Understanding material fracture is paramount in the nuclear industry to ensure the structural integrity and long-term safety of critical components. Therefore, accurately simulating the onset of cracks and their propagation is essential.

Among several approaches to simulate the fracture of materials, the phase-field approaches have gain popularity in the last years. In recent developments the phase-field approaches have been extended to situations where both the mechanical response and the crack-driving variable evolve dynamically. In such formulations, the mechanical equilibrium is governed by an hyperbolic equations, while the phase-field variable itself can also follow an hyperbolic evolution law that captures inertia or rate-dependent effects in the damage process. Explicit schemes are attractive for dynamic fracture because they naturally accommodate wave propagation and avoid the repeated solution of large nonlinear systems. Yet, they are only conditionally stable, and the admissible time step is usually estimated through CFL-type conditions derived from simplified arguments. Some of our investigations have suggested that phase field equations conditions might be very unfavorable since its associated critical timestep can fall to zero. However, it is still unclear if breaking this condition is prohibitive, since some calculations have been performed by this way [1, 2].

The aim of this internship is to investigate these issues through a numerical study of the coupled hyperbolic system. The student will try to assess if classical stability bounds may become overly conservative or, find a way to overcome these rules if it is not.

To do so, the candidate will come on board the Manta project [3], which is the framework of the nextgen finite element software for computational mechanics at CEA, and the “Laboratoire d’Etudes de DYNamique” lab, which hosts some of CEA leading experts in structural dynamics for civil nuclear applications.

References

[1] David Kamensky, Georgios Moutsanidis, Yuri Bazilevs, Hyperbolic phase field modeling of brittle fracture: Part I—Theory and simulations, Journal of the Mechanics and Physics of Solids, Volume 121, 2018, Pages 81-98, https://doi.org/10.1016/j.jmps.2018.07.010.

[2] Lamia Mersel, Pascal Bouda, Jérémy Germain and Julien Réthoré. Dynamic damage modelling through phase-field approaches: assessment, critical analysis and comparison. Comptes Rendus. Mécanique, Volume 353 (2025), pp. 687-724. doi : https://doi.org/10.5802/crmeca.297

[3] Olivier Jamond, Nicolas Lelong et al. ‘MANTA‘ : un code HPC généraliste pour la simulation de problèmes complexes en mécanique. In CSMA 2022 15ème Colloque National en Calcul des Structures. https://hal.science/hal-03688160v1

Compétences recherchées:
Analyse numérique, mécanique, développement informatique (C++)

Formations/écoles cibles:
Grande école d'ingénieur, Master2 dans le domaine de la simulation numérique