Defense of thesis "Coupled discrete/continuous adaptive approach for shaping".

Summary

The development of forming processes generally involves numerical simulation, and in particular the Finite Element Method, in order to detect, among other things, possible cracking risks and their propagation, both in the forged part and the tooling.

The classical finite element method, as well as specific variants applied to crack modeling, present limitations when it comes to simulating multi-cracking problems due to material, geometric and contact non-linearities. The very nature of a crack - a discontinuity - contradicts the Continuum Mechanics framework. The Discrete Element Method, on the other hand, stands out for its ability to deal effectively with discontinuities. It is used to model fragile granular or cohesive media. However, this approach also has its limitations, particularly with regard to the consideration of material nonlinearities and computation times, which can require large computing capacities to simulate complex problems.

The aim of this thesis work is to develop a dynamic remeshing method, enabling the user to switch from one method to the other in order to benefit from the advantages of both approaches. This objective will be achieved in three stages. Firstly, a non-overlapping coupling method, based on the Lagrange multiplier method, has been developed. This method aims to ensure a velocity compatibility condition between the discrete element and finite element subdomains, in order to ensure communication of physical quantities between the two subdomains.

The second step is to ensure the continuity of physical quantities within the same zone during its remeshing. This is achieved using polynomial interpolation of displacements. This approach makes it possible to determine the fields within the discrete elements at the moment of transition between a finite element subdomain and a discrete element subdomain. To validate these two approaches, test cases were set up. Finally, a method was developed to automate the management of coupling and field transfer operations. This approach involves the use of a remeshing technique that automatically generates discrete subdomains from the geometry of the finite element set to be replaced. The dynamic remeshing method implemented in this thesis work is applied to a Kalthoff-type test case and validated by comparison of the crack propagation angle with experiments from the bibliography.

Jury

Mr Carl Labergère, Professeur des Universités, LASMIS, UTT (Rapporteur)
Mr Jérémie Girardot, Ingénieur-Chercheur HDR, I2M, ENSAM (Rapporteur)
Mrs. Elisabeth Massoni, Director of Research, CEMEF, Mines Paris - PSL (Examiner)
M. Laurent Dubar, Professeur des Universités, LAMIH UMR CNRS 8201, UPHF (Thesis supervisor)
M. Nicolas Leconte, Chargé de recherche HDR, ONERA  (Thesis supervisor)
M. Cédric Hubert, Maître de Conférences, LAMIH UMR CNRS 8201, UPHF (Supervisor)
Mr Francois Demilly, Sales and Technical Director, MG-VALDUNES (Guest)
Mr Stéphane Salengro, Engineer,  MG-VALDUNES (Guest)

Key words

Finite Element Method, Discrete Element Method, Coupling, Field transfer, Remeshing, Cracking
.