Applied Mathematics and Mechanics

, Volume 22, Issue 9, pp 1028–1034 | Cite as

Constitutive Theory of Plasticity Coupled with Orthotropic Damage for Geomaterials

  • Xin-pu Shen
  • Zenon Mroz
  • Bing-ye Xu


Constitutive theory of plasticity coupled with orthotropic damage for geomaterials was established in the framework of irreversible thermodynamics. Prime results include: 1) evolution laws are presented for coupled evolution of plasticity and orthotropic damage; 2) the orthotropic damage tensor is introduced into the Mohr-Coulomb criterion through homogenization. Both the degradation of shear strength and degradation of friction angle caused by damage are included in this model. The dilatancy is calculated with the so-called damage strain.

damage plasticity coupling dilatancy geomaterial 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Lemaitre J. A Course on Damage Mechanics [M]. 2nd ed. Berlin: Springer, 1990.Google Scholar
  2. [2]
    Hansen N R, Schreyer H L. A thermodynamically consistent framework for theories of elastoplasticity coupled with damage [J]. Int J Solids Structures, 1994, 31(2):359–389.Google Scholar
  3. [3]
    Hayakawa K, Murakami S. Thermodynamic modeling of elastic-plastic damage and experimental validation of damage potential [J]. Int J Dama Mech, 1997, 6(2):333–363.Google Scholar
  4. [4]
    Mariotti de Sciarra F. A new variational theory and a computational algorithm for coupled elastoplastic damage models [J]. Int J Solids Structures, 1997, 34(9):1761–1796.Google Scholar
  5. [5]
    Basista M, Gross D. The sliding crack model of brittle deformation: an internal variable approach[J]. Int J Solids Structures, 1998, 35(3): 487–509.Google Scholar
  6. [6]
    Dragon A, Halm D. A mesocrack damage and friction coupled model for brittle materials [A]. In: Voyiadjis G Z, Ju J W, Chaboche J L Eds. Damage Mechanics in Engineering Materials [C]. Amsterdam: Elsevier Science, 1998, 321–336.Google Scholar
  7. [7]
    Meschke G, Lackner R, Mang H A. An anisotropic elastoplastic-damage model for plain concrete[J]. Int J Numer Mech Engng, 1998, 42(3): 703–727.Google Scholar
  8. [8]
    Yazdani S, Karnawat S. A constitutive theory for brittle solids with application to concrete [J]. Int J Dama Mech, 1996, 5(1): 93–110.Google Scholar
  9. [9]
    Vutukuri V S, Lama R D, Saluja S S. Handbook on Mechanical Properties of Rocks [M]. Vol. 1. Berlin: Trans Tech Publisher, 1974.Google Scholar
  10. [10]
    Duveau G, Shao J F. A modified single plane of weakness theory for the failure of highly stratified rocks [J]. Int J Rock Mech Min Sci, 1998, 35(6): 807–813.Google Scholar
  11. [11]
    Hoek E, Brown E T. Practical estimation of rock mass strength [J]. Int J Rock Mech Min Sci, 1997, 34(8), 1165–1186.Google Scholar
  12. [12]
    Muller D, Kratochvil J, Berveiller M. Nonlocal versus local elastoplastic behavior of heterogeneous materials [J]. Int J Plasticity, 1993, 9(3): 633–645.Google Scholar
  13. [13]
    Rice J R. Inelastic constitutive relations for solids: an internal variable theory and its application to metal plasticity [J]. J Mech Phys Solids,1971, 19(2): 433–455.Google Scholar
  14. [14]
    Swoboda G, Shen X P, Rosas L. Damage model for jointed rock mass and its application to tunneling[J]. Computer and Geotechnics, 1998, 22(3/4): 183–203.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Xin-pu Shen
    • 1
  • Zenon Mroz
    • 2
  • Bing-ye Xu
    • 3
  1. 1.Department of Architectural EngineeringShenyang University of TechnologyShenyangP R China
  2. 2.IFTR, Polish Academy of SciencesWarsawPoland
  3. 3.Department of Engineering MechanicsTsinghua UniversityBeijingP R China

Personalised recommendations