Skip to main content

Non-Associated Flow Rules in Description of Plastic Flow of Granular Materials

  • Chapter
Limit Analysis and Rheological Approach in Soil Mechanics

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 217))

Abstract

In most engineering problems related to determination of limit capacity of soil foundation and its interaction with a structure, only static field was considered. Starting from the Coulomb yield condition, the stress field was determined in a more or less accurate way and the estimate of limit safety factor was found. However, the knowledge of the associated velocity field is indispensable in many cases when the problems are statically indeterminate and the solution depends on velocity boundary conditions. A separate class of problems is constituted by such cases as flow of granular materials in silos and chemical reactors, during transport or in earth-working machines (cutting, filling, bulldozing, etc.) In these problems, the mechanism of flow is of primary importance and the constitutive law used in the analysis may essentially affect the solution.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D.C. Drucker and W. Prager, Soil mechanics and plastic analysis or limit design, Quart. AppL Math., voL 10, 157–165, 1952.

    Google Scholar 

  2. E. Melan, Zur Plastizitat des raumlichen Kontinuums, Ingenieur Archiv, vol. 9, 1938, 116–126.

    Article  MATH  Google Scholar 

  3. R. Hill, The mathematical theory of plasticity, Clarendon Press, 1950.

    Google Scholar 

  4. A. Yu. Ishlinsky, On plane flow of sand, (in Russian), Ukr. Math. Journ. vol. 6, 1954.

    Google Scholar 

  5. A.W. Jenike and R.T. Shield, On the plastic flow of Coulomb solids beyond original failure, J. AppL Mech. vol. 27, 599–602, 1959.

    MathSciNet  Google Scholar 

  6. R.T. Shield, Mixed boundary-value problems in soil mechanics, vol. 11, 1953, 61–75.

    MATH  MathSciNet  Google Scholar 

  7. S. Takagi, Plane plastic deformation of soils, Journ. Eng. Mech. Div. ASCE, vol. 88, 1962, 101–151.

    Google Scholar 

  8. De Josselin de Jong, Statics and kinematics in the failable zone of a granular material, Delft, 1959.

    Google Scholar 

  9. J. Mandel, Sur les equations d’écoulement des sols ideaux en deformation plane et le concept du double glissement, Journ. Mech. Phys. Solids, vol. 14, 1968, 303–308.

    Article  MathSciNet  Google Scholar 

  10. G. Mandl, and F.R. Luque, Fully developed plastic shear flow of granular materials, Géotechnique, vol. 20, 1970, 277–307.

    Article  Google Scholar 

  11. G.A. Geniev, Problems of dynamics of granular media, Akad. Stroit. i Arch. Moscow, 1959.

    Google Scholar 

  12. W.W. Sokolovskii, Statics of soil media, Moscow, 1960.

    Google Scholar 

  13. A.J.M. Spencer, A theory of kinematics of ideal soil under plane strain conditions, Journ. Mech. Phys. Solids, vol. 12, 1964, 337–351.

    Article  MATH  Google Scholar 

  14. Z. Mrbz, Non-associated flow laws in plasticity, Journ. de Mécanique, vol. 2, 1963, 21–42.

    Google Scholar 

  15. V.N. Nikolaevski, Constitutive equations of plastic flow of deforming granular materials, Prikl. Math and Mekch., 1971, vol. 35, 1070–1082.

    Google Scholar 

  16. A. Drescher, K. Kwaszczynska and Z. Mrbz, Statics and kinematics of the granular medium in the case of wedge identation, Arch. Mech. Stos., vol. 19, 1967, 99–113.

    Google Scholar 

  17. Z. Mrbz and A. Drescher, Limit plasticity approach to some cases of flow of bulk solids, Journ. Eng. for Industry, vol. 91, 1969, 357–365.

    Google Scholar 

  18. A. Drescher, Some remarks on plane flow of granular media, Arch. Mech. Stos. vol. 24, 1972, 837–848.

    Google Scholar 

  19. A. Drescher and A. Dragon, On kinematics of slopes and embankments, Arch. Inz. Lad. (in Polish), vol. 20, 1974.

    Google Scholar 

  20. Z. Mrôz and A. Drescher, - Foundations of plasticity for granulated materials, (in Polish ), Ossolineum, 1972.

    Google Scholar 

  21. W. Szczepinski, On the motion of flat landslides and avalanches treated as a problem of plasticity, Arch. Mech. Stos. vol. 24, 1972, 919–930.

    Google Scholar 

  22. Z. Mrôz and K. Kwaszczynska, Axially symmetric plastic flow of soils treated by the graphical methods, Arch. Mech. Inz. Lad. vol. 14, 1968, 27–37.

    Google Scholar 

  23. A. Drescher and A. Bujak, Kinematics of a granular material in the case of punch identation (in Polish) Rozpr. Inz. 1966, vol. 14, 313–325.

    Google Scholar 

  24. J.I. Dais, An isotropic frictional theory for a granular material with or without cohesion, Int. J. Solids a. Struct. a. Struct., 1970, vol. 6, 1185–1191.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1978 Springer-Verlag Wien

About this chapter

Cite this chapter

Mróz, Z., Szymański, C. (1978). Non-Associated Flow Rules in Description of Plastic Flow of Granular Materials. In: Olszak, W., Šuklje, L. (eds) Limit Analysis and Rheological Approach in Soil Mechanics. International Centre for Mechanical Sciences, vol 217. Springer, Vienna. https://doi.org/10.1007/978-3-7091-4352-0_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-4352-0_2

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-81511-3

  • Online ISBN: 978-3-7091-4352-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics