Comptes Rendus
A secure version of asymptotic numerical method via convergence acceleration
[Une version sécurisée de la méthode asymptotique numérique avec accélération de convergence]
Comptes Rendus. Mécanique, Volume 348 (2020) no. 5, pp. 361-374.

L’article étudie le calcul numérique de problèmes difficiles nécessitant de nombreux pas et un grand nombre de degrés de liberté, comme l’étude par éléments finis du plissement de systèmes film–substrat. La méthode asymptotique numérique (ANM) est bien adaptée à de tels calculs, mais avec une lente perte de précision lors de l’enchainement de nombreux pas de calculs. Donc des étapes de correction sont indispensables, ce qui est rarement fait lors de calculs par ANM. L’algorithme de cheminement est complété par une méthode d’accélération de convergence et par une technique d’adaptation de la longueur de pas pour minimiser le temps de calcul et pour fiabiliser la procédure. Cette version modifiée de la méthode asymptotique numérique a été évaluée par la simulation de l’apparition de plis sinusoïdaux en compression uniaxiale.

The paper deals with the numerical computation of difficult problems requiring many steps and many degrees of freedom such as the finite element analysis of wrinkling of film–substrate systems. The asymptotic numerical method (ANM) is well adapted to such computations but with a progressive loss of accuracy during step chaining. Thus, correction phases are necessary, which are rarely carried out within ANM. A convergence acceleration algorithm and a step-length adaptation have been included to limit the growth of computation time and to strengthen the reliability of the procedure. This modified version of the ANM is assessed by simulating the appearance and evolution of sinusoidal wrinkles under uniaxial compression.

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Révisé le :
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DOI : 10.5802/crmeca.48
Keywords: Asymptotic numerical method, Convergence acceleration, Path-following technique, Wrinkling, Film–substrate systems
Mot clés : Méthode asymptotique numérique, Accélération de convergence, Algorithme de cheminement, Plissement, Systèmes film–substrat
Pascal Ventura 1 ; Michel Potier-Ferry 1 ; Hamid Zahrouni 1

1 Université de Lorraine, CNRS, Arts et Métiers ParisTech, LEM3, F-57000 Metz, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {A secure version of asymptotic numerical method via convergence acceleration},
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     year = {2020},
     doi = {10.5802/crmeca.48},
     language = {en},
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Pascal Ventura; Michel Potier-Ferry; Hamid Zahrouni. A secure version of asymptotic numerical method via convergence acceleration. Comptes Rendus. Mécanique, Volume 348 (2020) no. 5, pp. 361-374. doi : 10.5802/crmeca.48. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.48/

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