, Volume 51, Issue 2, pp 309–317 | Cite as

Hyper-reduced predictions for lifetime assessment of elasto-plastic structures

  • David Ryckelynck
  • Komlanvi Lampoh
  • Stéphane Quilicy
Computational Micromechanics of Materials


Finite element (FE) elasto-plastic or elasto-viscoplastic simulations of complex components can still be prohibitive for lifetime predictions. There is a need for fast estimation methods of plasticity in a given region of interest, where a crack could be initiated. Some rules are already available for fast predictions of elasto-plastic stress and strain, by using elastic simulations. Furthermore, as shown by the Herbland’s model, inclusion theory can be incorporated in simplified rules to improve their accuracy. Recent advances in model reduction methods for nonlinear mechanical models give access to fast elasto-plastic or elasto-viscoplastic predictions having both accuracy and computational complexity in between usual FE predictions and these simplified rules. Hyper-reduction performs quite well in the simplification of elasto-plastic or elasto-viscoplastic models. Similarly to Herbland’s model, we show in this paper a first attempt to improve hyper-reduced models by the recourse to a virtual inclusion placed in the region of interest. In the proposed numerical example, a finite element model involving 5000 degrees of freedom is reduced to 12 variables. The mesh is also reduced to 550 elements over a total of 900 elements for the original mesh. The approximation error on the predicted plastic strains and stresses is lower than 3 % and the computational time is reduced up to a factor 5.


Plasticity Singular value decomposition Hyper-reduction Non-confined plasticity 


  1. 1.
    Alexandrov N, Dennis J, Lewis R, Torczon V (1998) A trust-region framework for managing the use of approximation models in optimization. Struct Optim 15:16–23CrossRefGoogle Scholar
  2. 2.
    Arian E, Fahl M, Sachs EW (2000) Trust-region proper orthogonal decomposition for flow control. Technical report 25 ICASE, Ohio UniversityGoogle Scholar
  3. 3.
    Astrid P (2004) Reduction of process simulation models: a proper orthogonal decomposition approach. PhD thesis, Technische Universiteit Eindhoven, ISBN 90-386-1653-8Google Scholar
  4. 4.
    Barrault M, Maday Y, Nguyen NC, Patera AT (2004) An ‘empirical interpolation’ method: application to efficient reduced-basis discretization of partial differential equations. C R Acad Sci Paris Ser I 339:667–672MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Bergmann M, Cordier L (2008) Optimal control of the cylinder wake in the laminar regime by trust-region methods and POD reduced-order models. J Comput Phys 227:7813–7840ADSMathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Besson J, Cailletaud G, Chaboche J-L, Forest S (2001) Mécanique non-lineaire des matériaux. Hermes, ParisMATHGoogle Scholar
  7. 7.
    Cailletaud G, Chaboche JL (1982) Lifetime predictions in 304 stainless steel by damage approach. In: ASME-PVP conference, Orlando, FloridaGoogle Scholar
  8. 8.
    Carlberg K, Bou-Mosleh C, Farhat C (2011) Efficient non-linear model reduction via a least-squares Petrov-Galerkin projection and compressive tensor approximations. Int J Numer Methods Eng 86:155–181MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Carlberg K, Cortial J, Amsallem D, Zahr M, Farhat C (2011) The GNAT nonlinear model reduction method and its application to fluid dynamics problems. 6th AIAA Theoretical Fluid Mechanics Conference, Honolulu, Hawaii, June 27–30, pp 2011–3112Google Scholar
  10. 10.
    Chouman M, Gaubert A, Chaboche J, Kanout P, Cailletaud G, Quilici S (2014) Elastic-viscoplastic notch correction methods. Int J Solids Struct 51(18):3025–3041. doi: 10.1016/j.ijsolstr.2014.04.017 CrossRefGoogle Scholar
  11. 11.
    Dvorak GJ (1992) transformation field analysis of inelastic composite-materials. Proc R Soc Lond Ser A Math Phys Eng Sci 437(1900):311–327ADSMathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Everson R, Sirovich L (1995) Karhunen-Loève procedure for gappy data. J Opt Soc Am A 12:1657–1664ADSCrossRefGoogle Scholar
  13. 13.
    Galbally D, Fidkowski K, Willcox K, Ghattas O (2010) Non-linear model reduction for uncertainty quantification in large-scale inverse problems. Int J Numer Methods Eng 81:1581–1608MathSciNetMATHGoogle Scholar
  14. 14.
    Lampoh K, Charpentier I, Daya EM (2011) A generic approach for the solution of nonlinear residual equations. part III: sensitivity computations. Comput Methods Appl Mech Eng 200:2983–2990ADSMathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Lorenz EN (1956) Empirical orthogonal functions and statistical weather prediction. Scientific report 1, MIT Departement of Meteorology, Statistical Forecasting ProjectGoogle Scholar
  16. 16.
    Lumley J (1967) The structure of inhomogeneous turbulence. Atmospheric turbulence and wave propagation. Nauka, Moscow, pp 166–178Google Scholar
  17. 17.
    Michel J, Suquet P (2003) Nonuniform transformation field analysis. Int J Solids Struct 40:6937–6955MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Neuber H (1961) Theory of stress concentration for shear-strained prismatic bodies with arbitrary non-linear stressstrain law. J Appl Mech 28:544–551MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Ryckelynck D (2005) A priori hypereduction method: an adaptive approach. Int J Comput Phys 202:346–366ADSCrossRefMATHGoogle Scholar
  20. 20.
    Ryckelynck D (2009) Hyper reduction of mechanical models involving internal variables. Int J Numer Methods Eng 77(1):75–89MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Ryckelynck D, Gallimard L, Jules S (2015) Estimation of the validity domain of hyper-reduction approximations in generalized standard elastoviscoplasticity. Adv Model Simul Eng Sci 2(1):6. doi: 10.1186/s40323-015-0027-7 CrossRefGoogle Scholar
  22. 22.
    Ryckelynck D, Missoum Benziane D (2010) Multi-level a priori hyper reduction of mechanical models involving internal variables. Comput Methods Appl Mech Eng 199:1134–1142ADSMathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Schmidt A, Potschka A, Koerkel S, Bock HG (2013) Derivative-extended pod reduced-order modeling for parameter estimation. SIAM J Sci Comput 35:A2696–A2717CrossRefMATHGoogle Scholar
  24. 24.
    Sirovich L (1987) Turbulence and the dynamics of coherent structures part I : coherent structures. Q Appl Math 65(3):561–571MathSciNetGoogle Scholar
  25. 25.
    Sirovich L (1987) Turbulence and the dynamics of coherent structures part III : dynamics and scaling. Q Appl Math 65(3):583–590MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • David Ryckelynck
    • 1
  • Komlanvi Lampoh
    • 1
  • Stéphane Quilicy
    • 1
  1. 1.Centre des MatérauxMines ParisTech - PLS* Research UniversityEvryFrance

Personalised recommendations