Advertisement

Failure Criteria and Compliance Variation of Anisotropically Damaged Materials

Conference paper
  • 369 Downloads
Part of the Lecture Notes in Applied and Computational Mechanics book series (LNACM, volume 9)

Abstract

The damage state is usually described by introducing damage tensor of the second or fourth order. An alternative approach would be based on damage distribution function specifying the damage state on any physical plane. This approach is assumed in the paper. First, the limit state failure condition for a material element is specified by assuming crack density distribution on physical planes. The critical plane approach is next used and the limit condition is obtained in the parametric form with the plane orientation vector to be determined from the maximization of the failure function. The resulting failure condition is applied to the analysis of directional strength evolution of uniaxially compressed specimens with varying orientation of principal stress and damage tensor axes. The damage evolution in a stressed element can also be described by postulating the damage state on the physical plane and its growth due to increasing stress or strain. The damage growth function is assumed and the resulting damage distribution is specified. The associated compliance variation is next determined by accounting for the effect of frictional slip at compressed crack interfaces and opening modes for crack under tensile tractions.

Keywords

Failure condition anisotropic damage critical plane strength variation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andrieux, S., Bamberger, Y. and Marigo, J. (1986). Un modele de materiau microfissure pour les betons et les roches, J. Mec. Theor. Appl. 5: 471–513.Google Scholar
  2. Boehler, J. and Sawczuk, A. (1970). Equilibre limite des sols anisotropes, J. de Mecanique 3: 5–33.Google Scholar
  3. Budiansky, B. and O’Connell, R. (1976). Elastic moduli of a cracked solid, Int. J. Solids Struct. 12: 81–97.zbMATHCrossRefGoogle Scholar
  4. Cazacu, O., Cristescu, N., Shao, J. and Henry, J. (1998). A new anisotropic failure criterion for transversely isotropic solids, Mech. Cohesive-Frictional Mat. 3: 89–103.CrossRefGoogle Scholar
  5. Duveau, G., Shao, J. and Henry, J. (1998). Assessment of some failure criteria for strongly anisotropic geomaterials, Mech. Cohesive-Frictional Mat. 3: 1–26.CrossRefGoogle Scholar
  6. Gambarotta, L. and Lagomarsino, S. (1993). A microcrack damage model for brittle materi­als, Int. J. Solids Struct. 30: 177–198.zbMATHCrossRefGoogle Scholar
  7. Hill, R. (1950). The mathematical theory of plasticity, Clarenddon Press, Oxford.zbMATHGoogle Scholar
  8. Hoek, E. (1983). Strength of jointed rock masses, Geotechnique 33: 187–205.CrossRefGoogle Scholar
  9. Hoek, E. and Brown, E. (1980). Empirical strength criterion for rock masses, J. Geotech. Eng. Div. ASCE 106: 1013–1035.Google Scholar
  10. Horii, H. and Nemat-Nasser, S. (1983). Overall moduli of solids with microcracks: load-induced anisotropy, J. Mech. Phys. Solids 31: 155–171.zbMATHCrossRefGoogle Scholar
  11. Kachanov, M. (1982a). A microcrack model of rock inelasticity. Part 1: Frictional sliding on microcracks, Mech. Mater. 1: 19–28.CrossRefGoogle Scholar
  12. Kachanov, M. (1982b). A microcrack model of rock inelasticity. Part 2: Propagation of mi­crocracks, Mech. Mater. 1: 29–41.CrossRefGoogle Scholar
  13. Lubarda, V. and Krajcinovic, D. (1994). Tensorial representation of the effective elastic prop­erties of the damaged materials, Int. J. Damage Mech. 3: 38–56.CrossRefGoogle Scholar
  14. Mroz, Z. and Jemiolo, A. (1991). Constitutive modeling of geomaterials with account for deformation anisotropy, in E. Onate et al. (ed.), The Finite Element Method in 90’s, Springer-Verlag, pp. 274–284.Google Scholar
  15. Mroz, Z. and Maciejewski, J. (2002). Failure criteria of anisotropically damaged materials based on the critical plane concept, Int. J. Num. Anal. Meth. Goemech 26: 407–131.zbMATHCrossRefGoogle Scholar
  16. Mroz, Z. and Seweryn, A. (1998). Non-local failure and damage evolution rule: Application to a dilatant crack model, J. Phys. IV, France 8: 257–268.CrossRefGoogle Scholar
  17. Niandou, H. (1994). Etude de comportement reologique et modelisation de Vargilite de Tournemire. Application a la stabilite des ouvrages souterrains, PhD thesis, University of Lille.Google Scholar
  18. Nova, R. (1980). The failure of transversally anisotropic rocks in triaxial compression, Int. J. Rock Mech. & Min. Sci. 17: 325–332.CrossRefGoogle Scholar
  19. Ortiz, M. and Popov, E. (1982). A physical model for the inelasticity of concrete, Proc. Royal Soc. London 383: 101–125.zbMATHCrossRefGoogle Scholar
  20. Pariseau, W. (1972). Plasticity theory for anisotropic rock and soils, Proceedings of 10th Symposium on Rock Mechanics, AIME.Google Scholar
  21. Pietruszczak, S. and Mroz, Z. (2000). Formulation of anisotropic failure criteria incorporating a microstructure tensor, Comp. & Geotech. 24: 105–112.CrossRefGoogle Scholar
  22. Pietruszczak, S. and Mroz, Z. (2001). Formulation of failure criteria for anisotropic frictional materials, Comp. & Geotech. 25: 509–524.zbMATHGoogle Scholar
  23. Seweryn, A. and Mroz, Z. (1995). A non-local stress failure condition for structural elements under multiaxial loading, Eng. Fracture Mech. 51: 499–512.CrossRefGoogle Scholar
  24. Seweryn, A. and Mroz, Z. (1998). On the criterion of damage evolution for variable multiaxial stress states, Int. J. Solids Struct. 35(14): 1589–1616.zbMATHCrossRefGoogle Scholar
  25. Sneddon, I. (1969). Crack problems in the classical theory of elasticity, J. Wiley, New York.zbMATHGoogle Scholar
  26. Tsai, S. and Wu, E. (1971). A general theory of strength of anisotropic materials, J. Composite Mater. 5: 58–80.CrossRefGoogle Scholar
  27. Walsh, J. and Brace, J. (1964). A fracture criterion for brittle anisotropic rock, J. Geoph. Res. 69: 3449–3456.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Institute of Fundamental Technological ResearchWarsawPoland

Personalised recommendations