Context : Understanding the behavior of metals at high deformation rate [4] (between 104 and 108 s-1) is a huge scientific and technologic challenge. This irreversible (plastic) deformation is caused by linear defects in the crystal lattice : these are called dislocations, which interact via a long-range elastic field and contacts.
Nowadays, the behavior of metals at high deformation rate can only be studied experimentally by laser shocks. Thus, simulation is of paramount importance. Two approaches can be used : molecular dynamics and elastodynamics simulations. This thesis follows the second approache, based on our recent works [1, 2], thanks to which the first complete numerical simulations of the Peierls-Nabarro Equation (PND) [5] was performed. The latter equation describes phenomena at the scale of the dislocation.
PND is a nonlinear integrodifferential equation, with two main difficulties : the non-locality in time and space of the involved operators. We simulated it thanks to an efficient numerical strategy [1] based on [6]. Nevertheless, the current implementation is limited to one CPU –thus forbidding thorough investigations on large-scale systems and on long-term behaviors.

Thesis subject : There are two main objectives :
- Numerics. Based on the algorithmic method of [1], implement a HPC solver (High Performance Computing) for the PND equation, parallel in time and space, with distributed memory.
- Physics. Using the solver developped, investigate crucial points regarding the phenomenology of dislocations in dynamic regime. For exploiting the numerical results, advanced data-processing techniques will be employed, potentially enhanced by resorting to AI techniques.
Depending on the time remaining, the solver might be employed for investigating dynamic fractures [3].

Candidate profile : The proposed subject is multidisciplinary, between scientific computing, mechanics, and data-processing. The candidate shall have a solid background in scientific computing applied to Partial Differential Equations. Mastering C++ with OpenMP and MPI is recommended. Moreover, interest and knowledge in physics –especially continuum mechanics- will be a plus.
The PhD will take place at the CEA/DES/IRESNE/DEC in Cadarache (France), with regular journeys to Paris, for collaboration with CEA/DAM and CEA/DRF.

[1] Pellegrini, Josien, Shock-driven motion and self-organization of dislocations in the dynamical Peierls model, submitted.
[2] Josien, Etude mathématique et numérique de quelques modèles multi-échelles issus de la mécanique des matériaux. Thèse. (2018).
[3] Geubelle, Rice. J. of the Mech. and Phys. of Sol., 43(11), 1791-1824. (1995).
[4] Remington et coll., Metall. Mat. Trans. A 35, 2587 (2004).
[5] Pellegrini, Phys. Rev. B, 81, 2, 024101, (2010).
[6] Lubich & Schädle. SIAM J. on Sci. Comp. 24(1), 161-182. (2002).