, Volume 11, Issue 4, pp 227–235 | Cite as

Coupling of elastic and plastic deformations of bulk solids

  • Tomasz Hueckel


In such solids like rocks, soils, ceramics, grain en masse the plastic deformation strongly aects the current unloading modulus. The consequences of this effect referred to as the elastoplastic coupling both to the elastic and the plastic part of the constitutive law are examined. Particularly, it appears that such phenomenon induces a specific kind of the non-normality in the plastic flow law. The departure from the normality is studied in connection with the form of the elastic modulus variation basing on the notion of a coupling potential.


Mechanical Engineer Elastic Modulus Plastic Deformation Civil Engineer Alla 
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Il modulo di scarico elastico di solidi come le rocce, i suoli, i materiali ceramici e granulari dipende dalla entità delle deformazioni plastiche. Le conseguenze di questo fenomeno, chiamato nel seguito accoppiamento elastoplastico, vengono esaminate sia in relazione alla parte elastica che alla parte plastica della legge costitutiva. In particolare si dimostra che l'accoppiamento elastoplastico determina la non-normalità della legge di scorrimento plastico. La deviazione della normalità legata alla variazione del modulo elastico è studiata per mezzo di un potenziale di accoppiamento derivato da quello elastico.


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  1. [1]
    Bieniawski Z. T.,Deformational Behaviour of Fractured Rock under Multiaxial Compression, Proc. Structures, Solid Mechanics and Engineering Design, Southampton 1969, Ed. M. Te'Eni, Wiley Intersciences, Part. 1, 589–598.Google Scholar
  2. [2]
    Edmond J. M., Paterson M. S.,Volume Changes during Deformation of Rocks at High Pressures, Int. Jour. Rock Mech. Min. Sci., Vol. 9, 1972, 161–182.Google Scholar
  3. [3]
    Hardy M. P., Hudson J. A. andFairhurst C.,The Failure of Rock Beams. Int. J. Rock Mech. Min. Sci. Part I and II, Vol. 10, 1973, 53–67, 69–82.Google Scholar
  4. [4]
    Karsan D., Jirsa J. O.,Behaviour of Concrete under Compressive Loadings, Proc. ASCE, 95, ST. 42, Dec. 1969, 2543–2561.Google Scholar
  5. [5]
    Hueckel T., Drescher A.,On Dilatational Effects of Inelastic Granular Media, Archives of Mechanics, 27, 1, 157–172, 1975.Google Scholar
  6. [6]
    Green D. J., Nicholson P. S., Embury J. D.,Microstructural Development and Fracture Toughness of Calcia Partially Stabilized Zirconia, in:Fracture Mechanics of Ceramics, Vol. 2, Eds: Bradt-Hasselman-Lang, Plenum Press, 541–553, 1972.Google Scholar
  7. [7]
    Scholz C. H.,Microfracturing and the Inelastic Deformation of Rock in Compression, Jnl. Geophysical Research, Vol. 73, 4, 1968. 1417–1432.Google Scholar
  8. [8]
    Hueckel T.,A Note on the Behaviour of Hardening-Softening Granular Media, in:Proc. Problems of Plasticity, 1972 Ed. A. Sawczuk, Noordhoff Int.Google Scholar
  9. [9]
    Weidler J. B., Paslay D. R.,Constitutive Relations for Inelastic Grannular Medium, Proc. A.S.C.E., EM4, 1970, 1970, 395–406.Google Scholar
  10. [10]
    Hueckel T.,On Plastic Flow of Granular and Rocklike Materials with Variable Elasticity Moduli, Bull. Polish Acad. Sci. Ser. Sci. Tech. Vol. XXIII, No. 8, 1975, 405–414.Google Scholar
  11. [11]
    Noble B., Sewell M. J.,On Dual Extremum Principles in Applied Mathematics, Jnl. of Inst. of Mathematics and its Applications, 9, 1972, 123–193.Google Scholar
  12. [12]
    Mroz Z.,Non-Associated Flow Laws in Plasticity (an additive note to the paper in J. Mécanique, 2, 1, 1963, 21–42) J. Mécanique V. 3, 4 1964, 531–532.Google Scholar
  13. [13]
    Palmer A. C., Maier G., Drucker D. C.,Normality Relations and Convexity of Yield Surface for Unstable Materials or Structural Elements, J. Applied Mech., V. 3, 4, 1967, 464–470.Google Scholar
  14. [14]
    Iliushin A. A.,On the Postulate of Plasticity, Prikl. Matem. i, Mekhanika, 25, No. 3, 1961.Google Scholar
  15. [15]
    Mroz Z.,Non-Associated Flow Rules in Description of Plastic Flow of Granular Materials, Lecture Notes, Centre Int. Sci. Mécanique, Udine, 1974.Google Scholar
  16. [16]
    Maier G., Hueckel T.,On Non-Associated and Coupled Flow Rules of Elasto-Plasticity for Rock-like Media, to appear.Google Scholar
  17. [17]
    Hueckel T., Maier G.,Incremental Boundary Value Problems in the Presence of Coupling Between Elastic and plastic Deformations; A Rock Mechanics Oriented Theory,Int. J. Solids Structures 1, 1977, 1–15.Google Scholar

Copyright information

© Masson Italia Editori 1977

Authors and Affiliations

  • Tomasz Hueckel
    • 1
  1. 1.Institute of Fundamental Technological Research Polish Academy of Sciences Swietokrzyska 21WarsawaPoland

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