The Proper Generalized Decomposition as a space–time integrator for elastoplastic problems - 10/11/16

Doi : 10.1016/j.crme.2016.06.002

Jean-Michel Bergheau ^a , Sylvain Zuchiatti ^a , Jean-Christophe Roux ^a,^{^⁎} , Éric Feulvarch ^a , Samuel Tissot ^b , Gilles Perrin ^c
^a Université de Lyon, ENISE, LTDS, UMR 5513 CNRS, 58, rue Jean-Parot, 42023 Saint-Étienne cedex 2, France
^b AREVA NP, 10–12, rue Juliette-Récamier, 69456 Lyon cedex 06, France
^c AREVA NP, Tour Areva, 1, place Jean-Millier, 92084 Paris La Défense cedex, France

^⁎Corresponding author.

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Abstract

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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Keywords : Proper Generalized Decomposition, Space–time finite elements, Elastoplasticity