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A generalized Mohr–Coulomb criterion implied by the revised Goodman–Cowin theory

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Abstract

In the present study, the constitutive relations derived in the revised Goodman–Cowin theory for granular matter are shown to imply a generalized Mohr–Coulomb criterion for impending flows. Due to the concept of microcontinuum and the incorporation of the internal friction into the expression of the Cauchy stress tensor, a constrained equilibrium stress state characterized by the Mohr–Coulomb criterion is yet obtained under uniform distributions of the grains.

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References

  1. Sokolovski V.V. (1965). Statics of Granular Media. Pergamon Press, Oxford

    Google Scholar 

  2. Cowin S.C. (1974). Constitutive relations that imply a generalized Mohr–Coulomb criterion. Acta Mech. 20: 41–46

    Article  MATH  Google Scholar 

  3. Fang C., Wang Y. and Hutter K. (2006). Shearing flows of a dry granular material—hypoplastic constitutive theory and numerical simulations. Int. J. Numer. Anal. Geomech. 30: 1409–1437

    Article  Google Scholar 

  4. Fang, C.: Modeling dry granular mass flows as elasto-visco-hypoplastic continua with microstructural effects. I. Thermodynamically consistent constitutive model. Acta Mech. (2008, in press)

  5. Fang, C.: Modeling dry granular mass flows as elasto-visco-hypoplastic continua with microstructural effects. II. Numerical simulations of benchmark flow problems. Acta Mech. (2008, in press)

  6. Ericksen J.L. (1960). Transversely isotropic fluids. Koll. Z. 173: 117

    Article  Google Scholar 

  7. Ericksen J.L. (1960). Poiseuille flow of certain anisotropic fluids. Arch. Rat. Mech. Anal. 8: 1

    Article  MathSciNet  Google Scholar 

  8. Fang C., Wang Y. and Hutter K. (2006). A thermo-mechanical continuum theory with internal length for cohesionless granular materials. Part I. A class of constitutive models. Continuum Mech. Thermodyn. 17(8): 545–576

    Article  MATH  MathSciNet  Google Scholar 

  9. Fang C., Wang Y. and Hutter K. (2008). An unified evolution equation for the cauchy stress tensor of an isotropic elasto-visco-plastic material. I. On thermodynamically consustent evolution. Continuum Mech. Thermodyn. 19(7): 423–440

    Article  MathSciNet  Google Scholar 

  10. Liu I.-S. (2002). Continuum Mechanics. Springer, Berlin

    MATH  Google Scholar 

  11. Svendsen B., Hutter K. and Laloui L. (1999). Constitutive models for granular materials including quasi-static frictional behaviour: toward a thermodynamic theory of plasticity. Continuum Mech. Thermodyn. 4: 263–275

    Article  MathSciNet  Google Scholar 

  12. Duran J. (2000). Sands, Powders and Grains. Springer, Berlin

    MATH  Google Scholar 

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Correspondence to Chung Fang.

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Fang, C. A generalized Mohr–Coulomb criterion implied by the revised Goodman–Cowin theory. Arch Appl Mech 79, 169–173 (2009). https://doi.org/10.1007/s00419-008-0226-5

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  • DOI: https://doi.org/10.1007/s00419-008-0226-5

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