A k‐means clustering machine learning‐based multiscale method for anelastic heterogeneous structures with internal variables

A new machine‐learning based multiscale method, called k‐means FE2, is introduced to solve general nonlinear multiscale problems with internal variables and loading history‐dependent behaviors, without use of surrogate models. The macro scale problem is reduced by constructing clusters of Gauss poin...

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Bibliographic Details
Published inInternational journal for numerical methods in engineering Vol. 123; no. 9; pp. 2012 - 2041
Main Authors Benaimeche, Mohamed Amine, Yvonnet, Julien, Bary, Benoit, He, Qi‐Chang
Format Journal Article
LanguageEnglish
Published Hoboken, USA John Wiley & Sons, Inc 15.05.2022
Wiley Subscription Services, Inc
Wiley
Subjects
Anelasticity
Clustering
Dependent variables
Elastoplasticity
Engineering Sciences
FE2
Finite element method
homogenization
k‐means clustering
Load history
Machine learning
Mechanical properties
multiscale
Multiscale analysis
nonlinear
Radioactive wastes
Homogenization
FE2
k-means clustering
Nonlinear
Multiscale
Machine learning
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Summary:A new machine‐learning based multiscale method, called k‐means FE2, is introduced to solve general nonlinear multiscale problems with internal variables and loading history‐dependent behaviors, without use of surrogate models. The macro scale problem is reduced by constructing clusters of Gauss points in a structure which are estimated to be in the same mechanical state. A k‐means clustering—machine learning technique is employed to select the Gauss points based on their strain state and sets of internal variables. Then, for all Gauss points in a cluster, only one micro nonlinear problem is solved, and its response is transferred to all integration points of the cluster in terms of mechanical properties. The solution converges with respect to the number of clusters, which is weakly depends on the number of macro mesh elements. Accelerations of FE2 calculations up to a factor 50 are observed in typical applications. Arbitrary nonlinear behaviors including internal variables can be considered at the micro level. The method is applied to heterogeneous structures with local quasi‐brittle and elastoplastic behaviors and, in particular, to a nuclear waste package structure subject to internal expansions.
Bibliography:Funding information
Commissariat à l'Energie Atomique et aux Energies Alternatives
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.6925