Advertisement

Numerical Simulation of Plastic Localization Using Fe-Mesh Realignment

  • R. Larsson
  • K. Runesson
  • A. Samuelsson
Part of the International Centre for Mechanical Sciences book series (CISM, volume 321)

Abstract

Proper design of the computational algorithm is absolutely essential in order to account for the failure mechanisms that are responsible for the development of a strongly localized mode of deformation. In this paper we discuss how to simulate numerically localized behavior of the deformation due to incorporation of non-associated plastic flow and/or softening behavior in the elasto-plastic material model. The development of a localization zone of a slope stability problem is captured by the use of a FE-mesh adaptation strategy, which aims at realigning the inter-element boundaries so that the most critical kinematical failure mode is obtained. Based on the spectral properties of the characteristic material operator we define a criterion for discontinuous bifurcation. As a by-product from this criterion, we obtain critical bifurcation directions which are used to realign the element mesh in order to enhance the ability of the model to describe properly the failure kinematics. Moreover, a successful algorithm also includes consideration of stability properties of the elasto-plastic solution.

Keywords

Shear Band Plastic Zone Flow Rule Associate Flow Rule Incremental Solution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. Nadai, Plasticity, McGraw-Hill Book Company (1931)Google Scholar
  2. 2.
    T.Y. Thomas, Plastic Flow and Fracture in Solids, Academic Press (1961)Google Scholar
  3. 3.
    Z.P. Bazant, “Mechanics of distributed cracking”, Appl. Mech. Rev., 39, 675–705 (1986)CrossRefGoogle Scholar
  4. 4.
    Y. Leroy and M. Ortiz, “Finite element analysis of strain localization in frictional materials”, Int. J. Num. Anal. Meth. Geomech., 13, 53–74 (1989)CrossRefGoogle Scholar
  5. 5.
    Y. Leroy and M. Ortiz, “Finite element analysis of transient strain localization phenomena in frictional materials”, Int. J. Num. Anal. Meth. Geomech., 14, 93–124 (1990)CrossRefMATHGoogle Scholar
  6. 6.
    M. Ortiz and J.J. Quigley, “Element design and adaptive remeshing in strain localization problems”, in: D.R.J Owen, E. Hinton and E. Onate (eds.), Computational Plasticity, COMPLAS II pp. 213–236 Swansea: Pineridge Press (1989)Google Scholar
  7. 7.
    Z.P. Bazant, “Stable states and paths of structures with plasticity of damage”, J. Engng. Mech., ASCE, 114, 2013–2034 (1988)CrossRefGoogle Scholar
  8. 8.
    K. Runesson, R. Larsson and S. Sture, “Characteristics and computational procedure in softening plasticity”, J. Engng. Mech., ASCE, 115 1628–1646, (1989)CrossRefGoogle Scholar
  9. 9.
    K. Runesson, R. Larsson and N. S. Ottosen, “Extremal Properties of Incremental Solutions in Plasticity at Implicit Integration - Localization”, submitted to ASCE, J. Engng Mech. (1991)Google Scholar
  10. 10.
    R. Hill, “A general theory of uniqueness and stability in elastic-plastic solids.” J. Mech. Phys. Solids, 6, 236–249 (1958)CrossRefMATHGoogle Scholar
  11. 11.
    V. Tvergaard, A. Needleman and K. K. Lo, “Flow localization in the plane strain tensile test”, J. Mech. Phys. Solids, 29, 115–142 (1981)CrossRefMATHGoogle Scholar
  12. 12.
    N. Triantafyllidis, A. Needleman and V. Tvergaard, “On the development of shear bands in pure bending”, Int. J. Solids Struct., 18, 121–138 (1982)CrossRefMATHGoogle Scholar
  13. 13.
    A. Needleman and V. Tvergaard, “Finite element analysis of localization in plasticity”, in: J.T. Oden and C.F. Carey (eds.), Finite elements: Special problems in solid mechanics, 5, pp.. 94–157 Prentice-Hall (1984)Google Scholar
  14. 14.
    J.H. Prevost, “Localization of deformations in elastic-plastic solids”, Int. J. Num. Anal. Meth. Geomech., 8, 187–196 (1984)CrossRefMATHGoogle Scholar
  15. 15.
    R. de Borst, “Numerical methods for bifurcation analysis in geomechanics”, Ingenieur-Archiv, 59, 160–174 (1989)CrossRefGoogle Scholar
  16. 16.
    R. de Borst, “Bifurcations in finite element methods with a non-associated flow law”, Int. J. Num. Anal. Meth. Geomech., 12, 99–116 (1988)CrossRefMATHGoogle Scholar
  17. 17.
    J.P. Bardet, “A note on the finite element simulation of strain localization”, in: O.Z. Zienkiewicz, G.N. Pande and J. Middleton (eds.), Numerical Methods in Engineering: Theory’and Applications, NUMETA 87, Martinus Nijhoff (1987)Google Scholar
  18. 18.
    J.P. Bardet and S. M. Mortazavi, “Simulation of shear band formation in over consolidated”, in: C.S. Desai, E. Krempl, P.D. Kiousis and T. Kundu (eds.), Constitutive Laws for Engineering Materials and Applications, pp. 805–812 Elsevier (1987)Google Scholar
  19. 19.
    L. Nilsson and M. Oldenburg, “Non-linear wave propagation in plastic fracturing materials”, in: U. Nigel and J. Engelbrecht (eds.), Nonlinear Deformation Waves, IUTAM Symp., pp. 209–217 Berlin: Springer (1983)CrossRefGoogle Scholar
  20. 20.
    J.G. Rots, P. Nauta, G.M.A. Kusters and J. Blaauwendraad, “Smeared crack approach and fracture localization in concrete”, Heron, 30, 1–48 (1985)Google Scholar
  21. 21.
    R. de Borst, “Computation of post-bifurcation and post-failure behavior of strain-softening solids”, Computers and Structures, 25, 211–224 (1987)CrossRefMATHGoogle Scholar
  22. 22.
    O. Dahlbom and N.S. Ottosen, “Smeared crack analysis using generalized fictitious crack model”, J. Engng. Mech., ASCE, 116, 55–76 (1990)CrossRefGoogle Scholar
  23. 23.
    R. Glemberg, Dynamic analysis of concrete structures, Publ. 84:1 (Ph. D. Dissertation), Dept. of Structural Mechanics, Chalmers University of Technology, (1984)Google Scholar
  24. 24.
    M. Ortiz, Y. Leroy and A. Needleman, “A finite element method for localized failure analysis”, Comp. Meth. Appl. Mech. Engng., 61, 189–214 (1987)CrossRefMATHGoogle Scholar
  25. 25.
    R. Larsson, Numerical Simulation of Plastic Localization, Publ. 90:5 (Ph. D. Dissertation), Dept. of Structural Mechanics, Chalmers University of Technology, (1990)Google Scholar
  26. 26.
    K. Runesson and Z. Mroz, “A Note on Non-associated Plastic Flow Rules”, Int. J. Plasticity, 5, 639–658 (1989).CrossRefMATHGoogle Scholar
  27. 27.
    R. Larsson, K. Runesson and S. Sture, “Numerical simulation of localized plastic deformation”, Ingenieur-Archiv, in print (1990)Google Scholar
  28. 28.
    C. Johnson and R. Scott, “A finite element method for problems in perfect plasticity using discontinuous trial functions”, in: W. Wunderlich, E. Stein and K.-J. Bathe (eds.), Non-linear Finite Element Analysis in Structural Mechanics, pp. 307–324. Berlin: Springer (1981)CrossRefGoogle Scholar
  29. 29.
    M. Klisinski, Z. Mroz and K. Runesson, “Structure of constitutive equations in plasticity for different choices of state and control variables”, in printGoogle Scholar
  30. 30.
    K. Runesson, S. Sture and K. Wiliam, “Integration in computational plasticity”, Computers and Structures, 30, 119–130 (1987)CrossRefGoogle Scholar
  31. 31.
    C. Johnson, “On finite element methods for plasticity problems”, Numer. Math., 26, 79–84 (1976)MathSciNetCrossRefMATHGoogle Scholar
  32. 32.
    C. Johnson, “On plasticity with hardening”, J. Math. Anal. and Appl., 62, 325–336 (1976)CrossRefGoogle Scholar
  33. 33.
    C. Johnson, “A mixed finite element method for plasticity problems with hardening”, J. Numer Anal., SIAM, 14, 575–583 (1977)MATHGoogle Scholar
  34. 34.
    C. Johnson and R. Scott, “A finite element method for problems in perfect plasticity using discontinuous trial functions”, in: W. Wunderlich, E. Stein and K.-J. Bathe (eds.), NonLinear Finite Element Analysis in Structural Mechanics, pp. 307–324 Springer-Verlag (1981)Google Scholar
  35. 35.
    N.S. Ottosen and K. Runesson, “Properties of bifurcation solutions in elasto-plasticity”, Int. J. Solids Struct., 27, 401–421 (1991)MathSciNetCrossRefMATHGoogle Scholar
  36. 36.
    K. Runesson, N.S. Ottosen and D. Peric, “Discontinuous bifurcations of elastic-plastic solutions at plane stress and plane strain”, Int. J. Plasticity (1990), in printGoogle Scholar
  37. 37.
    F. Molenkamp, “Comparison of frictional material models with respect to shear band initiation”, Geotechnique, 35, 127–143 (1985)CrossRefGoogle Scholar
  38. 38.
    N.A. Sobh, Bifurcation analysis of tangential material operators, (Ph. D. Dissertation) Univ. of Colorado, Boulder (1987)Google Scholar
  39. 39.
    K. Wiliam and N. Sobh, “Bifurcation analysis of tangential material operators”, in: O. Z. Zienkiewicz, G.N. Pande and J. Middleton (eds.), Numerical Methods in Engineering: Theory and Applications, NUMETA 87, Martinus Nijhoff (1987)Google Scholar
  40. 40.
    S.A. Sabban, Property analysis and incremental formulation of J2 elasto-plastic solids in plane stress, (Ph. D. Dissertation) Univ. of Colorado, Boulder (1989)Google Scholar
  41. 41.
    P.V. Lade, “Effects of voids and volume changes on the behavior of frictional materials”, Int. J. Anal. Num. Meth. Geomech., 12, 351–370 (1988)CrossRefGoogle Scholar
  42. 42.
    S. Sture, K. Runesson and E. J. Macari-Pasqualino, “Analysis and calibration of a three-invariant plasticity model for granular materials”, Ingenieur-Archiv, 59, 253–266 (1989)CrossRefGoogle Scholar
  43. 43.
    P.V. Lade, “Experimental observations of stability, instability and shear planes in granular materials”, Ingenieur-Archiv, 59, 114–123 (1989)CrossRefGoogle Scholar
  44. 44.
    I. Vardoulakis, “Bifurcation analysis of the plane rectilinear deformation test on dry sand samples”, Int. J. Solids Struct., 17, 1085–1101 (1981)CrossRefMATHGoogle Scholar
  45. 45.
    J. Mandel, “Conditions de stabilité et postulat de Drucker”, in: J. Kravtchenko and P.M. Siryies (eds.), Proc. IUTAM Symposium on Reology and Soil-Mechanics, pp. 58–68. Berlin: Springer (1964)Google Scholar
  46. 46.
    J.W. Rudnicki and J.R. Rice, “Conditions for the localization of deformation in pressure-sensitive dilatant materials”, J. Mech. Phys. Solids, 23, 371–394 (1975)CrossRefGoogle Scholar
  47. 47.
    J.R. Rice, “The localization of plastic deformation”, in: W.T. Koiter (ed.), Theoretical and Applied Mechanics, Proc. 14th IUTAM, Congress pp. 207–220. Amsterdam: North-Holland (1977)Google Scholar
  48. 48.
    T.S. Hsu, J.F. Peters and S.K. Saxena, “Importance of mesh design for capturing strain localization”, in: C.S. Desai, E. Krempl, P.D. Kiousis and T. Kundu (eds.), Constitutive Laws for Engineering Materials and Applications, pp. 857–864 Elsevier (1987)Google Scholar
  49. 49.
    H. Jin and N.E. Wiberg, “Two dimensional mesh generation, adaptive remeshing and refinement”, Int. J. Num. Meth. Engng, 29, 1501–1526 (1990)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 1993

Authors and Affiliations

  • R. Larsson
    • 1
  • K. Runesson
    • 1
  • A. Samuelsson
    • 1
  1. 1.Chalmers University of TechnologyGöteborgSweden

Personalised recommendations