Hybrid High-Order methods for Phase-field modeling of fracture propagation

In this thesis, we are interested in the modeling of fracture propagation. Historical formulations have two types of drawbacks. In the case of local damage models, the limitations come from the fact that the results depend on the computational mesh. On the other hand, when each fracture is modeled independently, the limiting factor is the computational cost. The phase-field fracture modeling method has the advantage of being a continuous method that integrates naturally with Continuous Media Mechanics and the associated numerical tools. Moreover, this method, which is similar to a non-local damage model, allows to describe the fracture initiation as well as their propagation in a mesh independent way and with a great robustness. On the numerical level, we are interested in the developments of Hybrid High-Order (HHO) methods. These methods have many advantages: (i) support of arbitrary approximation orders; (ii) use of polyhedral meshes with possibly non-conforming interfaces; (iii) robustness with respect to physical parameters (elastic incompressibility, dominant advection...); (iv) low computational cost thanks to static condensation which eliminates the unknowns carried by the cells while keeping a compact stencil; and (v) local conservation of the fluxes on each cell of the mesh.
The objective of this thesis is to develop a variational framework for phase field modeling of fracture using a precise and efficient HHO method. The targeted technical achievements are the development and evaluation of an HHO method for the treatment of fracture propagation by phase field that will support all types of meshes, the implementation of this method in a mechanical calculation code, and the study of the possible extension to other coupled models.

Keywords: Phase-field modeling, Hybrid High-Order methods, fracture propagation.

• Academic supervisor    Professor DI PIETRO  Daniele Antonio, Institut Montpelliérain Alexander Grothendieck, Université de Montpellier, ORCID   (0000-0003-0959-8830)
• Doctoral School    ED 166 I2S (Information technology Structures Systems) , https://www.adum.fr/as/ed/I2S/home.pl 
• IFPEN supervisor     Dr., YOUSEF Soleiman , applied mathematics, Soleiman.yousef@ifpen.fr  , ORCID  (0000-0003-2458-6264)
• PhD location    IFP Energies nouvelles, Rueil-Malmaison, France
• Duration and start date    3 years, starting in fourth quarter 2022
• Employer    IFP Energies nouvelles, Rueil-Malmaison, France
• Academic requirements    University Master degree in applied mathematics 
• Language requirements    Fluency in English, willingness to learn French 
• Other requirements     C++, LaTeX