Yin, G., and Luo, H., “Measurements of Interfacial Thermal Contact Conductance between Pressed Alloys at Low Temperatures”, Cryogenics, 80:Part 1 (2016), 33–43 | DOI

[78] Sviridenok, A. I., Chizhik, S. A., and Petrokovets, M. I., Mechanics of Discrete Frictional Contact, Nauka i tekhnika, Minsk, 1990, 272 pp. (Russian)

[79] Witenberg, Yu. R., Surface Roughness and Methods of Its Assessment, Sudostroenie, Leningrad, 1971, 108 pp. (Russian)

[80] Nayak, P. R., “Random Process Model of Rough Surfaces”, J. Lubr. Technol., 93:3 (1971), 398–407 | DOI

[81] Semenyuk, N. F. and Sirenko, G. A., “Description of the Topography of Anisotropic Rough Friction Surfaces Using a Random Field Model”, Trenie i Iznos, 1:6 (1980), 1010–1020 (Russian)

[82] Husu, A. P., Witenberg, Yu. R., and Pal'mov, V. A., Surface Roughness: A Probability-Theoretic Approach, Nauka, Moscow, 1971, 344 pp. (Russian)

[83] Suslov, A. G., Technological Support of Contact Stiffness of Joints, Nauka, Moscow, 1977, 102 pp. (Russian)

[84] Rudzit, Ya. A., Microgeometry and Contact Interaction of Surfaces, Zinatne, Riga, 1975, 210 pp. (Russian)

[85] Ogar, P. M. and Korsak, I. I., Influence of Characteristics of a Heavily Loaded Joint of Rough Surfaces on Tightness, BrII, Bratsk, 1989, 110 pp. (Russian)

[86] Izmailov, V. V. and Novoselova, M. V., “On the Actual and Physical Areas of Discrete Contact”, Mechanics and Physics of Processes on the Surface and in Contact of Solid Bodies, Parts of Technological and Power Equipment: Vol. 8, TvGTU, Tver, 2015, 4–10 (Russian)

[87] Ryzhov, E. V., Contact Stiffness of Machine Parts, Mashinostroenie, Moscow, 1966 (Russian)

[88] Osipov, A. P., “Modeling of a Rough Surface by Superposition of Relative Reference Curves”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki, 16 (2002), 168–174 (Russian) | DOI

[89] Pashovkin, S. A., “Contact Model of Rough Surfaces Taking into Account Oil Capacity in the Contact Zone”, Izv. Vyssh. Uchebn. Zaved. Mashinostr., 2008, no. 12, 67–72 (Russian)

[90] Tarasov, V. V. and Sivtsev, N. S., “Numerical Simulation of Contact of Rough Surfaces”, Vestn. IzhGTU, 2007, no. 1, 160–165 (Russian)

[91] Bhushan, B., Principles and Applications of Tribology, 2nd ed., Wiley, New York, 2013, 1006 pp.

[92] Peng, W. and Bhushan, B., “A Numerical Three-Dimensional Model for the Contact of Layered Elastic/Plastic Solids With Rough Surfaces by a Variational Principle”, J. Tribol., 123:2 (2001), 330–342 | DOI

[93] Lazarev, V. E., Gram, M. I., Lazarev, E. A., Lavrik, A. N., Franek, F., Pauschitz, A., Forlaufer, G., and Jayza, R., “Mathematical Model of a Rough Surface of a Contact Tribo-Conjugation”, Vestn. Yuzhno-Ural. Gos. Univ. Ser. Mashinostr., 2006, no. 11(66), 54–58 (Russian)

[94] Popov, V. L., Kontaktmechanik und Reibung: Ein Lehr- und Anwendungsbuch von der Nanotribologie bis zur numerischen Simulation, Springer, Berlin, 2009, 340 pp.

[95] Johnson, K. L., Contact Mechanics, Cambridge Univ. Press, Cambridge, 1985, 456 pp. | Zbl

[96] Popov, V. L., Contact Mechanics and Friction: Physical Principles and Applications, Springer, Berlin, 2010, 362 pp. | Zbl

[97] Hyun, S. and Robbins, M. O., “Elastic Contact between Rough Surfaces: Effect of Roughness at Large and Small Wavelengths”, Trobol. Int., 40:10–12 (2007), 1413–1422 | DOI

[98] Sneddon, I. N., “The Relation between Load and Penetration in the Axisymmetric Bossiness Problem for a Punch of Arbitrary Profile”, Int. J. Eng. Sci., 3:1 (1965), 47–57 | DOI | MR | Zbl

[99] Chernov, D. O., Sergeev, D. A., and Meshkov, V. V., “On Modeling the Kinetics of the Formation of the Contact Area of Rough Surfaces”, Vestn. TvGTU, 2012, no. 20, 42–46 (Russian)

[100] Majumdar, A. and Bhushan, B., “Role of Fractal Geometry in Roughness Characterization and Contact Mechanics of Surfaces”, J. Tribology, 112:2 (1990), 205–216 | DOI

[101] Yan, W. and Komvopoulos, K., “Contact Analysis of Elastic-Plastic Fractal Surfaces”, J. Appl. Phys., 84:7 (1998), 3617–3624 | DOI

[102] Hyun, S., Pei, L., Molinari, J.-F., and Robbins, M. O., “Finite-Element Analysis of Contact between Elastic Self-Affine Surfaces”, Phys. Rev. E, 70:2 (2004), Art. 026117, 12 pp. | DOI | MR

[103] Thompson, M. K., “A Comparison of Methods to Evaluate the Behavior of Finite Element Models with Rough Surfaces”, Scanning, 33:5 (2011), 353–369 | DOI

[104] Thompson, M. K. and Thompson, J. M., “Considerations for the Incorporation of Measured Surfaces in Finite Element Models”, Scanning, 32:4 (2010), 183–198 | DOI

[105] Kwon, O. H., Thompson, J. M., and Thompson, M. K., “The Effect of Surface Smoothing and Mesh Density of Real Surfaces in Contact”, Proc. of the Internat. Conf. on Surface Metrology (Worcester Polytechnic Institute, Worcester, Mass., USA, Oct 2009), 5 pp.

[106] Wriggers, P., Computational Contact Mechanics, 2nd ed., Springer, Berlin, 2006, xii, 518 pp. | MR | Zbl

[107] Komvopoulos, K. and Choi, D. H., “Elastic Finite Element Analysis of Multi-Asperity Contact”, J. Tribol., 114:4 (1992), 823–831 | DOI

[108] GOST 25142-82: Surface Roughness: Terms and Definitions, Stadartinform, Moscow, 1982 (Russian)

[109] Demkin, N. B., “Topographic Characteristics of the Surface and the Accuracy of Their Determination”, Mechanics and Physics of Contact Interaction, KGU, Kalinin, 1978, 16–29 (Russian)

[110] Zavarise, G., Borri-Brunetto, M., and Paggi, M., “On the Reliability of Microscopical Contact Models”, Wear, 257:3–4 (2004), 229–245 | DOI

[111] Izmailov, V. V. and Kourova, M. S., “Correlation between Surface Topography and Profile Statistical Parameters”, Wear, 59:2 (1980), 409–420 | DOI

[112] Berkovich, I. I., “Calculation of Statistical Characteristics of a Rough Surface”, Mechanics and Physics of Contact Interaction: Vol. 3, KGU, Kalinin, 1977, 3–16 (Russian)

[113] Bengtsson, A. and Renberg, A., “Obtaining a Topographic Image of a Surface Using a Profiler”, Trenie i Iznos, 7:1 (1986), 27–35 (Russian) | MR

[114] Trenie i Iznos, 31:1 (2010), 68–77 (Russian) | DOI

[115] Goryacheva, I. G., Mechanics of Frictional Interaction, Nauka, Moscow, 2001 (Russian)

[116] Bhushan, B., “Contact Mechanics of Rough Surfaces in Tribology: Multiple Asperity Contact”, Tribol. Lett., 4:1 (1998), 1–35 | DOI | MR

[117] Bolotov, A. N., Sutyagin, O. V., and Rachishkin, A. A., “Computer Modeling of the Topography of Rough Surfaces”, Mechanics and Physics of Processes on the Surface and in Contact of Solid Bodies, Parts of Technological and Power Equipment: Vol. 7, TvGTU, Tver, 2014, 29–41 (Russian)

[118] Gryazev, V. M., “Modeling of the Real Surface of the Part”, Izv. TulGU. Tekhn. Nauki, 2013, no. 1, 192–200 (Russian)

[119] Voynov, K. N., Khodakovsky, V. A., and Schwartz, M. A., “Mathematical Modeling of Rough Surfaces”, Trenie Iznos Smazka, 2009, no. 41, 1–9 (Russian)

[120] Memnonov, V. P. and Morozov, A. O., “An Experimental Estimation of Statistical Characteristics for the Surface Roughness”, Vestn. Sankt-Peterburgsk. Univ. Matem., Mekh., Astronom., 2009, no. 2, 100–104 (Russian)

[121] Uspekhi Fiz. Nauk, 179:9 (2009), 945–970 (Russian) | DOI | DOI

[122] Rachishkin, A. A., Bolotov, A. N., and Sutyagin, O. V., “Computer Modeling of Physical Interactions of Technical Surfaces at the Microlevel”, Komp. i Inform. Nauki, 32:1 (2019), 109–114 (Russian)

[123] Ezhov, A. D., Bykov, L. V., and Mesnyankin, S. Yu., “Numerical Method for Determining the Real Contact Area of Contacting Bodies”, J. Surf. Investig., 12:5 (2018), 914–917 | DOI

[124] Bykov, L. V. and Ezhov, A. D., “Three-Dimensional of Modeling Microgeometry of Contact Pairs in Technical Systems”, IOP Conf. Ser.: Mater. Sci. Eng., 709:1 (2020), 5 pp.

[125] Ezhov, A. D., Mesnyankin, S. Yu., and Bykov, L. V., Determination of Coordinates of Points of a Rough Flat Surface, Certificate of State Registration of Computer Programs No. 2015618021 (Russian)