Multi-level a priori Hyper-Reduction of mechanical models involving internal variables

Computer Methods in Applied Mechanics and Engineering

Volumn 199, Issue 17-20, 2010, Pages 1134-1142

  Ryckelynck, D ^a   Missoum Benziane, D ^a  

^a PSL RESEARCH UNIVERSITY   (France)

Author keywords

APHR method; Domain decomposition; FETI; Parallel computing; POD; Viscoplasticity

Indexed keywords

DOMAIN DECOMPOSITION METHODS; PARALLEL PROCESSING SYSTEMS; VISCOPLASTICITY;

APHR METHOD; ELASTO-VISCOPLASTIC; FETI; INCREMENTAL RESPONSE; INTERNAL VARIABLES; MECHANICAL PROBLEMS; PARALLEL COMPUTATION; REDUCED ORDER MODELS;

DEGREES OF FREEDOM (MECHANICS);

EID: 78650679450     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2009.12.003     Document Type: Article

References (38)

1. B. Tanguy, J. Besson, R. Piques, A. Pineau, Ductile to brittle transition of an A508 steel characterized by Charpy impact test. Part II: Modeling of the Charpy transition curve, Engrg. Fract. Mech. 72 (2005) 413-434.
2. E. Nicouleau, F. Feyel, S. Quilicy, G. Cailletaud, Structural calculation and lifetime-prediction in thermomechanical fatigue of engine components, Eur. Struct. Integr. Soc. 29 (2002) 331-340.
3. M. Mazière, J. Besson, S. Forest, B. Tanguy, H. Chalons, F. Vogel, Overspeed burst of elastoviscoplastic rotating disks. Part I: Analytical and numerical stability analyses, Eur. J. Mech. A/Solids 28 (2009) 36-44.
4. M.A. Biot, Mechanics of Incremental Deformations, Wiley, New York, 1965.
5. H. Ziegler, Some extremum principles in irreversible thermodynamics with applications to continuum mechanics, in: I.N. Sneddon, R. Hill (Eds.), Progress in Solid Mechanics, vol. IV, North-Holland, Amsterdam, 1963.
6. P. Germain, Cours de mecanique des milieux continus, Masson et Cie, Paris, 1973.
7. B. Halpen, Q.S. Nguyen, Sur les materiaux standards generalises, J. de Mec. 40 (1975) 39-63.
8. J. Lemaitre, J.-L. Chaboche, Mecanique des materiaux solides, first ed., Dunod, Paris, 1985 (English version published by Cambridge University Press, Cambridge, 1990).
9. P. Germain, Q.S. Nguyen, P. Suquet, Continuum thermodynamics, J. Appl. Mech. 50 (1983) 1010-1020.
10. D.N. Daescu, I.M. Navon, Efficiency of a POD-based reduced second-order adjoint model in 4D-Var data assimilation, Int. J. Numer. Methods Fluids 53 (6) (2007) 985-1004.
11. S. Ganapathysubramanian, N. Zabaras, Design across length scales: a reducedorder model of polycrystal plasticity for the control of microstructuresensitive material properties, Comput. Methods Appl. Mech. Engrg. 193 (2004) 5017-5034.
12. E. Monteiro, J. Yvonnet, Q.C. He, Computational homogenization for nonlinear conduction in heterogeneous materials using model reduction, Comput. Mater. Sci. 42 (4) (2008) 704-712.
13. O. Balima, Y. Favennec, M. Girault, D. Petit, Comparison between the modal identification method and the POD-Galerkin method for model reduction in nonlinear diffusive systems, Int. J. Numer. Methods Engrg. 67 (7) (2006) 895-915.
14. S. Niroormandi, I. Alfaro, E. Cueto, F. Chinesta, Real-time deformable models of non-linear tissues by model reduction techniques, Comput. Methods Prog. Biomed. 91 (2008) 223-231.
15. K. Karhunen, Uber lineare methoden in der wahrscheinlichkeitsrechnung, Ann. Acad. Sci. Fennicae, ser. Al. Math. Phys. 37 (1946).
16. M.M. Loève, Probability theory, The University Series in Higher Mathematics, third ed., Van Nostrand, Princeton, NJ, 1963.
17. P.J. Holmes, J.L. Lumley, G. Berkooz, J. Mattingly, R.W. Wittenberg, Lowdimensional models of coherent structures in turbulence, Phys. Rep. 287 (1997) 337-384.
18. L. Sirovich, Turbulence and the dynamics of coherent structures. Part I: Coherent structures, Quart. Appl. Math. XLV (3) (1987) 561-571.
19. P. Ladevèze, Sur une famille d'algorithmes en mècanique des structures, C. R. Acad. Sci. Paris, Sèrie II (1985) 41-44.
20. O. Allix, P. Vidal, A new multi-solution approach suitable for structural identification problems, Comput. Methods Appl. Mech. Engrg. 191 (2002) 2727-2758.
21. P.A. Boucard, S. Buytet, P.A. Guidault, A multiscale strategy for structural optimization, Int. J. Numer. Methods Engrg. 78 (1) (2009) 101-126.
22. P. Ladevèze, A. Nouy, On a multiscale computational strategy with time and space homogenization for structural mechanics, Comput. Methods Appl. Mech. Engrg. 192 (2003) 3061-3087.
23. D. Ryckelynck, Réduction a priori de modèles thermomécaniques, C.R. Mécanique 330 (2002) 499-505.
24. N.C. Nguyen, A posteriori error estimation and basis adaptivity for reducedbasis approximation of nonaffine-parametrized linear elliptic partial differential equations, J. Comput. Phys. 227 (2007) 983-1006.
25. D. Ryckelynck, A priori hyperreduction method: an adaptive approach, Int. J. Comput. Phys. 202 (2005) 346-366.
26. N. Verdon, C. Allery, C. Béghein, D. Ryckelynck, Reduced-Order modelling for solving linear and non-linear equations. Commun. Numer. Meth. Engrg. (2009), in press.
27. A. Ammar, D. Ryckelynck, F. Chinesta, R. Keunings, On the reduction of kinetic theory models related to finitely extensible dumbbells, J. Non-Newton. Fluid Mech. 134 (1-3) (2006) 136-147.
28. D. Ryckelynck, F. Chinesta, E. Cueto, A. Ammar, On the a priori model reduction: overview and recent developments, Arch. Comput. Methods Engrg., State Art Rev. 13 (1) (2006) 91-128.
29. D. Ryckelynck, Hyper-reduction of mechanical models involving internal variables, Int. J. Numer. Methods Engrg. 77 (2009) 75-89.
30. R. Markovinovic, J.D. Jansen, Accelerating iterative solution methods using reduced-order models as solution predictors, Int. J. Numer. Methods Engrg. 68 (2006) 525-541.
31. C. Farhat, F.-X. Roux, Implicit parallel processing in structural mechanics, Comput. Mech. Adv. 2 (1994) 1-124.
32. P. Ladevèze, D. Nèron, P. Gosselet, On mixed and multiscale domain decomposition method, Comput. Methods Appl. Mech. Engrg. 196 (2007) 1526-1540.
33. O.C. Zienkiewicz, R.L. Taylor, Finite Element Method, vols. 1-3, Butterworth-Heinmann, London, 2000.
34. I.G. Banerjee, M.G. Lerapetritou, An adaptive reduction scheme to model reactive flow, Combust. Flame 144 (2006) 619-633.
35. F. Feyel, Application du calcul parallèle aux modèles à grand nombre de variables internes, Thesis, Ecole Nationale Supérieure des Mines de Paris, 1998.
36. F. Feyel, S. Calloch, D. Marquis, G. Cailletaud, Computation of a triaxial specimen using a polycrystalline model, CMS 9 (1997) 141-157.
37. J. Besson, R. Foerch, Large scale object-oriented finite element code design, Comput. Methods Appl. Mech. Engrg. 142 (1997) 165-187.
38. P. Raghavan, Domain-Separator Codes for the parallel solution of sparse linear systems, Tech. Rep. CSE-02-004, Department of Computer Science and Engineering, The Pennsylvania State University, University Park, PA 16802-6106, 2002.