Mathématiques numériques, Calcul intensif et Données

SFA - Sciences Fondamentales et Appliquées

BERNACKI Marc

Centre de Mise en Forme des Matériaux

01/10/2021

Jumeaux numériques, HPC, métallurgie computationnelle, réseaux d'interface, algorithmes ToRealMotion, algorithmes basés sur le maillage

Digital twins, HPC, Computational Metallurgy, Interface networks, Front tracking, ToRealMotion algorithms

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Context and goals of the PHD
The in-use properties and durability of metallic materials are strongly related to their microstructures, which are themselves inherited from the thermomechanical treatments. Hence, under-standing and predicting microstructure evolutions are nowadays a key to the competitiveness of industrial companies, with di-rect economic and societal benefits in all major economic sectors (aerospace, nuclear, renewable energy, and automotive industry).

Multiscale materials modeling, and more precisely simulations at the mesoscopic scale, constitute the most promising numeri-cal framework for the next decades of industrial simulations as it compromises between the versatility and robustness of physically-based models, computation times, and accuracy. The digimu con-sortium is dedicated to this topic at the service of major industrial companies.

In this context, the efficient and robust modeling of evolving in-terfaces like grain boundary networks is an active research topic, and numerous numerical frameworks exist [1]. In the context of hot metal forming and when large deformation of the calculation domain and the subsequent migration of grain boundary inter-faces are involved, a new promising, in terms of computational cost, 2D front tracking method called ToRealMotion algorithms [2,3] was recently developed.

This PhD will be firstly dedicated to developing a 3D ToReal-Motion algorithm. If the extension of the data structure will be quite natural, the 3D meshing/remeshing procedures/operators enabling to preserve valid data structure, a good quality of the finite element mesh while remaining frugal in terms of numerical cost remain to be invented.

Moreover, kinetics equations behind the interface networks migra-tion will be enriched to increase the number of modeled physical mechanisms. Finally, a supervised neural network-based remesh-ing strategy will also be developed to improve repetitive and non-optimal operations in the existing remeshing procedures.

The developments will be validated thanks to pre-existing ex-perimental and numerical data concerning the evolution of grain boundary interfaces during recrystallization and related phenom-ena for different materials. They will also be integrated in the DIGIMU® software.

The 3-year PhD will take place in CEMEF, an internationally-recognized research laboratory of MINES ParisTech located in Sophia-Antipolis, on the French Riviera. It offers a dynamic research environment, exhaustive training opportunities and a strong link with the industry. Annual gross salary: about 26kN. She/He will join the Metallurgy µStructure Rheology (MSR) research teams under the supervision of Prof. M. Bernacki and Dr. S. Florez in ”Numerical Mathematics, High Performance Computing and Data” doctoral speciality.

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Numerical Mathematics, High Performance Computing and Data

Diplôme: MSc ou MTech en mathématiques appliquées, avec un excellent dossier académique.
Compétences: Modélisation numérique, programmation, maîtrise de l'anglais, capacité à travailler au sein d'une équipe multidisciplinaire.

Degree: MSc or MTech in Applied Mathematics, with excellent academic record.
Skills: Numerical Modeling, programming, proficiency in English, ability to work within a multi-disciplinary team.

[1]A. Rollett, G. S. Rohrer, and J. Humphreys, Recrystallization and Related Annealing Phenomena. 3rd Edition, 2017.

[2]S. Florez, K. Alvarado, and M. Bernacki. A new front-tracking lagrangian model for the modeling of dynamic and post-dynamic recrystallization. Modelling and Simulation in Materials Science and Engineering, In press, 2021.

[3]S. Florez, K. Alvarado, D. Pino Muñoz and M. Bernacki. A novel highly e icient lagrangian model for massively multidomain simulation applied to microstructural evolutions. Computer Meth-ods in Applied Mechanics and Engineering, 367:113107, 2020.

Financement par une entreprise

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