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A monolithic hyper ROM FE2 method with clustered training at finite deformations

  • The usage of numerical homogenization to obtain structure–property relations by applying the finite element method at both the micro- and macroscale has gained much interest in the research community. The computational cost of this so-called FE2 method, however, is typically so high that algorithmic modifications and reduction methods are essential. In the present contribution, a monolithic solution algorithm is combined with reduced order modeling (ROM) and the empirical cubature method (ECM) for hyper integration. It is further complemented by a clustered training strategy, which lowers the training effort and the number of necessary ROM modes immensely. The applied methods can be combined modularly as desired in finite element approaches. An implementation in terms of an extension to the previously established MonolithFE2 code is provided. Numerical examples show the efficiency and accuracy of the monolithic hyper ROM FE2 method and the advantages of the clustered training strategy. Even for two-scale problems with complex geometryThe usage of numerical homogenization to obtain structure–property relations by applying the finite element method at both the micro- and macroscale has gained much interest in the research community. The computational cost of this so-called FE2 method, however, is typically so high that algorithmic modifications and reduction methods are essential. In the present contribution, a monolithic solution algorithm is combined with reduced order modeling (ROM) and the empirical cubature method (ECM) for hyper integration. It is further complemented by a clustered training strategy, which lowers the training effort and the number of necessary ROM modes immensely. The applied methods can be combined modularly as desired in finite element approaches. An implementation in terms of an extension to the previously established MonolithFE2 code is provided. Numerical examples show the efficiency and accuracy of the monolithic hyper ROM FE2 method and the advantages of the clustered training strategy. Even for two-scale problems with complex geometry and complex, inelastic material behaviors it was shown that speedup factors of almost 1000 (i.e., three orders of magnitude) regarding the online simulation time and of up to 30 regarding all necessary computing effort are obtainable in comparison to the conventional FE2 scheme. The training stage requires only around 3% of that time, meaning that the offline phase is relatively inexpensive, in contrast to many Neural Network approaches, whose employment, in terms of total computational efficiency, only pays off if a large number of online simulations is to be conducted, without requiring additional training.show moreshow less

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Author: Nils LangeORCiD, Geralf HütterORCiD, Bjoern KieferORCiD
URL:https://www.sciencedirect.com/science/article/pii/S0045782523006461?via%3Dihub
DOI:https://doi.org/10.1016/j.cma.2023.116522
ISSN:0045-7825
Title of the source (English):Computer Methods in Applied Mechanics and Engineering
Document Type:Scientific journal article peer-reviewed
Language:English
Year of publication:2024
Contributing Corporation:TU Bergakademie Freiberg
Tag:FE2; Homogenization; Hyper integration; Monolithic scheme; Multiscale; Reduced Order Modelling (ROM)
Volume/Year:418
Article number:116522
Way of publication:Open Access
Faculty/Chair:Fakultät 6 Architektur, Bauingenieurwesen und Stadtplanung / FG Baumechanik und Numerische Methoden
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