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UNSUPERVISED LEARNING BASED MODEL ORDER REDUCTION FOR HYPERELASTOPLASTICITY
Vijayaraghavan, Soumianarayanan; Beex, Lars; Noels, Ludovic et al.
2021
 

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Keywords :
Elastoplasticity; Reduced Order Model; Clustering; Machine learning
Abstract :
[en] Many model order reduction approaches use solutions of a few ‘offline’ training simulations to reduce the number of degrees of freedom of the many ‘online’ simulations of interest. In proper orthogonal decomposition, singular value decomposition is applied to a matrix with the training solutions in order to capture the most essential characteristics in the first few modes - which are used as global interpolation bases. Proper orthogonal decomposition has proven itself as an accurate reduced order model approach for elliptical partial differential equations. In the field of solid mechanics, this means that it is accurate for (hyper)elastic material models, but not for (hyper)elastoplasticity. Based on the study of [1], the current contribution investigates how clustering of the training solutions and extracting global modes from each cluster can improve the accuracy of proper orthogonal decomposition for hyperelastoplasticity. Both centroid-based clustering (i.e. k-means clustering) and connectivity-based clustering (based on chinese whispers) are investigated. The approach is applied to a hyperelastoplastic representative volume element exposed to monotonic loading, quasi-monotonic loading and quasi-random loading. In case of monotonic and quasi-montonic loading, the components of the macroscopic deformation tensor are the variables to which clustering is applied. In case of quasi-random loading however, not only the components of the macroscopic deformation tensor and the incremental changes of these components are the variables to which clustering is applied, but also all history variables of all integration points. [1] David Amsallem1, Matthew J. Zahr2 and Charbel Farhat Nonlinear model order reduction based on local reduced-order bases. Int. J. Numer. Meth. Engng. VOL 92 IS-10 SN-0029-5981
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Vijayaraghavan, Soumianarayanan ;  Université de Liège - ULiège > A&M
Beex, Lars;  University of Luxembourg
Noels, Ludovic  ;  Université de Liège - ULiège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3)
Bordas, Stephane;  University of Luxembourg
Language :
English
Title :
UNSUPERVISED LEARNING BASED MODEL ORDER REDUCTION FOR HYPERELASTOPLASTICITY
Publication date :
January 2021
Event name :
WCCM-ECCOMAS 2020
Event date :
11-01-2021 to 15-01-2021
Audience :
International
Name of the research project :
FNR11019432 > Stéphane Bordas > EnLightenIt > Multiscale modelling of lightweight metallic materials accounting for variability of geometrical and material properties
Funders :
F.R.S.-FNRS - Fonds de la Recherche Scientifique [BE]
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since 12 May 2021

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