Réduction de Modèles et Réseaux Neuronaux Artificiels pour une Simulation Multi-échelle Rapide et Précise des Matériaux Composites à Microstructure Périodique

Model Order Reduction and Artificial Neural Networks Towards a Fast and Accurate Multiscale Simulation of Composite Materials with Periodic Microstructure

• Auteur / Autrice : Mohammed El fallaki idrissi
• Direction : Fodil Meraghni, Francisco Chinesta
• Type : Thèse de doctorat
• Discipline(s) : Mécanique (AM)
• Date : Soutenance le 19/01/2024
• Etablissement(s) : Paris, HESAM
• Ecole(s) doctorale(s) : École doctorale Sciences des métiers de l'ingénieur (Paris ; 2000-....)
• Partenaire(s) de recherche : Laboratoire : Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux (Metz ; 2011-....) - Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux
• Partenaire(s) de recherche : établissement de préparation de la thèse : École nationale supérieure d'arts et métiers (Paris ; 1780-....)
• Jury : Président / Présidente : Charbel Farhat
• Jury : Examinateurs / Examinatrices : Fodil Meraghni, Francisco Chinesta, Frédéric Lebon, Thomas Böhlke, Ivan Iordanoff, Laura De Lorenzis, Francis Praud
• Jury : Rapporteurs / Rapporteuses : Frédéric Lebon, Thomas Böhlke

Mots clés

Mots clés contrôlés

Mécanique non linéaire

Composites tressés

Thèses et écrits académiques

Mécanique

Mots clés libres

Modélisation Multi-Échelle

FE-MuTINN

PGD non intrusive

Matériaux Composites à Renfort Tissé

Solution Multiparamétrique

Simulation en temps-Réel

Multiscale Modeling

FE-MuTINN

Non-Intrusive PGD

Woven Composite Materials

Multiparametric Solution

Real-Time simulation

Résumé

Woven reinforced composites are often hindered by challenges in accurately predicting their mechanical behavior. This obstacle primarily stems from the heterogeneous nature of these materials. Consequently, employing multi-scale approaches becomes imperative to ascertain their overall responses under complex loading conditions, incorporating detailed descriptions of microstructure and the constitutive laws governing their components. However, effectively incorporating these methodologies into real-scale applications, particularly within FE² analyses, remains challenging due to the significant computational requirements. This challenge intensifies when numerous direct calculations are necessary for testing various configurations, a critical aspect in optimization, inverse analysis, or real-time simulations. The need for such calculations adds to the computational demands, posing a significant obstacle to integrated into practical applications. To address these issues, while considering the scale effects, this thesis aims to develop efficient numerical tools to achieve accurate and fast predictions of woven composite response. First, we develop virtual twins (multiparametric solution) for real-time prediction of composite response, using non-intrusive Proper Generalized Decomposition (PGD) based methods. This aims at providing an accurate approximation of these high-dimensional problems, that involved several microstructural parameters, with limited dataset. These multiparametric solutions are constructed for both linear and nonlinear behavior including history- and rate-dependent behaviors. Second, we develop an approach based on Artificial Neural Networks (ANNs) to perform a macroscopic surrogate model of composites. This model, referred to as Multiscale Thermodynamics Informed Neural Networks (MuTINN), is founded on thermodynamic principles and introduces specific quantities of interest that serve as internal state variables at the macroscopic level. This captures efficiently the state and evolution laws governing the history-dependent behavior of these composites while retaining the thermodynamic admissibility and the physical interpretability of their overall responses. This approach has successfully associated with FE code, streamlining the application of multiscale FE-MuTINN approach for composite structure computations. The prediction capabilities of the proposed approach are demonstrated across the material scales, exemplified through diverse instances of woven composite structures. These applications account for anisotropic yarn damage and an elastoplastic polymer matrix behavior. This promises a potential solution to alleviate the computational challenges associated with multiscale simulations of large composite structures and paving the way for the development of a hybrid twin solution.

Although woven reinforced composites are experiencing rapid growth across various engineering and industrial domains, their widespread adoption is often hindered by challenges in accurately predicting their mechanical behavior. This obstacle primarily stems from the heterogeneous nature of these materials. Consequently, employing multi-scale approaches becomes imperative to predict their overall response under complex loading conditions, incorporating detailed descriptions of microstructure and the constitutive laws governing their components. However, effectively incorporating these methodologies into real-scale applications, particularly within FE² analyses, remains challenging due to the significant computational requirements they entail. This challenge intensifies when numerous direct calculations are necessary for testing various configurations, a critical aspect in optimization, inverse analysis, or real-time simulations. The need for such calculations adds to the computational demands, posing a significant obstacle to integrated into practical applications. To address these issues, while considering the scale effects, this thesis aims to develop efficient numerical tools to achieve accurate and fast predictions of woven composite response. First, we develop virtual twins (multiparametric solution) for real-time prediction of composite response, using non-intrusive Proper Generalized Decomposition (PGD) based methods. This aims at providing an accurate approximation of high-dimensional problems, that involved several microstructural parameters, with limited dataset. These multiparametric solutions are constructed for both linear and nonlinear behavior including history- and rate-dependent behaviors. Second, we develop an approach based on ANN to perform a macroscopic surrogate model of composites. This model, referred to as Multiscale Thermodynamics Informed Neural Networks (MuTINN), is founded on thermodynamic principles and introduces specific quantities of interest that serve as internal state variables at the macroscopic level. This captures efficiently the state and evolution laws governing the history-dependent behavior of these composites while retaining the thermodynamic admissibility and the physical interpretability of their overall responses. This approach has successfully associated with FE code, streamlining the application of multiscale FE-MuTINN approach for composite structure computations. The prediction capabilities of the proposed approach are demonstrated across the material scales, exemplified through diverse instances of woven composite structures. These applications account for anisotropic yarn damage and an elastoplastic polymer matrix behavior. This promises a potential solution to alleviate the computational challenges associated with multiscale simulations of large composite structures and paving the way for the development of a hybrid twin solution.