This paper details the development of the Proper Generalized Decomposition as a space–time integrator of elastoplastic problems and shows its ability to determine the elastoplastic states resulting from cyclic loadings. The first part of this paper recalls the step-by-step resolution in time of an elastoplastic problem. The implementation of the Proper Generalized Decomposition is then developed in a second part. In the last third part, applications and numerical simulations are presented to show the relevance of the method.
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Jean-Michel Bergheau 1; Sylvain Zuchiatti 1; Jean-Christophe Roux 1; Éric Feulvarch 1; Samuel Tissot 2; Gilles Perrin 3
@article{CRMECA_2016__344_11-12_759_0,
author = {Jean-Michel Bergheau and Sylvain Zuchiatti and Jean-Christophe Roux and \'Eric Feulvarch and Samuel Tissot and Gilles Perrin},
title = {The {Proper} {Generalized} {Decomposition} as a space{\textendash}time integrator for elastoplastic problems},
journal = {Comptes Rendus. M\'ecanique},
pages = {759--768},
publisher = {Elsevier},
volume = {344},
number = {11-12},
year = {2016},
doi = {10.1016/j.crme.2016.06.002},
language = {en},
}
TY - JOUR AU - Jean-Michel Bergheau AU - Sylvain Zuchiatti AU - Jean-Christophe Roux AU - Éric Feulvarch AU - Samuel Tissot AU - Gilles Perrin TI - The Proper Generalized Decomposition as a space–time integrator for elastoplastic problems JO - Comptes Rendus. Mécanique PY - 2016 SP - 759 EP - 768 VL - 344 IS - 11-12 PB - Elsevier DO - 10.1016/j.crme.2016.06.002 LA - en ID - CRMECA_2016__344_11-12_759_0 ER -
%0 Journal Article %A Jean-Michel Bergheau %A Sylvain Zuchiatti %A Jean-Christophe Roux %A Éric Feulvarch %A Samuel Tissot %A Gilles Perrin %T The Proper Generalized Decomposition as a space–time integrator for elastoplastic problems %J Comptes Rendus. Mécanique %D 2016 %P 759-768 %V 344 %N 11-12 %I Elsevier %R 10.1016/j.crme.2016.06.002 %G en %F CRMECA_2016__344_11-12_759_0
Jean-Michel Bergheau; Sylvain Zuchiatti; Jean-Christophe Roux; Éric Feulvarch; Samuel Tissot; Gilles Perrin. The Proper Generalized Decomposition as a space–time integrator for elastoplastic problems. Comptes Rendus. Mécanique, Volume 344 (2016) no. 11-12, pp. 759-768. doi : 10.1016/j.crme.2016.06.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2016.06.002/
[1] A New Approach in Inelastic Analysis of Structures, CADLM, Gif-sur-Yvette, France, 1990
[2] Cyclic behaviour of structures under thermomechanical loadings: application to exhaust manifolds, Int. J. Fatigue, Volume 38 (2012), pp. 65-74
[3] A direct method to predict cyclic steady states of elastoplastic structures, Comput. Methods Appl. Mech. Eng., Volume 223 (2012) no. 224, pp. 186-198
[4] An optimal control approach to the analysis of inelastic structures under cyclic loading, J. Mech. Phys. Solids, Volume 51 (2003) no. 4, pp. 575-605
[5] Determination of the asymptotic response of a structure under cyclic thermomechanical loading, C. R. Mecanique, Volume 330 (2002) no. 10, pp. 703-708
[6] An efficient cycle jump technique for viscoplastic structure calculations involving large number of cycles, Barcelona, Spain (1989), pp. 591-602
[7] Integration methods for complex plastic constitutive equations, Comput. Methods Appl. Mech. Eng., Volume 133 (1996), pp. 125-155
[8] A new approach in non-linear mechanics: the large time increment method, Int. J. Numer. Methods Eng., Volume 29 (1990), pp. 647-663
[9] A large time increment approach for cyclic viscoplasticity, Int. J. Plast., Volume 9 (1993), pp. 141-157
[10] A direct method for the solution of evolution problems, C. R. Mecanique, Volume 334 (2006), pp. 317-322
[11] Solving parametric complex fluids models in rheometric flows, J. Non-Newton. Fluid Mech., Volume 165 (2010), pp. 1588-1601
[12] On the deterministic solution of multidimensional parametric models by using the Proper Generalized Decomposition, Math. Comput. Simul., Volume 81 (2010), pp. 791-810
[13] The Proper Generalized Decomposition for Advanced Numerical Simulations: A Primer, SpringerBriefs Appl. Sci. Technol., Springer, 2014
[14] The structure of inhomogeneous turbulent flows, Moscow (A.M. Yaglom; V.I. Tatarsky, eds.) (1967), pp. 166-178
[15] Efficient PGD-based dynamic calculation of non-linear soil behavior, C. R. Mecanique, Volume 344 (2016) no. 1, pp. 24-41
[16] A reduced simulation applied to the viscoelastic fatigue of polymers, C. R. Mecanique, Volume 342 (2014), pp. 671-691
[17] On the space–time separated representation of integral linear viscoelastic models, C. R. Mecanique, Volume 343 (2015) no. 4, pp. 247-263
[18] Nonlinear Finite Element Analysis of Solids and Structures, John Wiley & Sons, 2012
[19] Nonlinear Finite Element Methods, Springer Science & Business, Media, 2008
[20] On the elastic plastic initial-boundary value problem and its numerical integration, Int. J. Numer. Methods Eng., Volume 11 (1977), pp. 817-832
[21] Computational Inelasticity, Springer-Verlag, New York, 1998
[22] Finite Element Procedures, Prentice–Hall, 1996
[23] An evaluation of a large time increment method, Comput. Struct., Volume 58 (1996), pp. 633-637
[24] Simulation numerique de la solidification avec reduction de modele PGD appliquée à la fonderie, University of Technology of Compiègne, France, 2015 PhD thesis (in French)
[25] Modeling of cyclic plasticity in finite element codes (C.S. Desai, ed.), 2nd Int. Conf. on Constitutive Laws for Engineering Materials: Theory and Applications, Elsevier, Tucson, AZ, USA, 1987, pp. 1157-1164
[26] A review of some plasticity and viscoplasticity constitutive theories, Int. J. Plast., Volume 24 (2008), pp. 1642-1693
[27] A mathematical representation of the multiaxial Bauschinger effect, 1966 (CEGB report No. RD/B/N 731, UK)
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