Skip to main content
Log in

Updating Stress and the Related Elastoplastic Parameters for Lemaitre Damage Model

  • Research Paper
  • Published:
Iranian Journal of Science and Technology, Transactions of Mechanical Engineering Aims and scope Submit manuscript

Abstract

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.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

References

  • Armstrong PJ, Frederick CO (1966) A mathematical representation of the multiaxial Bauscinger effect. CEGB Rep. No. RD/B/N731, Central Electricity Generating Board, Berkeley, UK

  • 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 64:1133–1165

    MathSciNet  MATH  Google Scholar 

  • 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):449–498

    MathSciNet  MATH  Google Scholar 

  • Auricchio F, Beirao da Veiga L (2003) On a new integration scheme for Von-Mises plasticity with linear hardening. Int J Numer Methods Eng 56:1375–1396

    MATH  Google Scholar 

  • 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 4:731–740

    MATH  Google Scholar 

  • Besson J (2010) Continuum models of ductile fracture: a review. Int J Damage Mech 19(1):3–52

    Google Scholar 

  • de Souza Neto EA (2002) A fast, one-equation integration algorithm for the Lemaitre ductile damage model. Commun Numer Methods Eng 18:541–554

    MATH  Google Scholar 

  • Dodds RH (1987) Numerical techniques for plasticity computations in finite element analysis. Comput Struct 26:767–779

    MATH  Google Scholar 

  • 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 99:2–15

    Google Scholar 

  • Hopperstad OS, Remseth S (1995) A return mapping algorithm for a class of cyclic plasticity models. Int J Numer Methods Eng 38:549–564

    MATH  Google Scholar 

  • Kobayashi M, Ohno N (2002) Implementation of cyclic plasticity models based on a general from of kinematic hardening. Int J Numer Meth Eng 58:1523–1543

    MATH  Google Scholar 

  • 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 125–137

    Google Scholar 

  • Lemaitre J (1983) How to use damage Mechanics. Nucl Eng Des 80:235–245

    Google Scholar 

  • Lemaitre J (1985) Coupled elasto-plasticity and damage constitutive equations. Comput Methods Appl Mech Eng 51:31–49

    MATH  Google Scholar 

  • Lemaitre J, Desmorat R (2005) Engineering damage mechanics. Springer, Berlin

    Google Scholar 

  • Lemaitre J, Desmorat R, Sauzay M (2000) Anisotropic damage law of evolution. Eur J Mech A Solids 19:187–208

    MATH  Google Scholar 

  • 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 9:375–403

    MATH  Google Scholar 

  • Ohno N, Wang J-D (1994) Kinematic hardening rules for simulation of ratcheting behavior. Eur J Mech A Solids 13:519–531

    MATH  Google Scholar 

  • Ortiz M, Popov EP (1985) Accuracy and stability of integration algorithms for elasto-plastic constitutive relations. Int J Numer Meth Eng 21:1561–1576

    MATH  Google Scholar 

  • Rezaiee-Pajand M, Nasirai C (2007) Accurate integration scheme for Von-Mises plasticity with mixed-hardening based on exponential maps. Eng Comput 24(4):608–635

    MATH  Google Scholar 

  • 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):1502–1518

    Google Scholar 

  • Rezaiee-Pajand M, Sharifian M, Sharifian M (2014) Angles based integration for generalized non-linear plasticity model. Int J Mech Sci 87:241–257

    MATH  Google Scholar 

  • Simo JC, Taylor RL (1986) A return mapping algorithm for plane stress elasto-plasticity. Int J Numer Methods Eng 22:649–670

    MATH  Google Scholar 

  • Sloan SW, Ristinmaa M (2001) Refined explicit integration of elasto-plastic models with automatic error control. Eng Comput 18:121–194

    Google Scholar 

  • Wilkins ML (1964) Calculation of elastic-plastic flow. In: Alder B, et al (eds) Method of computational physics, vol 3. Academic Press, New York

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mehrzad Sharifian.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tavoosi, M., Sharifian, M. & Sharifian, M. Updating Stress and the Related Elastoplastic Parameters for Lemaitre Damage Model. Iran J Sci Technol Trans Mech Eng 44, 647–659 (2020). https://doi.org/10.1007/s40997-019-00282-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40997-019-00282-3

Keywords

Navigation