A review of higher order Newton type methods and the effect of numerical damping for the solution of an advanced coupled Lemaitre damage model

Morch, Hélène; Yuan, Sibo; Duchene, Laurent; Harzallah, Ridha; Habraken, Anne

doi:10.1016/j.finel.2022.103801

Article (Scientific journals)

A review of higher order Newton type methods and the effect of numerical damping for the solution of an advanced coupled Lemaitre damage model

Morch, Hélène; Yuan, Sibo; Duchene, Laurent et al.

2022 • In Finite Elements in Analysis and Design, 209, p. 103801

Peer Reviewed verified by ORBi

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https://hdl.handle.net/2268/292643

DOI
10.1016/j.finel.2022.103801

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Keywords :

Applied Mathematics; Computer Graphics and Computer-Aided Design; General Engineering; Analysis

Abstract :

[en] In this paper, several Newton-type methods of convergence order 2 or higher were tested on various nonlinear systems of equations and on an advanced material law implemented in a finite-element code. The computational speed, numerical efficiency, and robustness of each method were evaluated for each studied case. The effect of numerical damping was also studied. The results were then compared to put in light the strengths and weaknesses of each method. The most efficient and robust method for the material law in the finite-element code was identified as the Newton method with a selective numerical damping.

Disciplines :

Engineering, computing & technology: Multidisciplinary, general & others

Author, co-author :

Morch, Hélène ; Université de Liège - ULiège > Urban and Environmental Engineering

Yuan, Sibo ; Université de Liège - ULiège > Faculté des Sciences Appliquées > Doct. sc. ingé. & techno. (archi., génie civ. - paysage)

Duchene, Laurent ; Université de Liège - ULiège > Urban and Environmental Engineering

Harzallah, Ridha

Habraken, Anne ; Université de Liège - ULiège > Urban and Environmental Engineering

Language :

English

Title :

A review of higher order Newton type methods and the effect of numerical damping for the solution of an advanced coupled Lemaitre damage model

Publication date :

October 2022

Journal title :

Finite Elements in Analysis and Design

ISSN :

0168-874X

eISSN :

1872-6925

Publisher :

Elsevier BV

Volume :

209

Pages :

103801

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

https://api.elsevier.com/content/article/PII:S0168874X22000750?httpAccept=text/xml

Available on ORBi :

since 25 June 2022

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