Propositions de sujets de these
Problèmes multi-physiques en élastoplasticité utilisant des champs locaux hétérogènes
Multi-physics model-free problems in elastoplasticity using heterogeneous local fields
Mots-clés
Model-free, champ local, corrélation d'images numériques (DIC), auto-échauffement, polymères semi-cristallins
Model-free, local field, Digital Image Correlation (DIC), heat build-up, semi-crystalline polymers
Résumé
Dans ce sujet de thèse, nous proposons d'utiliser un paradigme connu sous le nom de modélisation pilotée par les données, consistant à formuler des calculs directement à partir de données expérimentales sur les matériaux et de contraintes essentielles et de lois de conservation pertinentes, en contournant complètement l'étape de modélisation empirique des matériaux de la simulation conventionnelle. Les contraintes essentielles et les lois de conservation telles que la compatibilité et l'équilibre restent inchangées, de même que tous les schémas numériques utilisés pour leur discrétisation : les éléments finis, les intégrateurs temporels, etc. Ces lois de conservation confèrent une structure mathématique aux calculs, et cette structure mathématique se retrouve dans le paradigme actuel axé sur les données. Cependant, dans la modélisation pilotée par les données, les points de données expérimentales sur les matériaux sont utilisés directement dans les calculs plutôt qu'un modèle empirique. De cette manière, l'empirisme, l'erreur et l'incertitude de la modélisation des matériaux sont entièrement éliminés et il n'y a pas de perte d'informations expérimentales.
In this work, we propose using a paradigm known as data-driven simulation, consisting of formulating calculations directly from experimental material data and pertinent essential constraints and conservation laws, bypassing the empirical material modelling step of conventional computing altogether. Essential constraints and conservation laws such as compatibility and equilibrium remain unchanged, as do all the numerical schemes used in their discretization, such as finite elements, time-integrators, etc. Such conservation laws confer mathematical structure to the calculations, and this mathematical structure carries over to the present data-driven paradigm. However, in data-driven simulation the experimental material-data points are used directly in calculations rather than an empirical material model. In this manner, material modelling empiricism, error and uncertainty are eliminated entirely and no loss of experimental information is incurred.
Whereas the data-driven paradigm has been formulated in the context of computational mechanics and, specifically elastic quasi-static problems, we believe that its range and scope is much larger. By contrast, inelastic materials raise the fundamental problem of sampling history-dependent material behaviour. Such sampling should provide appropriate coverage of possible processes and evolutions of the system and is thus likely to result in exceedingly large and complex data sets. The use of tools from Data Science and Big Data management may be expected to be particularly beneficial in dealing with such data sets. Using the local fields – strain and surface temperature – the calculations will consider, for the first time, the global and local response of the material. Furthermore, the true temperature of the material will be taken into account.
Contexte
Engineering materials are increasingly used in industrial applications under different strain rates, temperatures and loading conditions. To ensure in-service robustness and to predict the durability of components, identifying reliable and consistent models is of prime importance. Besides, macroscopic mechanical behaviour is commonly characterised by the stress-strain curve obtained from uniaxial tests. This identification method – empirical modelling and identification linked with data from uniaxial tests – induces some limitations.
The prevailing simulation paradigm has been to calibrate empirical material models using observational data and then use the calibrated constitutive model in calculations. This process of modelling a fortiori adds error and uncertainty to the solutions, especially in systems with high-dimensional phase spaces and complex behaviour. This modelling error and uncertainty arise from imperfect knowledge of the form of the material laws, the phase space in which they are defined, and from scatter and noise in the experimental data. Besides, often the models used to fit the data are ad hoc, without a clear basis in physics criterion for their selection, and thus the process of modelling is based in empiricism and arbitrariness. Indeed, the entire process of empirical material modelling, and model validation thereof, is open-ended and no rigorous mathematical theory exists to date that makes it precise and quantitative, i.e. the model parameters are user-dependent.
During uniaxial loading, necking originates in smooth samples in a non-controlled location. As a consequence of this geometrical irregularity, a multiaxial stress state within the net cross section of the sample is induced. In notched samples, the multiaxial stress state is theoretically characterized and re-necking could be expected. The multiaxial stress state consists of high levels of hydrostatic stress, for which polymers are known to be sensitive. The stress field should be regarded as an additive decomposition of shear and hydrostatic pressure.
Due to the dissipative effects, the instantaneous temperature of the specimens during mechanical testing is not the same as the room temperature. Depending on the strain rate – among other variables, the heat build-up could be significantly high to modify the mechanical response of the material. Moreover, the heat build-up depending on the geometry and the deformation local field, the temperature rise would be heterogeneous on the surface of the geometry.
Encadrement
Directeur de thèse: Cristian OVALLE-RODAS
Co-Directeur de thèse: Jean-Luc BOUVARD
Profil du candidat
Ingénieur et/ou Master recherche - Bon niveau de culture générale et scientifique. Bon niveau de pratique du français et de l'anglais (niveau B2 ou équivalent minimum). Bonnes capacités d'analyse, de synthèse, d'innovation et de communication. Qualités d'adaptabilité et de créativité. Capacités pédagogiques. Motivation pour l'activité de recherche. Projet professionnel cohérent.
Pré-requis (compétences spécifiques pour cette thèse) :
Pour postuler : Envoyer votre dossier à recrutement_these@mat.mines-paristech.fr comportant
• un curriculum vitae détaillé
• une copie de la carte d'identité ou passeport
• une lettre de motivation/projet personnel
• des relevés de notes L3, M1, M2
• 2 lettres de recommandation
• les noms et les coordonnées d'au moins deux personnes pouvant être contactées pour recommandation
• une attestation de niveau d'anglais
Engineer and / or Master of Science - Good level of general and scientific culture. Good level of knowledge of French (B2 level in french is required) and English. (B2 level in english is required) Good analytical, synthesis, innovation and communication skills. Qualities of adaptability and creativity. Teaching skills. Motivation for research activity. Coherent professional project.
Prerequisite (specific skills for this thesis):
Applicants should supply the following :
• a detailed resume
• a copy of the identity card or passport
• a covering letter explaining the applicant's motivation for the position
• detailed exam results
• two references : the name and contact details of at least two people who could be contacted
• to provide an appreciation of the candidate
• Your notes of M1, M2
• level of English equivalent TOEIC
to be sent to recrutement_these@mat.mines-paristech.fr
Résultats attendus
• Experimental data at two scales:
◦ Macroscopic: experimental data from instrumented – DIC and IR – tensile tests on notched specimens at room and high temperature
◦ Microscopic: SEM observations of the microstructure: i) initial; ii) deformed; iii) broken; and possibly by 3D imaging (tomography/laminography) ex or in-situ;
• Model-free simulation taking into account the local fields of deformation and temperature rise;
• Implementation of the model-free paradigm in the in-house simulation interface
Objectifs
• to propose a new and different simulation framework in which the experimental material-data points are used directly in calculations rather than an empirical material model;
• to avoid material modelling empiricism, error and uncertainty as no loss of experimental information is incurred;
• to implement an efficient data-driven computing and demonstrate the practicality of the approach.
Références
[1] T. Kirchdoerfer and M. Ortiz. Comput. Methods Appl. Mech. Eng., 326:622–641, 2017.
[2] T. Kirchdoerfer and M. Ortiz. Comput. Methods Appl. Mech. Eng., 304:81–101, 2016.
[3] L. Stainier, A. Leygue, and M. Ortiz. Comput. Mech., 64:381–393, 2019.
[4] R. Eggersmann, T. Kirchdoerfer, S. Reese, L. Stainier, and M. Ortiz. Comput. Methods Appl. Mech. Eng., 350:81–99, 2019