Skip to main content

Investigation of Ice Rheology Based on Computer Simulation of Low-Speed Impact

  • Conference paper
  • First Online:
Mathematical Modeling and Supercomputer Technologies (MMST 2022)

Abstract

Ice is a complex heterogeneous medium that can be described using different mathematical models, for instance, elasticity, viscosity, plasticity, and viscoplasticity models. This work is aimed at the ice properties investigation based on the data of laboratory experiments. The dependencies between instantaneous force on the ball in the impact point and the depth of ball immersion into ice for different striking velocities were obtained experimentally by other scientists. In this work, linear elasticity, elastoplasticity, and Kukudzhanov elastoviscoplasticity models with different parameters were applied to the collision process simulation. The governing system of equations was solved using grid-characteristic method on structured moving meshes. The results of numerical experiments were compared with the dependencies from the laboratory experiments. Qualitative evaluation of the relation between the chosen model parameters and the calculated dependencies was performed.

The reported study was funded by the Russian Foundation for Basic Research, project no. 20-01-00649.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Petrov, I.B.: Problems of simulation of natural and anthropogenous processes in the arctic zone of the Russian federation. Matem. Mod. 30(7), 103–136 (2018)

    Article  Google Scholar 

  2. Neumeier, J.J.: Elastic constants, bulk modulus, and compressibility of H2O ice Ih for the temperature range 50 K–273 K. J. Phys. Chem. Ref. Data 47, 033101 (2018)

    Article  Google Scholar 

  3. Schwarz, J., Weeks, W.: Engineering properties of sea ice. J. Glaciol. 19(81), 499–531 (1977)

    Article  Google Scholar 

  4. Epifanov, V.P.: Contact fracture behavior of ice. Ice Snow 60(2), 274–284 (2020). [in Russian]

    Google Scholar 

  5. Beklemysheva, K.A., Golubev, V.I., Petrov, I.B., Vasyukov, A.V.: Determing effects of impact loading on residual strength of fiber-metal laminates with the grid-characteristic numerical method. Chin. J. Aeronaut. 34(7), 1–12 (2021)

    Article  Google Scholar 

  6. Petrov, I.B., Khokhlov, N.I.: Modeling 3D seismic problems using high-performance computing systems. Math. Models Comput. Simul. 6(4), 342–350 (2014). https://doi.org/10.1134/S2070048214040061

    Article  MathSciNet  MATH  Google Scholar 

  7. Golubev, V.I., Khokhlov, N.I., Grigorievyh, D.P., Favorskaya, A.V.: Numerical simulation of destruction processes by the grid-characteristic method. Procedia Comput. Sci. 126, 1281–1288 (2018)

    Article  Google Scholar 

  8. Beklemysheva, K.A., Petrov, I.B., Favorskaya, A.V.: Numerical simulation of processes in solid deformable media in the presence of dynamic contacts using the grid-characteristic method. Math. Models Comput. Simul. 6(3), 294–304 (2014). https://doi.org/10.1134/S207004821403003X

    Article  MATH  Google Scholar 

  9. Novatskii, V.: Theory of Elasticity. Mir, Moscow (1975). [in Russian]

    Google Scholar 

  10. Berdennikov, V.P.: Izuchenie modulya uprugosti lda. Trudi GGI 7(61), 13–23 (1948). [in Russian]

    Google Scholar 

  11. Lee, Yung-Li, Barkey, M.E.: Chapter 7 - Fundamentals of Cyclic Plasticity Theories. Metal Fatigue Analysis Handbook, pp. 253–297 (2012)

    Google Scholar 

  12. Kukudzhanov, V.N.: Numerical Solution of Stress Non-One-Dimensional Wave Propagation Problems in Solids. Vychisl. Tsentr Akad, Nauk SSSR, Moscow (1976). [in Russian]

    Google Scholar 

  13. Golubev, V.I., Guseva, E.K., Petrov, I.B.: Application of quasi-monotonic schemes in seismic arctic problems. Smart Innovations, Syst. Technol. 274, 289–307 (2022)

    Article  Google Scholar 

  14. Golubev, V.I., Shevchenko, A.V., Khokhlov, N.I., Petrov, I.B., Malovichko, M.S.: Compact grid-characteristic scheme for the acoustic system with the piece-wise constant coefficients. Int. J. Appl. Mech. 14(2), 2250002 (2022)

    Article  Google Scholar 

  15. Golubev, V.I., Shevchenko, A.V., Petrov, I.B.: Simulation of seismic wave propagation in a multicomponent oil deposit mode. Int. J. Appl. Mech. 12(8), 2050084 (2020)

    Article  Google Scholar 

  16. Rusanov, V.: The calculation of the interaction of non-stationary shock waves with barriers. J. Comput. Math. Phys. USSR. 1, 267–279 (1961)

    MathSciNet  Google Scholar 

  17. Kholodov, A.S., Kholodov, Y.A.: Monotonicity criteria for difference schemes designed for hyperbolic equations. Comput. Math. Math. Phys. 46(9), 1560–1588 (2006)

    Article  MathSciNet  Google Scholar 

  18. Nikitin, I.S., Golubev, V.I.: Higher order schemes for problems of dynamics of layered media with nonlinear contact conditions. Smart Innovations, Syst. Technol. 274, 273–287 (2022)

    Article  Google Scholar 

Download references

Acknowledgements

We thank Dr. E. Bazanova for critical reading of the paper and helpful recommendations. The reported study was funded by the Russian Foundation for Basic Research, project no. 20-01-00649.

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Evgeniya K. Guseva , Vasily I. Golubev or Igor B. Petrov .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Guseva, E.K., Beklemysheva, K.A., Golubev, V.I., Epifanov, V.P., Petrov, I.B. (2022). Investigation of Ice Rheology Based on Computer Simulation of Low-Speed Impact. In: Balandin, D., Barkalov, K., Meyerov, I. (eds) Mathematical Modeling and Supercomputer Technologies. MMST 2022. Communications in Computer and Information Science, vol 1750. Springer, Cham. https://doi.org/10.1007/978-3-031-24145-1_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-24145-1_15

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-24144-4

  • Online ISBN: 978-3-031-24145-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics