Sols, solides, structures, risques

Molecular dynamics simulations are ubiquitous in materials science, from drug discovery to design of advanced structural nanocomposites. Owing to the high-resolution of these simulations taking place at the atomic scale, predictions give access to data often complementary to experiments; be it characterisation of the nanostructure or even sophisticated instrumentation. I will begin the talk introducing the fundamentals of setting up molecular models and dynamics simulations to investigate the mechanics of materials. I will illustrate these aspects focusing on the collagen, the structural protein of choice in the human body and more largely the animal kingdom. I will present our recent investigations on the influence of hydration on the assembly of collagen microfibrils and the complex water dynamics within, trying to draw conclusions on the mechanical properties of the biopolymer.

While being quite popular, molecular dynamics simulations have several limitations (force field precision, ergodicity). Among these, the spectrum of spatiotemporal scales integrated within a simulation is extremely limited. This is particularly problematic when mechanical properties are of interest, as these emerge from the combination of scales ranging from the nanoscale (chemistry) to the macroscale (processing, testing). Unlike real-life experiments, all scales cannot be resolved simultaneously using computer simulations. I will give an overview of the existing multiscale simulation strategies: from rather cheap hierarchical to expensive concurrent approaches. I will illustrate their applicability with examples from my past research on the fracture of concrete under seismic loading and the dynamic behaviour of impacted shells of epoxy-graphene nanocomposites.

• 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.

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.

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.

• 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

• 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