Abstract
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.
Similar content being viewed by others
References
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.
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.
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.
Neilsen, M.K., Bifurcation in elastic-plastic materials, International Journal of Solids and Structures, Vol.30, No.4, 1993, 521–544.
Huang, T. and Li, G.C., The effects of nonuniformity on material bifurcation, Acta Mechanica Solida Sinica, Vol.17, No.2, 1996, 135–139.
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.
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.
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.
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.
Ju, J.W., Isotropic and anisotropic damage variables in continuum damage mechanics, Journal of Engineering Mechanics, ASCE, Vol.116, No.2, 1990, 2764–2770.
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported by the National Natural Sciences Foundation of China (No. 10172022).
Rights and permissions
About this article
Cite this article
Luan, M., Wang, Z. & Yang, Q. Study on damage bifurcation and instability of rock-like materials. Acta Mech. Solida Sin. 19, 275–282 (2006). https://doi.org/10.1007/s10338-006-0633-5
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10338-006-0633-5