Stochastic deep material networks as efficient surrogates for stochastic homogenisation of non-linear heterogeneous materials

Wu, Ling; Noels, Ludovic

doi:10.1016/j.cma.2025.117994

Article (Scientific journals)

Stochastic deep material networks as efficient surrogates for stochastic homogenisation of non-linear heterogeneous materials

Wu, Ling; Noels, Ludovic

2025 • In Computer Methods in Applied Mechanics and Engineering, 441, p. 117994

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https://hdl.handle.net/2268/330920

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10.1016/j.cma.2025.117994

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NOTICE: this is the author’s version of a work that was accepted for publication in Computer Methods in Applied Mechanics and Engineering. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computer Methods in Applied Mechanics and Engineering 441 (2025), DOI: 10.1016/j.cma.2025.117994

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Keywords :

Deep-Material Network; Stochastic; Composites; Stochastic Volume Elements (SVEs); Homogenisation

Abstract :

[en] The Interaction-Based Deep Material Network (IB-DMN) is reformulated to decouple the phase volume fraction from the topological parameters of the IB-DMN. Since the phase volume fraction is no longer influenced by the topological parameters, on the one hand the stochastic IBDMN can predict the response of arbitrary phase volume fraction, and on the other hand the stochastic IB-DMN can be constructed by introducing uncertainties to the topological parameters of a reference IB-DMN, which is trained using data obtained from full-field linear elastic homogenisation, allowing to capture the variability resulting from the micro-structure organisation such as a phase clustering. The non-linear predictions of the proposed stochastic IB-DMN are compared to those from Direct Numerical Simulation (DNS) on 2D Stochastic Volume Elements (SVEs) of unidirectional fibre-reinforced matrix composites in a finite-strain setting. The results from in-plane uni-axial stress and shear tests show that the proposed stochastic IB-DMN is capable of reproducing random non-linear responses with the same stochastic characteristics as the predictions of the DNS conducted on SVE realisations.

Research Center/Unit :

A&M - Aérospatiale et Mécanique - ULiège

Disciplines :

Mechanical engineering
Aerospace & aeronautics engineering

Author, co-author :

Wu, Ling ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3)

Noels, Ludovic ; Université de Liège - ULiège > Département d'aérospatiale et mécanique > Computational & Multiscale Mechanics of Materials (CM3)

Language :

English

Title :

Stochastic deep material networks as efficient surrogates for stochastic homogenisation of non-linear heterogeneous materials

Publication date :

01 June 2025

Journal title :

Computer Methods in Applied Mechanics and Engineering

ISSN :

0045-7825

eISSN :

1879-2138

Publisher :

Elsevier

Volume :

441

Pages :

117994

Peer reviewed :

Peer Reviewed verified by ORBi

Development Goals :

9. Industry, innovation and infrastructure

Additional URL :

https://api.elsevier.com/content/article/PII:S004578252500266X?httpAccept=text/xml

European Projects :

HE - 101056682 - DIDEAROT - Digital Design strategies to certify and mAnufacture Robust cOmposite sTructures 

Name of the research project :

DIDEAROT

Funders :

EC - European Commission
EU - European Union

Funding number :

101056682

Funding text :

This project has received funding from the European Union’s Horizon Europe Framework Programme under grant agreement No. 101056682 for the project ‘‘DIgital DEsign strategies to certify and mAnufacture Robust cOmposite sTructures (DIDEAROT)’’. The contents of this publication are the sole responsibility of ULiege and do not necessarily reflect the opinion of the European Union. Neither the European Union nor the granting authority can be held responsible for them.

Data Set :

http://dx.doi.org/10.5281/zenodo.15120313

The raw/processed data required to reproduce these findings is available on https://gitlab.uliege.be/didearot/didearotPublic/publicationsData/2025_StochasticIBDMN under the Creative Commons Attribution 4.0 International (CC BY 4.0) licence

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since 18 April 2025

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