Robust and efficient simulation of brittle cracking in nuclear fuels is essential to describe their behaviour in normal and incidental situations. Recent work has highlighted the benefits of using a regularised gradient damage approach combined with the Hybrid High Order (HHO) method, which belongs to the family of discontinuous Galerkin methods (PhD thesis by D. Siedel, 2023). The practical use of these models is hampered by very small mesh sizes and their inability to handle large relative movements of the crack lips.

This subject proposes to exploit the specific capabilities of the HHO method to deal with these two difficulties:

- HHO methods greatly simplify the development of adaptive refinement algorithms.
- HHO methods can be used to simplify the damage/rupture transition, which involves inserting surfaces at the crack propagation locations predicted by the gradient damage model. These surfaces can then have arbitrary relative movements.

This thesis aims at introducing those tools in the new-generation solver Manta, developed at CEA/DES.

The thesis will be carried out at the IRESNE Institute (CEA Cadarache, in south-east France), in collaboration with teams from CEA Saclay, the Centre des Matériaux des Mines de Paris and Onera.

Robust and efficient simulation of brittle cracking in nuclear fuels is essential to describe their behaviour in normal and incidental situations.

Recent work has highlighted the benefits of using a regularised gradient damage approach combined with the Hybrid High Order (HHO) method, which belongs to the family of discontinuous Galerkin methods (PhD thesis by D. Siedel, 2023). The practical use of these models is hampered by very small mesh sizes and their inability to handle large relative movements of the crack lips.This PhD topic proposes to exploit the specific capabilities of the HHO method to deal with these two difficulties:
- HHO methods greatly simplify the development of adaptive refinement algorithms,
- HHO methods can be used to simplify the damage/rupture transition, which involves inserting surfaces at the crack propagation locations predicted by the gradient damage model. These surfaces can then have arbitrary relative movements.

This thesis aims at introducing those tools in the new-generation solver Manta, developed at CEA/DES. The thesis will be carried out at CEA Cadarache in south-east France, in collaboration with teams from CEA Saclay, the Centre des Matériaux des Mines de Paris and Onera. As a first step, the PhD student will have to extend the Manta solver and verify its ability to handle brittle cracking with a damage gradient model using the HHO approach. This will be verified by cross-comparison with the A-Set code. Secondly, adaptative mesh refinement with HHO will be addressed. Finally, the insertion of cracks along the paths predicted by the damage gradient model will be carried out in collaboration with Onera.

The thesis work will be presented at national and international conferences and in peer-reviewed journals.