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Moscow University Mechanics Bulletin

, Volume 74, Issue 5, pp 111–117 | Cite as

Mathematical Modeling of Processes in a Stressed Medium for the Case of a Sudden Break in Continuity

  • A. S. KimEmail author
  • Yu. R. ShpadiEmail author
Article
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Abstract

The nonstationary processes are considered in a prestressed medium for the case of a sudden viscoelastic break in continuity under the conditions of longitudinal shear. It is assumed that the break proceeds along a semi-infinite strip coincident with the plane of maximum shear stresses. The problem is solved analytically in terms of displacements by the Wiener-Hopf method.

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References

  1. 1.
    A. S. Kim, Mechanics of Nonstationary Processes in Nidal Zones of the Earth’s Crust (Gylym Ordasy, Almaty, 2017) [in Russian].Google Scholar
  2. 2.
    A. S. Kim, Yu. R. Shpadi, A. P. Stikharnyi, and Yu. G. Litvinov, “Mathematical Modeling of Non-Stationary Processes in Nidal Zone at Sudden Appearance of Break,” Vestn. Tsentra Kosmich. Issled. Kazakhstan, No 2, 74–82 (2016).Google Scholar
  3. 3.
    A. Kim, “Shear Waves in a Nidal Zone at Sudden Appearance of Break,” Izv. Kakhak Nauch.-Tekh. Obshchest., No. 2, 4–31 (2015).Google Scholar
  4. 4.
    A. Kim, “Non-Stationary Processes in Nidal Zone at Sudden Appearance of Break,” in Proc. 24th Int. Congr. on Theoretical and Applied Mechanics, Montreal, Canada, August 21–26, 2016 (Int. Union Theor. Appl. Mech., Montreal, 2016), pp. 2263–2264.Google Scholar
  5. 5.
    B. V. Kostrov, Mechanics of a Tectonic Earthquake Source (Nauka, Moscow, 1975) [in Russian].Google Scholar
  6. 6.
    K. B. Broberg, “The Propagation of a Brittle Crack,” Arkiv Fysik. 18 (2), 159–192 (1960).MathSciNetGoogle Scholar
  7. 7.
    F. Erdogan, “Theory of Crack Propagation,” in: Fracture (Academic, New York, 1968; Mir, Moscow, 1975), Vol. 2, pp.497–590.Google Scholar
  8. 8.
    G. S. Sih, “Stress Distribution Near Internal Crack Tips for Longitudinal Shear Problems,” J. Appl. Mech. 32 (1), 51–58 (1965).ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    A. E. Molchanov an L. V. Nikitin, “Dynamics of Cracks after the Loss of Stability,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 2, 60–68 (1972).Google Scholar
  10. 10.
    R. Burridge and I. R. Willis, “The Self-Similar Problem of the Expanding Elliptical Crack in an Anisotropic Solid,” Proc. Cambridge Phil. Soc. 66, 443–468 (1969).ADSCrossRefGoogle Scholar
  11. 11.
    G. P. Cherepanov, “The Propagation of Cracks in a Continuous Medium,” Prikl. Mat. Mekh. 31 (3), 476–488 (1967) [J. Appl. Math. Mech. 31 (1), 503–512 (1967)].Google Scholar
  12. 12.
    P. A. Martynyuk, “Dynamic Loading of a Half-Plane with a Crack under Antiplane Strain Conditions,” in: Dynamics of Continuous Media (Nauka, Novosibirsk, 1975), Issue 2, pp. 216–230.Google Scholar
  13. 13.
    L. M. Flitman, “Waves Caused by a Sudden Crack in a Continuous Elastic Medium,” Prikl. Mat. Mekh. 27 (4), 618–628 (1963) [J. Appl. Math. Mech. 27 (4), 938–953 (1963)].zbMATHGoogle Scholar
  14. 14.
    Kh. A. Rakhmatulin, B. Mardonov, O. Ibragimov, and M. Turdiev, “An Earthquake Mechanical Model,” Izv. Akad. Nauk Uzb. SSR, Ser. Tekh. Nauk, No. 5, 53–56 (1976).Google Scholar
  15. 15.
    P. G. Richards, “Dynamic Motions Near an Earthquake Fault: A Three-Dimensional Solution,” Bull. Seismol. Soc. Amer. 66 (1), 1–32 (1976).MathSciNetGoogle Scholar
  16. 16.
    M. Dragoni and S. Santini, “A Two-Asperity Fault Model with Wave Radiation,” Phys. Earth Planet. Inter. 248, 83–89 (2015).ADSCrossRefGoogle Scholar
  17. 17.
    M. M. Nemirovich-Danchenko, “Shear and Cleavage Fracture in Some Geodynamic Problems,” in Proc. All-Russian Conf. on Modern Geodynamics of Central Asia, Irkutsk, Russia, September 23–29, 2012 (Inst. Earth’s Crust, Irkutsk, 2012), Vol. 2, pp. 50–52.Google Scholar
  18. 18.
    Yu.F. Vasil’ev, “Seismic Joint Simulation,” Izv. Akad. Nauk SSSR, Fiz. Zemli, No. 3, 11–18 (1968).Google Scholar
  19. 19.
    F. T. Wu, K. C. Thomson, and H. Kuenzler, “Stick-Slip Propagation Velocity and Seismic Source Mechanism,” Bull. Seismol. Soc. Amer. 62 (6), 1621–1628 (1972).Google Scholar
  20. 20.
    O. G. Shamina, A. A. Pavlov, and S. A. Strizkov, “Modeling of Shear Displacement along a Preexisting Fault with Friction,” in Studies in the Physics of Earthquakes (Nauka, Moscow, 1976), pp. 55–67.Google Scholar
  21. 21.
    K. W. Chang and P. J. Segall, “Injection-Induced Seismicity on Basement Faults Including Poroelastic Stressing,” J. Geophys. Res. B 121 (4), 2708–2726 (2016).ADSCrossRefGoogle Scholar
  22. 22.
    G. G. Kocharyan, V. A. Novikov, and A. A. Ostapchuk, “Realization of Various Fault Slip Modes and the Radiation of Seismic Waves,” in Proc. 10th Int. Conf. on Physical Foundations of Rock Fracture Prediction, Apatity, Russia, June 13–17, 2016 (Kol’skii Nauch. Tsentr Akad. Nauk, Apatity, 2016), p. 23.Google Scholar
  23. 23.
    A. P. Bobryakov, “Modeling Trigger Effects in Faulting Zones in Rocks,” Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 6, 35–44 (2013) [J. Mining Sci. 49 (6), 873–880 (2013)].CrossRefGoogle Scholar
  24. 24.
    M. N. Perel’muter, “Cracks with the Interaction of Faces at the Boundary of a Material Joint. Models and Numerical Methods,” in Proc. 11th All-Russian Conf. on Fundamental Problems of Theoretical and Applied Mechanics, Kazan, August 20–24, 2015 (Kazan Federal. Univ., Kazan, 2015), p. 220.Google Scholar
  25. 25.
    V. A. Saraikin, A. G. Chernikov, and E. N. Sher, “Wave Propagation in Two-Dimensional Block Media with Viscoelastic Layers (Theory and Experiment),” Zh. Prikl. Mekh. Tekh. Fiz. 56 (4), 170–181 (2015) [J. Appl. Mech. Tech. Phys. 56 (4), 668–697 (2015)].MathSciNetzbMATHGoogle Scholar
  26. 26.
    H. Zhang and Z. Ge, “Rupture Pattern of the Oct 23, 2011 Van-Merkez, Eastern Turkey Earthquake,” Earthquake Sci. 27 (3), 257–264 (2014).ADSCrossRefGoogle Scholar
  27. 27.
    Yu. P. Stefanov, A. A. Duchkov, S. V. Yaskevich, and A. S. Romanov, “Analysis of Elastic Wave Radiation during the Hydraulic Fracture Crack Growth,” in Proc. All-Russian Conf. on Trigger Effects in Geosystems, Moscow, Russia, June 16–19, 2015 (GEOS, Moscow, 2015), pp. 92–97.Google Scholar
  28. 28.
    B. Noble, Methods Based on the Wiener-Hopf Technique for the Solution of Partial Differential Equations (Pergamon, New York, 1958; Mir, Moscow, 1962).zbMATHGoogle Scholar
  29. 29.
    V. B. Poruchikov, Methods of the Dynamic Theory of Elasticity (Nauka, Moscow, 1986) [in Russian].Google Scholar

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© Allerton Press, Inc. 2019

Authors and Affiliations

  1. 1.National Center of Space Research and TechnologyInstitute of IonosphereAlmatyKazakhstan

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