Approches probabilistes en mécanique des matériaux

Les principaux thèmes traités sont les suivants :

Modèles et simulations de structures aléatoires (identification de modèles à partir d’analyse d’images de la microstructure, génération de réalisations de milieux aléatoires 3D).
Analyse morphologique des microstructures (en particulier en 3D, grâce aux progrès de la microtomographie) et des champs (par exemple de déplacements).
Homogénéisation des structures aléatoires (calcul de bornes avec prise en compte d’informations statistiques sur la microstructure, changement d’échelle par couplage d’un calcul par éléments finis et de la morphologie, à partir d’images ou de simulations).
Modèles probabilistes de rupture et d’endommagement (modèles analytiques et simulations), effets d’échelle sur le comportement en rupture.

Précédentes journées thématiques, colloques et annonces

La conférence internationale « Continuous Models and Discrete Systems 14 » (CMDS14), sponsorisée par Mécamat, a eu lieu à Paris les 26-30 juin 2023.

URL: https://cmds14.org

La session « Modeling and simulation of microstructures » a eu lieu le 13 juin 2023 (chair: F. Willot). Les orateurs invités étaient :

* Samantha Daly, UCSB: 3D Grain Shape Generation in Polycrystals Using Generative Adversarial Networks

This talk will discuss the general features and uses of generative adversarial networks (GANs) in experimental mechanics of materials, and present a generative adversarial network (GAN) capable of producing realistic microstructure morphology features with a demonstration of its capabilities on a dataset of crystalline titanium grain shapes. Alongside this, an approach will be presented that trains deep learning networks to understand material-specific descriptor features, such as grain shapes, based on existing conceptual relationships with established learning spaces, such as functional object shapes. A style-based GAN with Wasserstein loss, called M-GAN, was first trained to recognize distributions of morphology features from function objects in the ShapeNet dataset and was then applied to grain morphologies from a 3D crystallographic dataset of Ti–6Al–4V. Evaluation of feature recognition on objects showed comparable or better performance than state-of-the-art voxel-based network approaches. When applied to experimental data, M-GAN generated realistic grain morphologies comparable to those seen in Ti–6Al–4V. A quantitative comparison of moment invariant distributions showed that the generated grains were similar in shape and structure to the ground truth, but scale invariance learned from object recognition led to difficulty in distinguishing between the physical features of small grains and spatial resolution artifacts. The physical implications of M-GAN’s learning capabilities will be discussed, as well as the extensibility of this approach to other material characteristics related to grain morphology.

* Matthias Neumann (Ulm University): Stochastic 3D microstructure modeling: An efficient tool to quantify the morphology influence on effective macroscopic properties

For a wide field of functional materials, the underlying microstructure strongly influences effective macroscopic properties such as stress-strain curves or permeability of fluids. The progress of 3D imaging during the last decades enables the computation of well-defined morphological microstructure descriptors from real data, which can be
compared to effective macroscopic properties that are either measured experimentally or simulated numerically. Although this approach allows for a direct investigation of the relationships between morphology and effective macroscopic properties, it is limited due to the high costs of 3D imaging.
In order to overcome these limitations, stochastic 3D microstructure modeling combined with numerical simulations of effective macroscopic properties is a powerful tool. The use of stochastic microstructure models allows for generating large sets of virtual, but realistic microstructures in short time, where morphological descriptors can be
systematically varied. For these virtual structures, the corresponding effective macroscopic properties can be numerically simulated. By doing so, a large data base can be generated to quantitatively study the morphology influence on effective macroscopic properties. In this talk, we review the state of the art of stochastic 3D microstructure models for different types of microstructures such as particle packings, fiber-based materials, amorphous structures and
polycrystalline grain architectures. At this, conceptually different approaches for stochastic 3D microstructure modeling are reviewed. First, models based on methods from stochastic geometry and mathematical morphology such as random fields, random point processes and random
tessellations are presented. These models are compared to recent developments based on statistical learning like generative adversarial networks. The use of stochastic 3D microstructure modeling to elucidate the morphology influence on effective macroscopic properties is
illustrated at selected examples.

* Maxime Moreaud, IFPEN: Digitally accelerated design of materials

Since 2017, IFPEN has fully entered the race for accelerated design of new materials with models creating links between synthesis and effective properties. Offering new tools for the generation and digital characterization of microstructures of materials, this approach realistically considers the microstructure to capture morphological and topological details at scales of interest. Numerical models are linked to synthesis or forming processes and estimate textural and usage properties. In this talk, we will discuss the general ideas of this approach, examples of multiscale microstructures, and some recent work on numerical textural work on numerical textural characterizations such as tortuosity and accelerated physisorption simulation by deep learning.

Un numéro spécial de la revue « Journal of Mathematics in Industry » intitulé « Shape, Form and Patterns in Medecine, Biotechnology and Material Science » sera publié en 2022. Plus d’informations sur le lien suivant : https://www.springeropen.com/collections/sfp

En 2021, Symposium « Shape, Form and Patterns in Medecine, Biotechnology and Material Science » de la conférence « Industrial and Applied Mathematics » (https://ecmi2021.uni-wuppertal.de/de/programme/minisymposia.html)

Le symposium S20 « Advanced modelling techniques: Stochastics in materials mechanics » de la conférence EMMC20 à Madrid du 27 au 29 Mai 2020 est annulé pour cause de Covid.

Symposium « Stochastics in materials mechanics » de la conférence EMMC16 à Nantes du 26 au 28/03/2018

WORKSHOP INTERNATIONAL, avec le soutien de Mécamat
Physics and mechanics of random structures: from morphology to material properties, Workshop international en l’honneur et en présence de Dominique Jeulin, île d’Oléron, 17-23 juin 2018.

Workshop conjoint « Matériaux Numériques » (SF2M/Mécamat) et « Modèles probabilistes en Mécanique des Milieux Hétérogènes » se sont déroulés à l’École des Mines de Paris, en Décembre 2015

Les Journées thématiques Mécamat des Groupes « Approches Probabilistes en Mécanique des Milieux Hétérogènes » et « Rhéologie des Matériaux Hétérogènes – Traitements thermomécaniques » se sont déroulées à l’école des Mines de Paris les 11 et 12 mai 2015.