Updating Stress and the Related Elastoplastic Parameters for Lemaitre Damage Model

  • Maliheh Tavoosi
  • Mehrzad SharifianEmail author
  • Mehrdad Sharifian
Research Paper


Numerical methods are normally employed for elastoplastic analysis of structures due to complicated nature of the analyses alongside the absence of a closed analytical solution to these problems. Evidently, the chief part of the analyses comprises the computation of stress which is typically a function of strain history and the related elastoplastic parameters. Accordingly, the choice of the stress-updating method together with the characteristics considered for simulating material behavior directly affects the precision of the structural analysis results. Here, von Mises yield surface with nonlinear isotropic hardening is taken into account along with Lemaitre damage model. Subsequently, forward and backward Euler algorithms are developed for the integration of the pertinent constitutive equations. Finally, a broad set of numerical tests are conducted to evaluate the correctness, precision, convergence rate and efficiency of the suggested schemes.


von Mises plasticity Backward Euler Forward Euler Lemaitre damage mechanism Nonlinear hardening 


  1. Armstrong PJ, Frederick CO (1966) A mathematical representation of the multiaxial Bauscinger effect. CEGB Rep. No. RD/B/N731, Central Electricity Generating Board, Berkeley, UKGoogle Scholar
  2. Artioli E, Auricchio F, Beirao da Veiga L (2005) Integration scheme for Von-Mises plasticity models based on exponential maps: numerical investigations and theoretical considerations. Int J Numer Methods Eng 64:1133–1165MathSciNetCrossRefzbMATHGoogle Scholar
  3. Artioli E, Auricchio F, Beira͂ o da Veiga L (2006) A novel ‘optimal’ exponential- based integration algorithm for Von-Mises plasticity with linear hardening: theoretical analysis on yield consistency, accuracy, convergence and numerical investigations. Int J Numer Methods Eng 67(4):449–498MathSciNetCrossRefzbMATHGoogle Scholar
  4. Auricchio F, Beirao da Veiga L (2003) On a new integration scheme for Von-Mises plasticity with linear hardening. Int J Numer Methods Eng 56:1375–1396CrossRefzbMATHGoogle Scholar
  5. Benallal A, Billardon R, Doghri I (1988) An integration algorithm and the corresponding consistent tangent operator for fully coupled elastoplastic and damage equations. Commun Appl Numer Methods 4:731–740CrossRefzbMATHGoogle Scholar
  6. Besson J (2010) Continuum models of ductile fracture: a review. Int J Damage Mech 19(1):3–52CrossRefGoogle Scholar
  7. de Souza Neto EA (2002) A fast, one-equation integration algorithm for the Lemaitre ductile damage model. Commun Numer Methods Eng 18:541–554CrossRefzbMATHGoogle Scholar
  8. Dodds RH (1987) Numerical techniques for plasticity computations in finite element analysis. Comput Struct 26:767–779CrossRefzbMATHGoogle Scholar
  9. Gurson AL (1977) Continuum theory of ductile rupture by void nucleation and growth. Part I: yield criteria and flow rules for porpous ductile media. J Eng Mater Technol 99:2–15CrossRefGoogle Scholar
  10. Hopperstad OS, Remseth S (1995) A return mapping algorithm for a class of cyclic plasticity models. Int J Numer Methods Eng 38:549–564CrossRefzbMATHGoogle Scholar
  11. Kobayashi M, Ohno N (2002) Implementation of cyclic plasticity models based on a general from of kinematic hardening. Int J Numer Meth Eng 58:1523–1543CrossRefzbMATHGoogle Scholar
  12. Krieg RD, Key SW (1976) Implementation of a time dependent plasticity theory into structural computer programs. In: Stricklin JA, Saczalski KJ (eds) Constitutive equations in viscoplasticity: computational and engineering aspects, AMD-20. ASME, New York, pp 125–137Google Scholar
  13. Lemaitre J (1983) How to use damage Mechanics. Nucl Eng Des 80:235–245Google Scholar
  14. Lemaitre J (1985) Coupled elasto-plasticity and damage constitutive equations. Comput Methods Appl Mech Eng 51:31–49CrossRefzbMATHGoogle Scholar
  15. Lemaitre J, Desmorat R (2005) Engineering damage mechanics. Springer, BerlinGoogle Scholar
  16. Lemaitre J, Desmorat R, Sauzay M (2000) Anisotropic damage law of evolution. Eur J Mech A Solids 19:187–208CrossRefzbMATHGoogle Scholar
  17. Ohno N, Wang J-D (1993) Kinematic hardening rules with critical state of dynamic recovery: part I; formulation and basic features for ratcheting behavior. Part II; application to experiments of ratcheting behavior. Int J Plast 9:375–403CrossRefzbMATHGoogle Scholar
  18. Ohno N, Wang J-D (1994) Kinematic hardening rules for simulation of ratcheting behavior. Eur J Mech A Solids 13:519–531zbMATHGoogle Scholar
  19. Ortiz M, Popov EP (1985) Accuracy and stability of integration algorithms for elasto-plastic constitutive relations. Int J Numer Meth Eng 21:1561–1576CrossRefzbMATHGoogle Scholar
  20. Rezaiee-Pajand M, Nasirai C (2007) Accurate integration scheme for Von-Mises plasticity with mixed-hardening based on exponential maps. Eng Comput 24(4):608–635CrossRefzbMATHGoogle Scholar
  21. Rezaiee-Pajand M, Nasirai C, Sharifian M (2010) Application of exponential-based methods in integrating the constitutive equations with multi-component nonlinear kinematic hardening. ASCE J Eng Mech 136(12):1502–1518CrossRefGoogle Scholar
  22. Rezaiee-Pajand M, Sharifian M, Sharifian M (2014) Angles based integration for generalized non-linear plasticity model. Int J Mech Sci 87:241–257CrossRefzbMATHGoogle Scholar
  23. Simo JC, Taylor RL (1986) A return mapping algorithm for plane stress elasto-plasticity. Int J Numer Methods Eng 22:649–670CrossRefzbMATHGoogle Scholar
  24. Sloan SW, Ristinmaa M (2001) Refined explicit integration of elasto-plastic models with automatic error control. Eng Comput 18:121–194CrossRefGoogle Scholar
  25. Wilkins ML (1964) Calculation of elastic-plastic flow. In: Alder B, et al (eds) Method of computational physics, vol 3. Academic Press, New YorkGoogle Scholar

Copyright information

© Shiraz University 2019

Authors and Affiliations

  • Maliheh Tavoosi
    • 1
  • Mehrzad Sharifian
    • 1
    Email author
  • Mehrdad Sharifian
    • 1
  1. 1.Quchan University of TechnologyQuchanIran

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