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Contact Interaction of Layers

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Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 21))

Abstract

Algorithms for numerical implementation of conditions of dynamic contact interaction of deformable materials with a beforehand unknown zone of contact which varies in the process of motion are constructed. These algorithms take into account the influence of friction forces in a contact zone. On the basis of these algorithms a method for the numerical modeling of deformation of a body of a granular material in the presence of sliding surfaces is worked out. Results of testing an algorithm and results of the numerical solution of a problem for two layers of a medium consisting of an elastic-plastic material are presented. Computational algorithms are developed that simulate the dynamic interaction of elastic blocks through thin viscoelastic layers in structurally inhomogeneous media such as rocks.

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References

  1. Aleksandrova, N.I., Chernikov, A.G., Sher, E.N.: Experimental investigation into the one-dimensional calculated model of wave propagation in block medium. J. Min. Sci. 41(3), 232–239 (2005)

    Google Scholar 

  2. Aleksandrova, N.I., Sher, E.N., Chernikov, A.G.: Effect of viscosity of partings in block-hierarchical media on propagation of low-frequency pendulum waves. J. Min. Sci. 44(3), 225–234 (2008)

    Article  Google Scholar 

  3. Annin, B.D.: Mekhanika Deformirovaniya i Optimal’noe Proektirovanie Sloistykh Tel (Mechanics of Deformation and Optimal Design of Laminated Bodies). Izd, IGiL SO RAN, Novosibirsk (2005)

    Google Scholar 

  4. Annin, B.D., Sadovskaya, O.V., Sadovskii, V.M.: Numerical simulation of oblique impact of plates in the elastoplastic formulation. Phys. Mesomechanics 3(4), 23–28 (2000)

    Google Scholar 

  5. Annin, B.D., Sadovskaya, O.V., Sadovskii, V.M.: Dynamic contact problems of elasto-plasticity. Problems Mater. Sci. 33(1), 426–434 (2003)

    Google Scholar 

  6. Boreskov, A.V., Kharlamov, A.A.: Osnovy Raboty s Tekhnologiei CUDA (Basics of Operating with the CUDA Technology). DMK Press, Moscow (2010)

    Google Scholar 

  7. Bychek, O.V., Sadovskii, V.M.: Study of the dynamic contact interaction of deformable bodies. J. Appl. Mech. Tech. Phys. 39(4), 628–633 (1998)

    Article  Google Scholar 

  8. Duvaut, G., Lions, J.L.: Les Inéquations en Mécanique et en Physique. Dunod, Paris (1972)

    Google Scholar 

  9. Farber, R.: CUDA Application Design and Development. Morgan Kaufmann/Elsevier, San Fransisco/Amsterdam (2011)

    Google Scholar 

  10. Glowinski, R., Lions, J.L., Trémoliéres, R.: Analyse Numérique des Inéquations Variationnelles, vol. 1–2, Dunod, Paris (1976)

    Google Scholar 

  11. Godunov, S.K.: Uravneniya Matematicheskoi Fiziki (Equations of Mathematical Physics). Nauka, Moscow (1979)

    Google Scholar 

  12. Hwu, W.W. (ed.): GPU Computing Gems, Emerald edn. Morgan Kaufmann/Elsevier, San Fransisco/Amsterdam (2011)

    Google Scholar 

  13. Johnson, K.: Contact Mechanics. Cambridge University Press, Cambridge, UK (1985)

    Google Scholar 

  14. Kirk, D.B., Hwu, W.W.: Programming Massively Parallel Processors: A Hands-on Approach. Morgan Kaufmann/Elsevier, San Fransisco/Amsterdam (2010)

    Google Scholar 

  15. Kornev, V.M., Yakovlev, I.V.: Model of undulation in explosive welding. Combustion, Explosion, and Shock Waves 20(2), 204–207 (1984)

    Article  Google Scholar 

  16. Kravchuk, A.S.: On the Hertz problem for linearly and nonlinearly elastic bodies of finite dimensions. Dokl. Akad. Nauk SSSR 230(2), 308–310 (1976)

    Google Scholar 

  17. Kravchuk, A.S.: Formulation of the problem about contact of several deformable bodies as the problem of nonlinear programming. J. Appl. Math. Mech. 42(3), 489–489 (1978)

    Article  Google Scholar 

  18. Kravchuk, A.S.: On the theory of contact problems taking account of friction on the contact surface. J. Appl. Math. Mech. 44(1), 83–88 (1980)

    Article  Google Scholar 

  19. Kravchuk, A.S.: Variaczionnye i Kvazivariaczionnye Neravenstva v Mekhanike (Variational and Quasivariational Inequalities in Mechanics). MGAPI, Moscow (1997)

    Google Scholar 

  20. Kravchuk, A.S., Sursyakov, V.A.: Numerical solution of geometrically nonlinear contact problems. Dokl. Akad. Nauk SSSR 259(6), 1327–1329 (1981)

    Google Scholar 

  21. Kurlenya, M.V., Oparin, V.N., Vostrikov, V.I.: On formation of elastic wave packages at impulsive excitation of block media. Waves of pendulum type. Dokl. Akad. Nauk SSSR 333(4), 3–13 (1993)

    Google Scholar 

  22. Revuzhenko, A.F.: Mekhanika Uprugoplasticheskikh Sred i Nestandartnyi Analiz (Mechanics of Elastic-Plastic Media and Nonstandard Analysis). Izd. Novosib. Univ., Novosibirsk (2000)

    Google Scholar 

  23. Revuzhenko, A.F.: Mechanics of Granular Media. Springer, Berlin (2006)

    Google Scholar 

  24. Revuzhenko, A.F., Shemyakin, E.I.: Kinematics of deformation of granular medium with nonviscous friction. Prikl. Mekh. Tekhn. Fiz. 15(4), 119–124 (1974)

    Google Scholar 

  25. Revuzhenko, A.F., Stazhevskii, S.B., Shemyakin, E.I.: On mechanism of deformation of granular material under large shears. Fiz.-Tekhn. Probl. Razrab. Pol. Iskop. 3, 130–133 (1974)

    Google Scholar 

  26. Revuzhenko, A.F., Stazhevskii, S.B., Shemyakin, E.I.: Problems of mechanics of granular media in mining. Fiz.-Tekhn. Probl. Razrab. Pol. Iskop. 3, 19–25 (1982)

    Google Scholar 

  27. Sadovskaya, O.V.: On numerical analysis of the collision of elastic-plastic bodies taking into account finite rotations. In: Proceedings of the Continuum Dynamics Mathematical Problems of the Continuum Mechanics, Izd. IGiL SO RAN, Novosibirsk, vol. 114, pp. 196–199 (1999)

    Google Scholar 

  28. Sadovskaya, O.V.: Application of quasivariational inequalities to the solution of dynamic contact problems. In: Proceedings of the International Conference on Mathematical Models and Methods of Their Investigation, IVM SO RAN, Krasnoyarsk, vol. 2, pp. 165–171 (2001)

    Google Scholar 

  29. Sadovskaya, O.V.: Numerical solution of dynamic contact problems taking into account finite rotations. In: Proceedings of the Mathematical Centre by N. I. Lobachevskii, Models of the Continuum Mechanics, Izd. Kazansk. Mat. Obshhestva, Kazan, vol. 16, pp. 65–74 (2002)

    Google Scholar 

  30. Sadovskii, M.A.: Natural lumpiness of a rock. Dokl. Akad. Nauk SSSR 247(4), 829–831 (1979)

    Google Scholar 

  31. Saraikin, V.A.: Elastic properites of blocks in the low-frequency component of waves in a 2D medium. J. Min. Sci. 45(3), 207–221 (2009)

    Article  Google Scholar 

  32. Signorini, A.: Sopra alcune questioni di elastostatica. Atti Soc. Ital. Progr. Sci. 513–533 (1933)

    Google Scholar 

  33. Varygina, M.P., Pokhabova, M.A., Sadovskaya, O.V., Sadovskii, V.M.: Numerical algorithms for the analysis of elastic waves in block media with thin interlayers. Numer. Methods Program. Adv. Comput. 12(2), 190–197 (2011)

    Google Scholar 

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Correspondence to Oxana Sadovskaya .

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Sadovskaya, O., Sadovskii, V. (2012). Contact Interaction of Layers. In: Mathematical Modeling in Mechanics of Granular Materials. Advanced Structured Materials, vol 21. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29053-4_7

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