The numerical modelling of the behaviour of materials at the microstructural scale has been greatly developed over the last two decades. Unfortunately, conventional resolution methods cannot simulate polycrystalline aggregates beyond tens of loading cycles, and they do not remain quantitative due to the plasticity behaviour. This work presents the development of a numerical solver for the resolution of the Finite Element modelling of polycrystalline aggregates subjected to cyclic mechanical loading. The method is based on two concepts. The first one consists in maintaining a constant stiffness matrix. The second uses a time/space model reduction method. In order to analyse the applicability and the performance of the use of a space–time separated representation, the simulations are carried out on a three-dimensional polycrystalline aggregate under cyclic loading. Different numbers of elements per grain and two time increments per cycle are investigated. The results show a significant CPU time saving while maintaining good precision. Moreover, increasing the number of elements and the number of time increments per cycle, the model reduction method is faster than the standard solver.
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@article{CRMECA_2018__346_2_132_0,
author = {Mohamed Aziz Nasri and Camille Robert and Amine Ammar and Saber El Arem and Franck Morel},
title = {Proper {Generalized} {Decomposition} {(PGD)} for the numerical simulation of polycrystalline aggregates under cyclic loading},
journal = {Comptes Rendus. M\'ecanique},
pages = {132--151},
publisher = {Elsevier},
volume = {346},
number = {2},
year = {2018},
doi = {10.1016/j.crme.2017.11.009},
language = {en},
}
TY - JOUR AU - Mohamed Aziz Nasri AU - Camille Robert AU - Amine Ammar AU - Saber El Arem AU - Franck Morel TI - Proper Generalized Decomposition (PGD) for the numerical simulation of polycrystalline aggregates under cyclic loading JO - Comptes Rendus. Mécanique PY - 2018 SP - 132 EP - 151 VL - 346 IS - 2 PB - Elsevier DO - 10.1016/j.crme.2017.11.009 LA - en ID - CRMECA_2018__346_2_132_0 ER -
%0 Journal Article %A Mohamed Aziz Nasri %A Camille Robert %A Amine Ammar %A Saber El Arem %A Franck Morel %T Proper Generalized Decomposition (PGD) for the numerical simulation of polycrystalline aggregates under cyclic loading %J Comptes Rendus. Mécanique %D 2018 %P 132-151 %V 346 %N 2 %I Elsevier %R 10.1016/j.crme.2017.11.009 %G en %F CRMECA_2018__346_2_132_0
Mohamed Aziz Nasri; Camille Robert; Amine Ammar; Saber El Arem; Franck Morel. Proper Generalized Decomposition (PGD) for the numerical simulation of polycrystalline aggregates under cyclic loading. Comptes Rendus. Mécanique, Volume 346 (2018) no. 2, pp. 132-151. doi : 10.1016/j.crme.2017.11.009. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2017.11.009/
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