An inverse micro-mechanical analysis toward the stochastic homogenization of nonlinear random composites

Wu, Ling; Nguyen, Van Dung; Adam, Laurent; Noels, Ludovic

doi:10.1016/j.cma.2019.01.016

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An inverse micro-mechanical analysis toward the stochastic homogenization of nonlinear random composites

Wu, Ling; Nguyen, Van Dung; Adam, Laurent et al.

2019 • In Computer Methods in Applied Mechanics and Engineering, 348, p. 97-138

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https://hdl.handle.net/2268/231886

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10.1016/j.cma.2019.01.016

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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 348 (2019) 97–138, DOI: 10.1016/j.cma.2019.01.016

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Keywords :

Stochastic; Homogenization; Micro-Mechanics; Composite Materials; Data-driven

Abstract :

[en] An inverse Mean-Field Homogenization (MFH) process is developed to improve the computational efficiency of non-linear stochastic multiscale analyzes by relying on a micro-mechanics model. First full-field simulations of composite Stochastic Volume Element (SVE) realizations are performed to characterize the homogenized stochastic behavior. The uncertainties observed in the non-linear homogenized response, which result from the uncertainties of their micro-structures, are then translated to an incrementalsecant MFH formulation by defining the MFH input parameters as random effective properties. These effective input parameters, which correspond to the micro-structure geometrical information and to the material phases model parameters, are identified by conducting an inverse analysis from the full-field homogenized responses. Compared to the direct finite element analyzes on SVEs, the resulting stochastic MFH process reduces not only the computational cost, but also the order of uncertain parameters in the composite micro-structures, leading to a stochastic Mean-Field Reduced Order Model (MF-ROM). A data-driven stochastic model is then built in order to generate the random effective properties under the form of a random field used as entry for the stochastic MF-ROM embedded in a Stochastic Finite Element Method (SFEM). The two cases of elastic Unidirectional (UD) fibers embedded in an elasto-plastic matrix and of elastic UD fibers embedded in a damage-enhanced elasto-plastic matrix are successively considered. In order to illustrate the capabilities of the method, the stochastic response of a ply is studied under transverse loading condition.

Research Center/Unit :

A&M - Aérospatiale et Mécanique - ULiège

Disciplines :

Mechanical engineering
Materials science & engineering
Aerospace & aeronautics engineering

Author, co-author :

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

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

Adam, Laurent; e-Xstream

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

Language :

English

Title :

An inverse micro-mechanical analysis toward the stochastic homogenization of nonlinear random composites

Publication date :

01 May 2019

Journal title :

Computer Methods in Applied Mechanics and Engineering

ISSN :

0045-7825

eISSN :

1879-2138

Publisher :

Elsevier, Amsterdam, Netherlands

Volume :

348

Pages :

97-138

Peer reviewed :

Peer Reviewed verified by ORBi

Additional URL :

http://dx.doi.org/10.1016/j.cma.2019.01.016

European Projects :

H2020 - 685451 - M-ERA.NET 2 - ERA-NET for materials research and innovation

Name of the research project :

The research has been funded by the Walloon Region under the agreement no 1410246 - STOMMMAC (CT-INT2013-03-28) in the context of the M-ERA.NET Joint Call 2014.

Funders :

Service public de Wallonie : Direction générale opérationnelle de l'économie, de l'emploi et de la recherche - DG06
CE - Commission Européenne

Available on ORBi :

since 19 January 2019

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