Structural Engineering and Mechanics

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Modelling of strain localization in a large strain context

  • Cescotto, S. (M.S.M Department, University of Liege) ;
  • Li, X.K. (National Laboratory for Structural Analysis of Industrial Equipments, Dalian University of Technology)
  • Published : 1996.11.25
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Abstract

In order to avoid pathological mesh dependency in finite element modelling of strain localization, an isotropic elasto-plastic model with a yield function depending on the Laplacian of the equivalent plastic strain is implemented in a 4-node quadrilateral finite element with one integration point based on a mixed formulation derived from Hu-Washizu principle. The evaluation of the Laplacian is based on a least square polynomial approximation of the equivalent plastic strain around each integration point. This non local approach allows to satisfy exactly the consistency condition at each integration point. Some examples are treated to illustrate the effectiveness of the method.

Keywords

References

  1. Bazant, Z.P. and Belytschko, T.B. (1985), "Wave propagation in a strain softening bar: exact solution", ASCE, Journal of Eng. Mech., 111(3), 381-389. https://doi.org/10.1061/(ASCE)0733-9399(1985)111:3(381)
  2. Bazant, Z.P. and Pijaudier-Cabot, G. (1988), "Non-local continuum damage, localization instability and convergence", ASME, Journal of Appl. Mech., 55, 287-293. https://doi.org/10.1115/1.3173674
  3. Belytschko, T. and Fish, J. (1989), "Spectral superposition on finite elements for shear banding problems", Proc. 5th Int. Symp. on Num. Meth. in Eng., R. Gruber et al. Springer Verlag, 1, 19-29.
  4. Borst, R. de and Muhlhaus, H.B. (1992), "Gradient-dependent plasticity : formulation and algorithmic aspects", Int. Jl. Num. Meth. in Eng., 35, 521-539. https://doi.org/10.1002/nme.1620350307
  5. Desrues, J. (1984), "La localisation de la deformation dans les milieux granulaires", These de Doctorat d'Etat, Universite Joseph Fourrier de Grenoble.
  6. Jetteur, Ph. and Cescotto, S. (1991), "A mixed finite element for the analysis of large inelastic strain", Int. Jl. Num. Meth. in Eng., 31, 229-239. https://doi.org/10.1002/nme.1620310203
  7. Lasry, D. and Belytschko, T. (1988), "Localization limiters in transient problems", Int. Jl. Solids Struct., 24(6), 581-597. https://doi.org/10.1016/0020-7683(88)90059-5
  8. Li, X.K. and Cescotto, S. (1995), "Finite element method for gradient plasticity at large strains", To appear in Int. J. Num. Meth in Eng.
  9. Muhlhaus, H.B. (1989), "Application of Cosserat theory in numerical solutions of limit load problems", Ingenieur Archiv, 59, 124-137. https://doi.org/10.1007/BF00538366
  10. Muhlhaus, H.B. and Aifantis, E.C. (1992), "A variational principle for gradient plasticity", Int. Jl. Solids Struct., 28, 845-857.
  11. Rice, J.R. and Rudnicki, J.W. (1980), "A note on some features of the theory of localization of deformation", Int. Jl. Solids Structures, 16, 597-605. https://doi.org/10.1016/0020-7683(80)90019-0
  12. Sluys, L.J. (1992), "Ware propagation, localigation and dispersion in softening solids", Ph.D thesis, Technical University of Delft.
  13. Sluys, L.J., Bolck, J. and de Borst, R. (1992), "Wave propagation and localization in viscoplastic media", Proc. Int. Conf. on Computational Plasticity, Barcelona.
  14. Steinmann, P. and Williams, K. (1991), "Perfermance of enhanced finite element formulations in localized failure computations", Comp. Meth. Appl. Mech. Eng., 90, 845-867. https://doi.org/10.1016/0045-7825(91)90187-B
  15. Triantafyllidis, N., Needleman, A. and Tvergaard, V. (1992), "On the development of shear bands in pure bending", Int. Jl. Solids Struct., 18, 121-138.
  16. Vardoulakis, I. (1979), "Bifurcation analysis of the triaxial test on sand samples", Acta Mech., 32, 35-44. https://doi.org/10.1007/BF01176132
  17. Wang, X.C. (1993), "Modelisation numerique des problemes avec localisation de la deformation en bandes de cisaillement", These de Doctorat en Sciences Appliqyees, Departement M.S.M. de I'Universite de Liege.
  18. Zhu, Y.Y. (1992), "Contribution to the local approach of fracture in solid mechanics", These de Doctorat en Sciences Appliquees, Departement M.S.M. de I'Universite de Liege.

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