Skip to main content
SpringerLink
Log in

Elastoplastic model with damage for strain softening geomaterials

  • Contributed Papers
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Summary

The paper examines certain important aspects of a rate independent model that accounts for distributed damage due to microcrack growth. Material behavior is considered as a mixture of two elastic-plastic interacting components, one termed topical (undamaged), and the other termed damaged. Energy considerations show the equivalence of the two-component body to an elastic-plastic body containing cracks; the equivalence is considered in the Griffith sense. The mechanisms of failure are considered and discussed with respect to multiaxial stress paths. An explanation of failure, at the microlevel, is given. A series of laboratory tests on a concrete are used to illustrate the development of failure.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Hsu, T. C., Slate, F. D., Sturman, G. M., Winter, G.: Microcracking of plain concrete and the shape of the stress-strain curve. J. of the Amer. Concr. Inst.60, 227–239 (1963).

    Google Scholar 

  2. Gardner, N.: Triaxial behavior of concrete. Proc., Amer. Concr. Inst.,66 (1969).

  3. Spooner, O. C., Dougill, J. W.: A quantitative assessment of damage sustained in concrete during compressive loading. Mag. Concr. Res.27, 151–160 (1975).

    Google Scholar 

  4. Van Mier, J. G. M.: Strain softening of concrete under multiaxial loading conditions. Doctoral Dissertation, Eindhoven Univ. of Techn., The Netherlands (1984).

    Google Scholar 

  5. Bazant, Z. P., Kim, S. S.: Plastic fracturing theory for concrete. J. Engr. Mech. Div., ASCE105, 407–478 (1979).

    Google Scholar 

  6. Dragon, A., Mroz, Z.: A continuum model for plastic brittle behavior of rock and concrete. Int. J. Engr. Science17, 121–137 (1979).

    Google Scholar 

  7. Hueckel, T.: On plastic flow of granular and rock like materials with variable elasticity moduli. Publ. Polish Academy of Sci., Sec. Sci. Tech.23, 405–414 (1975).

    Google Scholar 

  8. Maier, G.: Nonassociated and coupled flow rules of elastoplasticity for geotechnical media. Proc., Int. Conf. on Soil Mech. and Found. Engr., Tokyo, 1977.

  9. Dafalias, Y. F.: Modeling cyclic plasticity: Simplicity versus sophistication, in: Mechanics of engineering materials (Desai, C. S., Gallagher, R. H., eds.), pp. 153–178. Chichester, U. K.: John Wiley and Sons 1984.

    Google Scholar 

  10. Young, B. L., Dafalias, Y. F., Herrmann, L. R.: A bounding surface plasticity model for concrete. J. Engr. Mech. Div., ASCE,111, 359–380 (1985).

    Google Scholar 

  11. Hudson, J. A., Brown, E. T., Fairhurst, C.: Shape of the complete stress strain curve for rock. Proc., 13th Symp. Rock Mechs., Univ. of Illinois, Urbana, Illinois, 1971.

  12. Hallbauer, D. K., Wagner, H., Cook, N. G. W.: Some observations concerning the microscopic and mechanical behavior of quartzite specimens in stiff, triaxial compression tests. Int. J. Rock Mechs. Min. Sci.10, 713–718 (1973).

    Google Scholar 

  13. Brady, B. T., Duvall, W. I., Hevino, F. G.: An experimental determination of the true uniaxial stress-strain behavior of brittle rock. Rock. Mechs.5, 107–116 (1973).

    Google Scholar 

  14. Drescher, A., Vardoulakis, I.: Geometric softening in triaxial tests on granular material. Geotechnique32, 291–303 (1982).

    Google Scholar 

  15. Sandler, J. S.: Strain softening for static and dynamic problems. ASME Winter Annual Meeting, Symposium on Constitutive Equations: Micro, Macro and Computational Aspects, CEQ, New Orleans, Dec. 1984.

  16. Read, H. E., Hegemier, G. A.: Strain softening of rock, soil and concrete — A review article. Mechs. of Matls.3, 271–294 (1984).

    Google Scholar 

  17. Pietruszczak, S. T., Mroz, Z.: Finite element analysis of deformation of strainsoftening materials. Int. J. Num. Meth. Engr.17, 327–334 (1981).

    Google Scholar 

  18. Valanis, K. C.: On the uniqueness of solution of the initial value problem in softening materials. J. Appl. Mechs., ASME29, 1–5 (1985).

    Google Scholar 

  19. Desai, C. S.: A consistent finite element technique for work-softening behavior. Proc., Int. Conf. on Comp. Meth. in Nonlinear Mechs. (Oden, J. T., et al., eds), Univ. of Texas, Austin, Texas, 1974.

    Google Scholar 

  20. Kachanov, L. M.: The theory of creep. English translation, ed. by Kennedy, A. J., Chs. IX, X. Boston: National Lending Library 1958.

    Google Scholar 

  21. Rabotnov, Y. N.: Creep problems in structural members. North-Holland 1967.

  22. Frantziskonis, G., Desai, C. S.: Constitutive behavior of geomaterials, part I: Constitutive model with strain softening, part II: Analysis of strain softening constitutive model. Report, Dept. of Civil Eng. and Eng. Mech., Univ. of Arizona, Tucson, AZ, Feb. 1986.

    Google Scholar 

  23. Frantziskonis, G., Desai, C. S.: Constitutive model with strain softening. Int. J. Solids Struct., in press.

  24. Frantziskonis, G., Desai, C. S.: Analysis of strain softening constitutive model. Int. J. Solids Struct., in press.

  25. Desai, C. S., Somasundaram, S., Frantziskonis, G.: A hierarchical approach for constitutive modelling of geologic materials. Int. J. Num. Analyt. Meth. in Geomech.10 (3) (1986).

    Google Scholar 

  26. Frantziskonis, G.: Progressive damage and constitutive behavior for geomaterials, including analysis and implementation. Doctoral Dissertation, Dept. of Civil Engr. and Engr. Mechs., Univ. of Arizona, 1986.

  27. Green, A. E., Naghdi, P. M.: A dynamical theory of interacting continua. Int. J. Engg. Sci.3, 231–241 (1965).

    Google Scholar 

  28. Bowen, R. M.: Theory of mixtures, in: Continuum physics (Eringen, A. C., ed.), Vol. 3, p. 1. New York: Academic Press 1975.

    Google Scholar 

  29. Bowen, R. M.: Thermochemistry of reacting materials. J. Chem. Phys.49, 1625–1637 (1969).

    Google Scholar 

  30. Bowen, R. M.: Thermochemistry of reacting materials. J. Chem. Phys.50, 4601–4602 (1969).

    Google Scholar 

  31. Ortiz, M.: A constitutive theory for the inelastic behavior of concrete. Mechs. of Matls.4, 67–93 (1985).

    Google Scholar 

  32. Hill, R.: The mathematical theory of plasticity. London: Oxford Press 1950.

    Google Scholar 

  33. Desai, C. S.: A general basis for yield, failure and potential functions in plasticity. Int. J. Num. Anal. Meth. in Geomech.4, 361–375 (1980).

    Google Scholar 

  34. Baker, R., Desai, C. S.: Induced anisotropy during plastic straining. Int. J. Num. Anal. Meth. in Geomech.8, 167–185 (1984).

    Google Scholar 

  35. Desai, C. S., Faruque, M. O.: Constitutive model for (geological) materials. J. of Eng. Mech. Div., ASCE110 (9), 1391–1408 (1984).

    Google Scholar 

  36. Rivlin, R. S., Ericksen, J. I.: Stress-deformation relations for isotropic materials. J. Rational Mech. Anal.4, 323–425 (1955).

    Google Scholar 

  37. Green, A. E., Naghdi, P. M.: A general theory of elastic-plastic continuum. Arch. of Rational Mech. and Anal.8 (4), (1965).

  38. Desai, C. S., Somasundaram, S., Faruque, M. O.: Constitutive modelling of geological materials, in: Developments in soil mechanics and foundation engineering (Banerjee, P. K., Butterfield, R., eds.), London: Elsevier Applied Science Publishers 1985.

    Google Scholar 

  39. Desai, C. S., Frantziskonis, G., Somasundaram, S.: Constitutive modelling for geologic materials. Proc., 5th Int. Conf. on Num. Meth. in Geomechanics, Nagoya, Japan, April 1985.

  40. Frantziskonis, G., Desai, C. S., Somasundaram, S.: Constitutive model for nonassociative behavior. J. of Eng. Mech. Div., ASCE112 (9), 932–946 (1986).

    Google Scholar 

  41. Griffith, A. A.: The phenomena of rupture and flow in solids. Phil. Trans. Roy. Soc. London, SeriesA 221, 163–168 (1920).

    Google Scholar 

  42. Griffith, A. A.: The theory of rupture. Proc., First Intl. Congress for Appl. Mechs., pp. 55–63, Delft 1924.

  43. Eftis, J., Liebowitz, H.: On fracture toughness evaluation for semi-brittle fracture. Engr. Fract. Mechs.7, 101–135, 1975.

    Google Scholar 

  44. Lotsberg, I.: Finite element analysis of some problems in fracture mechanics. Div. of Struct. Mech., The Norwegian Inst. of Technology Report No. 77-5, 1977.

  45. Davis, P. C., Sih, G. C.: Stress analysis of cracks, fracture toughness and its applications. ASTM STP 381, Philadelphia, 1965.

  46. Goodier, J. N.: Mathematical theory of equilibrium cracks in fracture (Liebowitz, H., ed), Vol. 2, New York: Academic Press 1968.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Civil Engineering and Engineering Mechanics, University of Arizona, 85721, Tucson, AZ, USA

    G. Frantziskonis & C. S. Desai

Authors
  1. G. Frantziskonis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. S. Desai
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

With 8 Figures

Rights and permissions

Reprints and permissions

About this article

Cite this article

Frantziskonis, G., Desai, C.S. Elastoplastic model with damage for strain softening geomaterials. Acta Mechanica 68, 151–170 (1987). https://doi.org/10.1007/BF01190880

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01190880

Keywords

Search

Navigation