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## Séminaires de Sciences Numériques pour la Mécanique

Ce séminaire, lié à l’axe Sciences Numériques pour la Mécanique, a pour objectif de discuter de travaux de recherche portant en particulier sur la modélisation et l’analyse numérique, à l’interface entre la mécanique, les mathématiques et l’informatique.

Il a lieu en général le jeudi à 11h30, en salle MSROE (C119 - rez de chaussée Bâtiment Dumas, voir plan d’accès), une fois par mois. Pour toute question relative à ce séminaire, vous pouvez contacter les organisateurs, Régis Cottereau, Andrea Barbarulo et Bing Tié .

Les transparents de certains conférenciers sont disponibles dans les archives.

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Prochains séminaires __

**Jeudi 4 Mai 2017 (11h30) - Mathieu Mazière** (Centre des Matériaux) - *Modelling Additive Manufacturing Processes : From Direct Metal Deposition to Selective Laser Melting* *-* salle C119

Résumé: Additive manufacturing is a family of processes allowing to build a component from CAD file by selectively adding material layer by layer. The main difference between the Selective Laser Melting (SLM) process and the Direct Metal Deposition (DMD) process is related to material feeding. In SLM, the powder is not deposited using a nozzle as in DMD but drawn in successive thin layers which are then scanned by the laser beam. A model for the DMD process has been developed in strong connection with the physical process, namely the thermal, metallurgical and mechanical problems. In order to reduce CPU time, but to stay with a relevant simulation, only the significant interactions are introduced in the model. The latent heat of fusion, the stress induced phase transformations and the heat originating from the viscoplastic dissipation are ignored. The three models (thermal, metallurgical and mechanical) are weakly coupled and are performed sequentially. The microstructural evolutions derive from the temperature history only, meanwhile the mechanical problem uses both thermal fields and phase volume fractions as inputs for its constitutive equations. The model is implemented in the Finite Element Code Z-Set [1] and a specific strategy is introduced to progressively activate the elements and follow a given fabrication route. The modelling strategy, the related assumptions and the original metallurgical model have been previously described in a PhD Thesis [2] and one article [3].

The same approach cannot be used directly for modelling the SLM process. Indeed the computation time would be increased dramatically because of the smaller size of all parameters (laser spot, melt pool, bead, layer,...) that are one order of magnitude smaller for SLM than for DMD. Another strategy has been proposed where the matter is added layer by layer. The interaction of the manufactured part with the powder bed has also to be accounted for. Most of the models giving the effective thermal conductivity of a powder layer are valid only for temperature below 500C. Some strong hypothesis must be made for temperatures from 500C to 1650C (melting temperature). An experimental procedure allowing to verify the validity of these hypothesis will then be exposed.

REFERENCES :

[1] www.zebulon-software.com

[2] A. Longuet,Modélisation du procédé de projection laser - Application au Ti-6Al-4V. Thèse Mines ParisTech, 2010

[3] G. Marion, G. Cailletaud, C. Colin, M. Mazière,A Finite Element Model for the simulation of Direct Metal Deposition, ICALEO, San Diego, USA, 19-23 octobre 2014.

**Mercredi 24 Mai 2017 (11h30) - Chloé Arson** (GeorgiaTech, USA) - *Micro-Macro Damage and Healing Rock* *-* salle C119

Résumé: The mining operations required to recover mineral resources, store energy underground and dispose of waste in deep geological layers involve coupled mechanical, physical and chemical rock microstructure changes. Damage and healing in rocks refer to variations of mechanical and physical properties induced by pore or crack evolution. The gap between microscopic and macroscopic models makes it infeasible to uniquely characterize the pore- and crack- scale mechanisms that control deformation and flow regimes, predict percolation thresholds coupled to changes of rock stiffness, or relate crack rebonding time to stiffness and permeability healing time. Therefore the objectives of the work presented in this lecture are to: Understand and predict chemo-mechanical changes of pore geometry; Model the dynamics of pore networks; Formulate and assess innovative microstructure- enriched models of damage and healing; and Interpret rock deformation and fluid flow instabilities resulting from chemo-mechanical damage and healing. Geological storage in salt is used as an illustrative problem for investigating the following fundamental scientific questions: Why do pores and cracks heal? How long does hydro-mechanical recovery take? How much energy does healing require? We first explain a top-to-bottom multi-scale approach: fabric-enriched damage and healing damage mechanics. Moments of probability of microstructure descriptors, found by image analysis, are used as internal variables. The mathematical framework makes it possible to predict the evolution of pore geometry and connectivity upon multi-physics damage and healing processes. We then present a bottom-to-top multi-scale approach based on the self-consistent method. Models allow simulating damage and subsequent accommodation in a polycrystal subject to time-dependent sliding mechanisms. Finally we focus on the processes driving flow network growth and transformation upon damage and healing processes. These are still poorly understood, especially under dynamic fluctuations. Astonishing similarities were noted between the geometry of networks formed by living organisms (e.g. roots, slime mold) and that of infrastructure facilities (e.g. railway systems). Therefore we hypothesize that natural systems can be emulated to understand flow network formation and evolution in a porous geomaterial subject to damage and healing. We present preliminary work done on root system architecture, leaf venation topology and slime mold networks.

**Jeudi 8 Juin 2017 (11h30) - Alice Cicirello** (Oxford, UK) - *Vibration performance assessment under uncertain structural properties* *-* salle C119

Résumé: Much industrial interest is focused on rapidly explore the performance of a structural design to dynamic loading by building virtual prototypes. Nonetheless, several parameters of a computational model (such as geometry, material properties, loadings, boundary conditions, and structural joints) required to investigate the behaviour of a built-up structures (such as cars, satellite, and so on) may not be known precisely, and yet an engineering assessment of a design must nonetheless be performed. Therefore, the challenge is not only to develop a mathematical model able to capture the physics of the problem, but also to account for these uncertainties.

In this talk, I will give an overview of the application uncertainty models in structural dynamics, with particular focus on recent advances on (i) the combination of probabilistic and non-probabilistic uncertainty models, and (ii) efficient strategies for developing imprecise probability models that can be readily used in engineering applications. A new approach for the random vibration analysis of aircraft structural components under imprecise probability is going to be presented.

**Jeudi 22 Juin 2017 (11h30) - Thiago Ritto** (UFRJ, Brésil) - *Drill-string dynamics and uncertainties* *-* salle C119

Résumé: The drill-string dynamic problem is fascinating. Many interesting physical aspects are present in this analysis, such as, bit–rock interaction, fluid-structure interaction, geometric nonlinearity, impact and rubbing, model and parameter uncertainties, and rigid body motions. In addition, from the economic perspective (we are dealing with a crucial operation of the oil industry), it is very important to understand the drill-string dynamics and control its behavior to avoid failures (environmental included) and to optimize its performance. A computational model for the drill string must include the main forces acting on the system, which depend on the type of formation, type of bit, etc. This presentation will tackle the drill-string modeling and simulation, including stochastic analysis for vertical and horizontal rigs. We consider axial, lateral, and torsional vibrations; nonlinear bit-rock interaction; impact; and fluid-structure interaction. Uncertainties are taken into account both for the system parameters and the bit-rock interaction model. Strategies for stochastic identification (including the Bayesian approach) and robust optimization are presented. Finally, field data of a 5 km drill-string is used to (1) partially validate the torsional vibration model and (2) identify a proposed stochastic model for the nonlinear bit-rock interaction. The drill-string stochastic dynamics is depicted in many forms, nevertheless, there are still many aspects to explore in this nonlinear dynamical model.

References:

- Non-linear dynamics of a drill-string with uncertain model of the bit-rock interaction Ritto, T.G., Soize, C., Sampaio, R. 2009 International Journal of Non-Linear Mechanics 44 (8), pp. 865-876

- Drill-string horizontal dynamics with uncertainty on the frictional force, Ritto, T.G., Escalante, M.R., Sampaio, R., Rosales, M.B. 2013 Journal of Sound and Vibration 332 (1), pp. 145-153

- Robust optimization of the rate of penetration of a drill-string using a stochastic nonlinear dynamical model Ritto, T.G., Soize, C., Sampaio, R. 2010 Computational Mechanics 45 (5), pp. 415-427

- Probabilistic model identification of the bit-rock-interaction-model uncertainties in nonlinear dynamics of a drill-string Ritto, T.G., Soize, C., Sampaio, R. 2010 Mechanics Research Communications 37 (6), pp. 584-589

- Probabilistic model identification of the bit-rock-interaction-model uncertainties in nonlinear dynamics of a drill-string Ritto, T.G., Soize, C., Sampaio, R. 2010 Mechanics Research Communications 37 (6), pp. 584-589

- Validation of a drill string dynamical model and torsional stability Ritto T.G., Aguiar R.R., Hbaieb S. 2017 Meccanica, accepted for publication