Skip to main content
SpringerLink
Log in

Patch based recovery in finite element elastoplastic analysis

  • Original Paper
  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

A new patch based stress recovery procedure for elastoplastic analysis is presented in this paper. The formulation derives from the extension to the elastic-perfectly plastic case of the Recovery by Compatibility in Patches procedure recently proposed by the authors. The present procedure is designed to simultaneously reconstruct both a new stress field and a new plastic strain field, so to ensure that elastoplastic consistency is satisfied. The numerical results on two common benchmark problems show the effectiveness of the new procedure.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Ainsworth M, Oden JT (2000) A posteriori error estimation in finite element analysis. Wiley, New York

    Book  MATH  Google Scholar 

  2. Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery and a posteriori error estimates. Part I: the recovery technique. Int J Numer Methods Eng 33:1331–1364

    Article  MathSciNet  MATH  Google Scholar 

  3. Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery and a posteriori error estimates. Part II: error estimates and adaptivity. Int J Numer Methods Eng 33:1365–1382

    Article  MathSciNet  MATH  Google Scholar 

  4. Zienkiewicz OC, Zhu JZ (1992) The superconvergent patch recovery (SPR) and adaptive finite element refinement. Comput Methods Appl Mech Eng 101:207–224

    Article  MathSciNet  MATH  Google Scholar 

  5. Blacker T, Belytschko T (1994) Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements. Int J Numer Methods Eng 37:517–536

    Article  MathSciNet  MATH  Google Scholar 

  6. Wiberg N, Abdulwahab F, Li XD (1997) Error estimation and adaptive procedures based on superconvergent patch recovery (SPR) techniques. Arch Comput Methods Eng 4:203–242

    Article  MathSciNet  Google Scholar 

  7. Lee T, Park HC, Lee SW (1997) A superconvergent stress recovery technique with equilibrium constraint. Int J Numer Methods Eng 40:1139–1160

    Article  MATH  Google Scholar 

  8. Park HC, Shin SH (1999) Element stress recovery technique with equilibrium constraints for superconvergence boundary stress extraction. AIAA J 37:623–628

    Article  Google Scholar 

  9. Kvamsdal T, Okstad KM (1998) Error estimation based on superconvergent patch recovery using statically admissible stress fields. Int J Numer Methods Eng 42:443–472

    Article  MathSciNet  MATH  Google Scholar 

  10. Okstad KM, Kvamsdal T, Mathisen KM (1999) Superconvergent patch recovery for plate problems using statically admissible stress resultant fields. Int J Numer Methods Eng 44:697–727

    Article  MATH  Google Scholar 

  11. Boroomand B, Zienkiewicz OC (1997) Recovery by equilibrium in patches (REP). Int J Numer Methods Eng 40:137–164

    Article  MathSciNet  Google Scholar 

  12. Boroomand B, Zienkiewicz OC (1997) An improved REP recovery and the effectivity robustness test. Int J Numer Methods Eng 40:3247–3277

    Article  MathSciNet  MATH  Google Scholar 

  13. Boroomand B, Zienkiewicz OC, Zhu JZ (1999) Recovery procedures in error estimation and adaptivity. Part I: adaptivity in linear problems. Comput Methods Appl Mech Eng 176:111–125

    Article  MathSciNet  MATH  Google Scholar 

  14. Boroomand B, Zienkiewicz OC (1999) Recovery procedures in error estimation and adaptivity. Part II: Adaptivity in nonlinear problems of elasto-plasticity behaviour. Comput Methods Appl Mech Eng 176:127–146

    Article  MathSciNet  MATH  Google Scholar 

  15. Prange C, Loehnert S, Wriggers P (2012) Error estimation for crack simulations using the XFEM. Int J Numer Methods Eng 91: 1459–1474

    Google Scholar 

  16. Payen DJ, Bathe K-J (2011) The use of nodal point forces to improve element stresses. Comput Struct 89:485–495

    Article  Google Scholar 

  17. Payen DJ, Bathe K-J (2012) A stress improvement procedure. Comput and Struct. http://dx.doi.org/10.1016/j.compstruc.2012.07.006

  18. Ubertini F (2004) Patch recovery based on complementary energy. Int J Numer Methods Eng 59:1501–1538

    Article  MATH  Google Scholar 

  19. Benedetti A, de Miranda S, Ubertini F (2006) A posteriori error estimation based on the superconvergent recovery by compatibility in patches. Int J Numer Methods Eng 67:108–131

    Article  MATH  Google Scholar 

  20. Daghia F, de Miranda S, Ubertini F, Viola E (2008) A hybrid stress approach for laminated composite plates within the First-order Shear Deformation Theory. Int J Solids Struct 45:1766–1787

    Article  MATH  Google Scholar 

  21. de Miranda S, Garikipati K, Molari L, Ubertini F (2009) A simple solution strategy for coupled piezo-diffusion in elastic solids. Comput Mech 44:191–203

    Article  MATH  Google Scholar 

  22. Castellazzi G, de Miranda S, Ubertini F (2010) Adaptivity based on the recovery by compatibility in patches. Finite Elem Anal Des 46:379–390

    Article  Google Scholar 

  23. Castellazzi G, de Miranda S, Ubertini F (2011) Patch based stress recovery for plate structures. Comput Mech 47:379–394

    Article  MATH  Google Scholar 

  24. de Miranda S, Patruno L, Ubertini F (2012) Transverse stress profiles reconstruction for finite element analysis of laminated plates. Composite Struct 94:2706–2715

    Article  Google Scholar 

  25. Carstensen C, Funken SA (2003) Averaging techniques for reliable a posteriori FE-error control in elastoplasticity with hardening. Comput Methods Appl Mech Eng 192:1435–1450

    Article  MATH  Google Scholar 

  26. Simo JC, Kennedy JG, Taylor RL (1989) Complementary mixed finite element formulations for elastoplasticity. Comput Methods Appl Mech Eng 74:177–206

    Article  MathSciNet  MATH  Google Scholar 

  27. Bilotta A, Leonetti L, Garcea G (2011) Three field finite elements for the elastoplastic analysis of 2D continua. Finite Elem Anal Des 47:1119–1130

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

Financial support by MIUR and University of Bologna is acknowledged. The computing facilities were provided by the LAMC - DICAM, University of Bologna, and by the LMT-Cachan.

Author information

Authors and Affiliations

  1. LMT-Cachan, ENS Cachan/CNRS/UPMC/PRES UniverSud Paris, 61 av. du President Wilson, 94235 , Cachan Cedex, France

    Federica Daghia

  2. DICAM, University of Bologna, Viale Risorgimento 2, 40136 , Bologna, Italy

    Stefano de Miranda & Francesco Ubertini

Authors
  1. Federica Daghia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stefano de Miranda
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Francesco Ubertini
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stefano de Miranda.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Daghia, F., de Miranda, S. & Ubertini, F. Patch based recovery in finite element elastoplastic analysis. Comput Mech 52, 827–836 (2013). https://doi.org/10.1007/s00466-013-0847-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-013-0847-6

Keywords

Search

Navigation