Toward “green” mechanical simulations in materials science
Hyper-reduction of a polycrystal plasticity model
DOI:
https://doi.org/10.13052/EJCM.19.365-388Keywords:
truncated integration, POD, surrogate model, Petrov-Galerkin formulationAbstract
Because of the developpement of materials science, there is a need to reduce the computational complexity of mechanical models. This paper aims to show that the Hyper Reduction method enables to reduce computational resources used for numerical simulations. Large mechanical models involving distributed nonlinearities require parallel computers to solve the governing equations related to these models. The proposed Hyper Reduction of such models provides reduced governing equations that enable simulations on a single-processor computer. This is achieved by using a reduced-basis and a selection of equilibrium equations of the detailed model. The use of a single processor during less time enables to save an amazing amount of the electrical energy during the numerical simulation.
Downloads
References
Anand L., “ Single-crystal elasto-viscoplasticity: application to texture evolution in polycrystalline
metals at large strains”, Computer Methods in Applied Mechanics and Engineering,
vol. 193, n° 48-51, p. 5359-5383, 2004.
Balima O., Favennec Y., Girault M., Petit D., “ Comparison between the modal identification
method and the POD-Galerkin method for model reduction in nonlinear diffusive systems”,
International Journal for Numerical Methods in Engineering, vol. 67, n° 7, p. 895-915,
Barbe F., Decker L., Jeulin D., Cailletaud G., “ Intergranular and intragranular behavior of
polycrystalline aggregates Part 1: model”, Int. J. of Plasticity, vol. 17, n° 4, p. 513-536,
a.
Barbe F., Forest S., Cailletaud G., “ Intergranular and intragranular behavior of polycrystalline
aggregates.Part 2: Results”, Int. J. of Plasticity, vol. 17, n° 4, p. 537-563, 2001b.
Cailletaud G., “ A micromechanical approach to inelastic behaviour of metals”, Int J of Plasticity,
vol. 8, n° 1, p. 55Ð73, 1992.
Craig R. J., Bampton M., “ Coupling of substructures for dynamic analyses”, AIAA Journal,
vol. 6, n° 7, p. 1313Ð1319, 1968.
Daescu D. N., Navon I. M., “ Efficiency of a POD-based reduced second-order adjoint model
in 4D-Var data assimilation”, International Journal for Numerical Methods in Fluids, vol.
, n° 6, p. 985-1004, 2007.
Diard O., Leclercq S., Rousselier G., Cailletaud G., “ Evaluation of finite element based analysis
of 3D multicrystalline aggregates plasticity: Application to crystal plasticity model identification
and the study of stress and strain fields near grain boundaries”, Int. J. of Plasticity,
vol. 21, n° 4, p. 691-722, 2005.
Farhat C., Roux F.-X., “ Implicit parallel processing in structural mechanics”, Computational
Mechanics Advances, vol. 2, p. 1-124, 1994.
Feyel F., Calloch S., Marquis D., Cailletaud G., “ F.E. Computation of a Triaxial Specimen
Using a Polycrystalline Model”, CMS, vol. 9, p. 141-157, 1997.
Forest S., Pilvin P., “ Modelling finite deformation of polycrystals using local objective frames”,
Z. Angew. Math. Mech., vol. 79, p. S199-S202, 1999.
Ganapathysubramanian S., Zabaras N., “ Design across length scales: a reduced-order model of
polycrystal plasticity for the control of microstructure-sensitive material properties”, Comput.
Methods Appl. Mech. Engrg., vol. 193, p. 5017-5034, 2004.
Gerard C., Nguyen F., Osipov N., Cailletaud G., Bornert M., “ Comparison of experimental
results and finite element simulations of strain localization scheme under cyclic loading
path”, Computational Materials Science, vol. 46, p. 755-760, 2009.
Germain P., Nguyen Q. S., Suquet P., “ Continuum Thermodynamics”, Journal of Applied Mechanics,
vol. 50, p. 1010-1020, 1983.
Holmes P., Lumley J.-L., G B., Turbulence, Coherent Structures, Dynamical Systems and
Symetry, 1st edn, Cambridge University Press, 1998.
Karhunen K., “ Uber lineare methoden in der wahrscheinlichkeitsrechnung”, Ann. Acad. Sci.
Fennicae, ser. Al. Math. Phys., 1946.
Khalila M., Adhikarib S., Sarkara A., “ Linear system identification using proper orthogonal
decomposition”, Mechanical Systems and Signal Processing, vol. 21, p. 3123Ð3145, 2007.
Ladevèze P., “ Sur une famille d’algorithmes en mécanique des structures”, Comptes Rendus
Acad. Sci. Paris Sèrie II, vol. 300, n° 2, p. 41-44, 1985.
Lemaitre J., Chaboche J.-L., Mecanique des materiaux solides, 1st edn, Dunod: Paris 1985,
English version published by Cambridge University Press: cambridge, 1990.
Lieu T., Farhat C., Lesoinne M., “ Reduced-order fluid/structure modeling of a complete aircraft
configuration”, Computer Methods in Applied Mechanics and Engineering, vol. 95, n° 41-
, p. 5730-5742, 2006.
Lorenz E. N., Empirical Orthogonal Functions and Statistical Weather Prediction, Scientific
Report n° 1, MIT Departement of Meteorology, Statistical Forecasting Project, 1956.
Loève M. M., Probability theory, The University Series in Higher Mathematics, 3rd edn, Van
Nostrand, Princeton, NJ, 1963.
Mandel J., “ Equations constitutives et directeurs dans les milieux plastiques et viscoplastiques”,
Int J Solids Structures, vol. 9, n° 6, p. 725Ð40, 1973.
Musienko A., Tatschl A., Schmidegg K., Kolednik O., Pippan R., Cailletaud G., “ Threedimensional
finite element simulation of a polycrystalline copper specimen”, Acta Materialia,
vol. 55, p. 4121-4136, 2007.
Osipov N., Gourgues-Lorenzon A.-F., Marini B., Mounoury V., Nguyen F., Cailletaud G., “ FE
modelling of bainitic steels using crystal plasticity”, Philosophical Magazine, vol. 88, n° 30-
, p. 3757-3777, 2008.
Ryckelynck D., “ A priori hypereduction method: an adaptive approach”, International Journal
of Computational Physics, vol. 202, p. 346-366, 2005.
Ryckelynck D., “ Hyper reduction of mechanical models involving internal variables”, International
Journal for Numerical Methods in Engineering, vol. 77, n° 1, p. 75-89, 2009.
Ryckelynck D., Benziane D.-M., “ Multi-level a priori hyper-reduction of mechanical models
involving internal variables”, Computer Methods in Applied Mechanics and Engineering,
vol. 199, n° 17-20, p. 1134-1142, 2010.
Sansour C., Kollmann F., “ On theory and numerics of large viscoplastic deformation”, Comput.
Methods Appli. Mech. Engrg., vol. 146, p. 351-369, 1997.
Sirovich L., “ Turbulence and the dynamics of coherent structures partI : coherent structures”,
Quaterly of applied mathematics, vol. XLV, n° 3, p. 561-571, 1987.
Tugcu P., Neale K.W.,Wu P. D., Inal K., “ Crystal plasticity simulation of the hydrostatic bulge
test”, Int. Jour. of Plasticity, vol. 20, p. 1603-1653, 2004.
Zienkiewicz O., Taylor RL. Finite Element Method, vol. 1-3, Butterworth-Heinomann, London,
