Acta Mechanica Solida Sinica

, Volume 19, Issue 3, pp 275–282 | Cite as

Study on damage bifurcation and instability of rock-like materials

  • Maotian Luan
  • Zhongchang Wang
  • Qing Yang


The critical bifurcation orientation and its corresponding hardening modulus for rock-like geomaterials are derived by considering the effect of stiffness degradation and volumetric dilatancy under the assumption of isotropic damage. The dependency of the localized orientation on the degree of damage and initial Poisson’s ratio of rock is examined and the bifurcation behavior of the uniaxial compression sample under the plane-stress condition is compared with that under plane-strain condition. It is shown that the localization orientation angle intimately depends on both the initial Poisson’s ratio and degree of damage for the rock sample under the uniaxial compression condition. As the initial Poisson’s ratio or degree of damage increases, the orientation angle of the plane on which localization tends to be initiated gets to decrease. At the same time, the localization orientation angle of a rock sample under the plane-stress condition is larger than that under the plane-strain condition.

Key words

damage degradation maximum hardening modulus bifurcation orientation of localization rock-like materials 


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  1. [1]
    Hill, R., A general theory of uniqueness and stability in elastic-plastic solids, Journal of the Mechanics and Physics of Solids, Vol.6, 1958, 236–249.CrossRefGoogle Scholar
  2. [2]
    Rudnicki, J.W. and Rice, J.R., Conditions for the localization of deformation in pressure-sensitive dilatant materials, Journal of the Mechanics and Physics of Solids, Vol.23, 1975, 371–394.CrossRefGoogle Scholar
  3. [3]
    Ottosen, N.S. and Runesson, K., Properties of discontinuous bifurcation solutions in elasto-plasticity, International Journal of Solids and Structures, Vol.27, No.4, 1991, 401–421.CrossRefGoogle Scholar
  4. [4]
    Neilsen, M.K., Bifurcation in elastic-plastic materials, International Journal of Solids and Structures, Vol.30, No.4, 1993, 521–544.CrossRefGoogle Scholar
  5. [5]
    Huang, T. and Li, G.C., The effects of nonuniformity on material bifurcation, Acta Mechanica Solida Sinica, Vol.17, No.2, 1996, 135–139.Google Scholar
  6. [6]
    Yin, G.Z. and Xian, X.F., The bifurcation analysis of shear band of rock under the plane strain condition, Journal of China Coal Society, Vol.24, No.4, 1999, 364–367.Google Scholar
  7. [7]
    Wang, X.B., Pan, Y.S. and Ma, J., Theoretical analysis of stability and unstable sliding of the system composed of shear band and elastic rock, Chinese Journal of Geotechnical Engineering, Vol.24, No.3, 2002, 360–363.Google Scholar
  8. [8]
    Carol, I., Rizzi, E. and Willam, K., A unified theory of elastic degradation and damage based on a loading surface, International Journal of Solids and Structures, Vol.31, No.20, 1994, 2835–2865.CrossRefGoogle Scholar
  9. [9]
    Carol, I., Rizzi, E. and Willam, K., An ‘extended’ volumetric /deviatoric formulation of anisotropic damage based on a pseudo-log rate, European journal of Mechanics-A/ Solids, Vol.21, No.5, 2002, 747–772.CrossRefGoogle Scholar
  10. [10]
    Ju, J.W., Isotropic and anisotropic damage variables in continuum damage mechanics, Journal of Engineering Mechanics, ASCE, Vol.116, No.2, 1990, 2764–2770.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2006

Authors and Affiliations

  1. 1.State Key Laboratory of Coastal and Offshore EngineeringDalian University of TechnologyDalianChina
  2. 2.Institute of Geotechnical Engineering, Scool of Civil and Hydraulic EngineeringDalian University of TechnologyDalianChina

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