Séminaire

Accurate models for the behaviour of materials are of fundamental importance in material science and mechanics. Traditionally, these models are derived from first principles (thermodynamics) and fine-tuned using heuristic/empirical methods to ensure calibration over experiments. However, heuristic constitutive modelling can fall short in describing the behaviour of complex materials that display path-dependent behaviours and possess multiple inherent scales, e.g. metamaterials, geomaterials, and biomaterials.
In recent years, the advent of Machine Learning, fuelled by a continuously increasing flow of data, has provided promising solutions to address the limitations of traditional constitutive modelling. Here, we present the Thermodynamics-based Artificial Neural Networks (Masi et al. 2021; Masi and Stefanou, 2022), which embed the fundamental laws of thermodynamics directly into their structure, thus ensure thermodynamically consistent predictions.

This talk mainly focuses on two major issues: (1) the non trivial identification of representative material state variables (Masi and Stefanou, 2023)—an essential ingredient in non-equilibrium thermodynamics—and (2) the shortcoming of ML in dealing with small data, i.e. limited and sparse material data sets (Masi and Einav, 2023). The capabilities of the methodology are demonstrated for the constitutive modelling of several complex, multiscale materials, displaying inelastic behaviour, path- and rate-dependency.
 

• F. Masi, I. Stefanou, P. Vannucci, V. Maffi-Berthier (2021). Thermodynamics-based Artificial Neural Networks for constitutive modeling. J Mech Phys Solids 147, 104277. doi: 10.1016/j.jmps.2020.104277.
• F. Masi, I. Stefanou (2022a). Multiscale modeling of inelastic materials with Thermodynamics-based Artificial Neural Networks (TANN), Comput Methods Appl Mech Eng 398, 115190. doi: 10.1016/j.cma.2022.115190.
• F. Masi, I. Stefanou (2023). Evolution TANN and the identification of internal variables and evolution
• equations in solid mechanics, J Mech Phys Solids 174, 105245. doi: 10.1016/j.jmps.2023.105245.
• F. Masi, I. Einav (2023). Neural differential constitutive equations for small data. Under preparation.

• En savoir plus sur Filippo Masi

Identifying governing equations from data and solving them to acquire spatio-temporal responses is desirable, yet highly challenging, for many practical problems. Machine learning (ML) has emerged as an alternative to influence knowledge discovery in complex geotechnical processes. To demonstrate feasibility, this study develops an ML-assisted data-driven approach to automatically recover Terzaghi’s consolidation theory from measured data and obtain the corresponding solutions. This process incorporates several algorithms including sparse regression and prior information based neural network (PiNet), transformed weak-form partial differential equations (PDEs) (to reduce sensitivity to noisy measurement), and Monte Carlo dropout to achieve a measure of prediction uncertainty. The results indicate that consolidation PDEs can be accurately extracted using the proposed approach which is also shown to be robust to noisy measurements. PDEs solved by PiNet are also shown to provide excellent agreement with actual results thus highlighting its potential for inverse analysis. The proposed approach is generic and provides an auxiliary method to verify heuristic interpretations of data or to directly identify patterns and obtain solutions without the need for expert intervention.

• En savoir plus sur Zhang Pin

L’objectif de cet exposé est de présenter quelques résultats sur la formalisation géométrique des milieux discrets. On s’attachera  à décrire la nature géométrique (ou intrinsèque) des objets intervenant dans l’écriture des lois de comportements des milieux discrets ainsi que de l’évolution incrémentale de tels milieux. Nous présenterons tout d’abord un aperçu historique des questions sous jacentes, aperçu qui  permettra de comprendre des motivations de ces développements. Ensuite selon le temps disponible nous avancerons dans la description géométrique des différents objets impliqués dans les lois et évolutions incrémentales: forces, déformations, taux de déformations, stabilité, élasticité, hyperélasticité, hypoélasticité, etc. 

• En savoir plus sur Jean Lerbet

The mechanism with which cells measure the dimension of the organ in which they are embedded, and slow down their growth when the final size is reached, is a long-standing problem in developmental biology. Feedback loops between growth and mechanical stress are increasingly believed to be important. In this presentation, I will introduce the concept of morphoelasticity as a standard continuum framework for modelling growing elastic tissues and provide insight into the feedback loops between growth and stress by considering simple 1D and 2D examples, such as a spring growing against a passive medium. However, without additional variables, the classical morphoelasticity theory often leads to either a collapse or unbounded growth of the tissue and prohibits reaching a finite asymptotic size. To address this issue, I will show how to modify the classical setting by including an energetic cost associated with growth, leading to the physical effect of size control.

These ideas will be applied to a specific system of a multicellular spheroid growing against the pressure of a medium in which it is embedded. The present model provides a qualitatively correct residual stress profile and has a naturally emerging necrotic core, both of which have been established experimentally in multicellular spheroids, and could be a step towards a better understanding of the role of mechanics in growing biological tissues.

• En savoir plus sur Alexander Erlich

• 08:30 Pierre-Simon Jouk (TIMC, Grenoble, France): La myoarchitecture cardiaque est un analogue biologique (...)
• 09:15 René Chambon (3SR, Grenoble, France): Unicité, Bifurcation, Contrôlabilité, Monotonicité, Inversibilité, (...)
• 10:00 COFFEE BREAK
• 10:30 Claudio Tamagnini (Università di Perugia, Italie): Second Gradient Poromechanics : Constitutive Modeling and Numerical (...)
• 11:15 Annie Raoult (Laboratoire MAP5, Paris, France): Quelques remarques en thermomécanique
• 12:00 présentation et clôture par Denis Caillerie : Préoccupations, occupations, postoccupations mathématiques

Programme (PDF, 999.18 Ko)

• En savoir plus sur Denis Caillerie

• 14:00 Robert Charlier (Université de Liège, Belgique) : Ouvrages souterrains de stockage de déchets nucléaires (...)
• 14:45 Stéphane Andrieux (ONERA, France) : Des outils basés sur la divergence de Bregman pour le traitement (...)
• 15:30 COFFEE BREAK
• 16:00 Pierre Suquet (CNRS, LMA, Marseille, France) : L’hétérogénéité dans tous ses états (ou presque !)
• 16:45 Michel Bornert (Laboratoire Navier, Paris, France) : Discontinuités dans les géomatériaux : vues panoramiques et plans serrés
• 17:30 présentation et clôture par Jacques Desrues : A la poursuite de la localisation dans les géomatériaux

Programme (PDF, 999.18 Ko)

• En savoir plus sur Jacques Desrues

• En savoir plus sur Recho Pierre

A set of triaxial compression tests on partially saturated dense sands to clarify the microscopic characteristics and their link to the macroscopic responses is presented. Constant suction tests (CS tests) and constant water content tests (CW tests) are conducted under low confining pressure to observe microscopic and macroscopic behaviors of the sands associated with dilative shear bands. X-ray micro-tomography and image analysis techniques are applied to investigate the continuity as a defined index to evaluate the morphology of the pore water, the number of liquid bridges and the principal curvature of the air–water interface, etc.

The relationship between the microscopic observation and overall specimen-scale behaviour is also discussed. The tendency of decreasing curvature corresponds to that of decreasing suction in the CW test. The peak deviator stress is higher in the CS test than in the CW test when the pore water is initially discontinuous, whereas it is identical between the two tests when the pore water is initially continuous. The residual stress is lower in the CW test than in the CS test, independent of the initial water retention states. The macroscopic responses at the different initial water retention states are qualitatively identical between poorly graded sand and well-graded sand

• En savoir plus sur Yosuke Higo

Cementitious materials and geomaterials are considered as complex porous civil engineering materials. Understanding the behaviour of such materials requires a multiscale hierarchical study of mechanisms occurring across multiple length scales (nano→micro→macro) where every phenomenon in a given scale can be understood through looking at the scale below. The molecular configuration and the bonding mechanism at the nano-scale define the interactions inside a multi-phase system (such as cement) at the micro-scale that characterize the material response to external mechanical loading and to chemical/physical attacks from the outside environment at the macro-scale.

We are interested in developing upscaling approaches based on Molecular Dynamics (MD), Monte Carlo (MC) and Density Theory functional (DFT) methods to study the multi-physics multiscale behaviour of geomaterials considering the multiscale features of the pore structure. Characterizing the structure of geomaterials at the nano-scale is not only important to predict the chemical, thermal and mechanical behaviour but also to efficiently optimize/manipulate the composition of the material in order to enhance the mechanical performance of civil engineering materials at the macro scale.

• En savoir plus sur Laanaiya Majdouline

The action of a fluid flow on a granular material is a common situation in nature and in many industrial processes. Numerous studies, based on both experiments and modelling, have led to a better understanding and description of the fluid-granular interaction in situations such as surface erosion or fluidization. The hydro-mechanical behaviour of cemented soils, and more particularly of cemented granular soils, remains less known although this type of material is also frequently encountered in sedimentary rocks (sandstones, conglomerates, breccia…) or engineering materials (mortars, concrete, asphalt…).
To address this problem, we consider here more specifically grains that are artificially cemented by creating, from an external solid phase, adhesive bridges whose tensile strength can be varied. This allows a gradual transition from the pure granular case to weakly cemented ones. In this presentation, I will report some recent studies carried out for various situations, such as impinging jet erosion, surface erosion, localized injection, with, almost systematically, an approach combining and comparing experiments on model systems with numerical simulations involving coupled Lattice Boltzmann (LBM) and Discrete Elements (DEM) methods.
 

• En savoir plus sur Philippe Pierre