Abstract
A micromechanics-based model is established. The model takes the interaction among sliding cracks into account, and it is able to quantify the effect of various parameters on the localization condition of damage and deformation for brittle rock subjected to compressive loads. The closed-form explicit expression for the complete stress-strain relation of rock containing microcracks subjected to compressive loads was obtained. It is showed that the complete stress-strain relation includes linear elasticity, nonlinear hardening, rapid stress drop and strain softening. The behavior of rapid stress drop and strain softening is due to localization of deformation and damage. Theoretical predictions have shown to be consistent with the experimental results.
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References
Simo J C, Ju J W. Strain- and stress-based continuum damage models[J].Internat J Solids and Structures, 1987,23(7): 821–840.
Ortiz M. A constitutive theory for the inelastic behavior of concrete[J].Mech Mater, 1985,4(1): 67–93.
Ju J W. On two-dimensional self-consistent micromechanical damage models for brittle solids[J].Internat J Solids and Structures, 1991,27(2): 227–258.
Nemat-Nasser S, Horii H. Compression induced microcrack growth in brittle solids: axial splitting and shear failure[J].Journal of Geophysics Research, 1985,90(B4): 3105–3125.
Ashby M F, Hallam S D. The failure of brittle solids containing small cracks under compressive states[J].Acta Metallica, 1986,34(3): 497–510.
Kachanov M. A microcrack model of rock inelasticity—Part I: frictional sliding on microcracks [J].Mechanics of Materials, 1982,1(1): 19–27.
Nemat-Nasser S, Obata M. A microcrack model of dilatancy in brittle materials[J].Journal of Applied Mechanics, 1988,55(1): 24–35.
Basista M, Gross D. The sliding crack model of brittle deformation: an internal variable approach [J].Internat J Solids and Structures, 1998,35(5/6): 487–509.
Okubo S, Nishimatsu Y, He C. Loading rate dependence of class II rock behavior in uniaxial and triaxial compression tests—an application of a proposed new control method[J].Internat J Rock Mech Min Sci & Geomech Abstr, 1990,27(6): 559–562.
Rice J R. Inelastic constitutive relations for solids: an internal-variable theory and its application to metal plasticity[J].Journal of the Mechanics and Physics of Solids, 1971,19(6): 433–455.
ZHOU Xiao-ping, HA Qiu-lin, ZHANG Yong-xing,et al. Analysis of the deformation localization and the complete stress-strain relation for brittle rock subjected to dynamic compressive loads[J].Internat J Rock Mech Min Sci, 2004,41(2): 311–319.
Tada H, Paris P C, Irwin G R.The Stress Analysis of Cracks Handbook[M]. St Louis Ed. Paris: Paris Production Incorporated, 1985.
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Communicated by XIE He-ping and CHEN Shan-lin
Foundation item: the National Natural Science Foundation of China (59879012, 59649008)
Biography: ZHOU Xiao-ping (1970~)
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Xiao-ping, Z., Yong-xing, Z., Qiu-ling, H. et al. Analysis of the localization of damage and the complete stress-strain relation for mesoscopic heterogeneous brittle rock subjected to compressive loads. Appl Math Mech 25, 1039–1046 (2004). https://doi.org/10.1007/BF02438353
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DOI: https://doi.org/10.1007/BF02438353
Key words
- compressive load
- mesoscopic heterogeneous rock
- complete stress-strain relation
- localization of damage and deformation