Reduction of reinforcement in reinforced concrete structures through nonlinear calculations and topological and evolutionary optimizations

Reinforcing steel plays a major role in the behavior of reinforced concrete structures. Nevertheless, significant conservatisms may sometimes be imposed by design codes, raising questions about the feasibility of construction or the viability of the structure (economic, environmental, etc.). It is within this context that the doctoral research takes place. Building on recent developments, the work aims to propose an innovative design approach relying on the use of nonlinear finite element calculations, combined with topological optimization algorithms (defining reinforcement directions and bar cross-sections) and evolutionary optimization algorithms (determining the placement of bars with fixed cross-sections).
The method should, through an iterative process, yield solutions that meet an optimal design configuration. Considering the multiple, potentially conflicting objectives to minimize (such as cost, feasibility, strength, and carbon footprint), the approach will guide the configuration of input parameters based on an analysis of the relevant output results.
Applying the method to complex, practice-based case studies (for example, beam-column junctions) will demonstrate its relevance compared with more conventional design methods. By the end of the thesis, the doctoral candidate will have developed advanced skills in the use and development of state-of-the-art tools, ranging from nonlinear finite element simulation to modern optimization techniques based on artificial intelligence.

Experimental study and numerical simulation of deformation mechanisms and mechanical behavior of zirconium alloys after irradiation

The cladding of nuclear fuel rods used in Pressurized Water Reactor, made of zirconium alloys, is the first barrier for the confinement of radioactive nuclei. In-reactor, the cladding is subjected to radiation damage resulting in a change of its mechanical properties. After in-reactor use, the fuel rods are transported and stored. During these various steps, the radiation damage is partially annealed, leading to another evolution of the material properties. All these evolutions are still not well understood.
The objective of this PhD work is to better understand the deformation mechanisms and the mechanical behavior of zirconium alloys after irradiation, and after a partial annealing of the radiation damage. This will help to better predict the behavior of the cladding tube after use and thus guaranty the confinement of radioactive nuclei.
In order to achieve this goal, original experimental methods and advanced numerical simulations will be used. Ion irradiations will be conducted in order to reproduce the radiation damage. Heat treatments will then be done on the specimens after irradiation. Small tensile samples will be strained in situ, after annealing, inside a transmission electron microscope, at room temperature or at high temperature. Deformation mechanisms observed at nanometer scale and in real time will be simulated using dislocation dynamics, at the same time and space scales. Large scale dislocation dynamics simulations will then be conducted in order to deduce the single-crystal behavior of the material. In parallel with this study at the nanometric scale, a study will also be conducted at the micrometric scale. Nanoindentation and micropillar compression tests will be performed to assess the mechanical behavior after irradiation and annealing. The results of mechanical tests will be compared with large-scale dislocation dynamics numerical simulations.
This study will allow a better understanding of the special behavior of zirconium alloys after irradiation and annealing and then help to develop physically based predictive models. In a future prospect, this work will contribute to improve the safety during transport and storage of spent nuclear fuel.

High-Fidelity Monte Carlo Simulations of Neutron Noise in Nuclear Power Reactors

Operating nuclear reactors are subject to a variety of perturbations. These can include vibrations of the fuel pins and fuel assemblies due to fluid-structure interactions with the moderator, or even vibrations of the core barrel, baffle, and pressure vessel. All of these perturbations can lead to small periodic fluctuations in the reactor power about the stable average power level. These power fluctuations are referred to as “neutron noise”. Being able to simulate different types of in-core perturbations allows reactor designers and operators to predict how the neutron flux could behave in the presence of such perturbations. In recent years, many different research groups have worked to develop computational models to simulate these sources of neutron noise, and their resulting effects on the neutron flux in the reactor. The primary objective of this PhD thesis will be to bring Monte Carlo neutron noise simulations to the scale of real-world industry calculations of nuclear reactor cores, with a high-fidelity continuous-energy physics representation. As part of this process, the student will add novel neutron noise simulation capabilities to TRIPOLI-5, the next-generation production Monte Carlo particle-transport code jointly developed by CEA and ASNR, with the support of EDF.

Fluid-structure interaction in a network of slender solids in a confined environment

As part of its study of progressive deformations in fuel assemblies within PWR cores, the CEA has developed two simulation tools. The first, Phorcys [1], calculates the flow of coolant in and around slightly deformed assemblies using a network of parametric pressure drops, then deduces the fluid forces acting on the structures. The second, DACC [2], uses finite element simulation to analyze thermomechanical behavior under irradiation and the interaction between assemblies during power cycles. Finally, fluid-structure interaction is analyzed using numerical coupling of these two tools, within which uncertainties can be propagated and analyzed [3].
The nuclear revival program (SMR, 4th generation reactors, PN, etc.) is providing new technologies and new core and fuel assembly topologies that need to be analyzed in terms of the risks associated with quasi-static deformations of core assemblies. With a view to both capitalizing on and extending the possibilities of simulation, the aim is to enable these two tools to handle the flow and deformation of slender structures in a more generic way in order to cover a wide range of nuclear technologies efficiently and quickly.
To do this, it will be necessary to identify, classify, and then model in a reduced but predictive manner the main flow structures that may occur within a fluid volume cluttered with slender structures with a large exchange surface area. The complete hydraulic model of the core will thus be created by concatenating elementary models that comply with strict interfacing conditions. A method for analyzing the overall flow obtained will then enable the quantification of the force field contributing to the deformations. A similar logic of classification and scaling would also be implemented with regard to the evaluation of reversible and irreversible deformations of a slender structure subjected to external stresses and severe irradiation. One difficulty is that the fine topology of a fuel assembly can exhibit nonlinearities at small scales that propagate in part to the macroscopic scale. Ultimately, a robust, cost-effective partitioned coupling will have to be implemented between the coolant flow and these individual structures, which deform and interact in a constrained environment.
The modeling framework thus constructed will make it possible to study the progressive deformations of assemblies and the associated risks for a wide range of nuclear reactor technologies.

Preconditioning of iterative schemes for the mixed finite element solution of an eigenvalue problem applied to neutronics

Neutronics is the study of the behavior of neutrons in matter and the reactions they induce, particularly the generation of power through the fission of heavy nuclei. Modeling the steady-state neutron flux in a reactor core relies on solving a generalized eigenvalue problem of the form:
Find (phi, keff) such that A phi=1/keff B phi and keff is the eigenvalue with the largest magnitude, where A is the disappearance matrix which is assumed invertible, B represents the production matrix, phi denotes the neutron flux, and keff is called the multiplication factor.

The neutronics code APOLLO3® is a joint project of CEA, Framatome, and EDF for the development of a next-generation code for reactor core physics to meet both R&D and industrial application needs [4].
The MINOS solver [2] is developed within the framework of the APOLLO3® project. This solver is based on the mixed finite element discretization of the neutron diffusion model or the simplified transport model. The strategy for solving the aforementioned generalized eigenvalue problem is iterative; it involves applying the inverse power method [6].

The convergence speed of this inverse power method algorithm depends on the spectral gap. In the context of large cores such as the EPR reactor, it is observed that the spectral gap is close to 1, which degrades the convergence of the inverse power method algorithm. It is necessary to apply acceleration techniques to reduce the number of iterations [7]. In neutron transport, the preconditioning called Diffusion Synthetic Acceleration is very popular for the so-called inner iteration [1] but has also recently been applied to the so-called outer iteration [3]. A variant of this method was introduced in [5] for solving a source problem. It is theoretically shown that this variant converges in all physical regimes.

[1] M. L. Adams, E. W. Larsen, Fast iterative methods for discrete-ordinates particle transport calculations, Progress in Nuclear Energy, Volume 40, Issue 1, 2002.

[2] A.-M. Baudron and J.-J. Lautard. MINOS: a simplified PN solver for core calculation. Nuclear Science and Engineering, volume 155(2), pp. 250–263 (2007).

[3] A. Calloo, R. Le Tellier, D. Couyras, Anderson acceleration and linear diffusion for accelerating the k-eigenvalue problem for the transport equation, Annals of Nuclear Energy, Volume 180, 2023.

[4] P. Mosca, L. Bourhrara, A. Calloo, A. Gammicchia, F. Goubioud, L. Mao, F. Madiot, F. Malouch, E. Masiello, F. Moreau, S. Santandrea, D. Sciannandrone, I. Zmijarevic, E. Y. Garcia-Cervantes, G. Valocchi, J. F. Vidal, F. Damian, P. Laurent, A. Willien, A. Brighenti, L. Graziano, and B. Vezzoni. APOLLO3®: Overview of the New Code Capabilities for Reactor Physics Analysis. Nuclear Science and Engineering, 2024.

[5] O. Palii, M. Schlottbom, On a convergent DSA preconditioned source iteration for a DGFEM method for radiative transfer, Computers & Mathematics with Applications, Volume 79, Issue 12, 2020.

[6] Y. Saad. Numerical methods for large eigenvalue problems: revised edition. Society for Industrial and Applied Mathematics, 2011.

[7] J. Willert, H. Park, and D. A. Knoll. A comparison of acceleration methods for solving the neutron transport k-eigenvalue problem. Journal of Computational Physics, 2014, vol. 274, p. 681-694.

Study of the behaviour of mixed oxide fuels with degrade isotopy at the beginning of life.

France has decided to adopt a 'closed' nuclear fuel cycle. This involves processing spent fuel to recover valuable materials such as uranium and plutonium, while other compounds such as fission products and minor actinides constitute final waste. UO2 fuel irradiated in pressurised water reactors (PWRs) is currently reprocessed to produce plutonium (PuO2), which is then reused in the form of mixed oxide (MOX) fuel. This fuel is then irradiated in PWRs, a process known as plutonium monorecycling. The CEA is currently studying the multi-recycling of materials using fuels containing Pu from the processing of spent MOX assemblies. However, this multi-recycled plutonium contains a higher proportion of highly alpha-active isotopes (Pu238, Pu240 and Pu241/Am241), resulting in more severe alpha self-irradiation than current MOX fuels experience [1]. This exacerbates certain physical phenomena [2-5], such as fuel swelling due to helium precipitation and the creation of crystal defects and decreased thermal conductivity [6-8], which can alter its behaviour in the reactor.
The proposed thesis will study the impact of these phenomena on the behaviour of MOX fuels at the beginning of the irradiation, using a combination of experimentation and modelling. Heat treatments will be employed to analyse the mechanisms of crystal defect healing and helium behaviour. Various experimental techniques will be employed to characterise the structure and microstructure (X-ray diffraction, scanning electron microscopy (SEM), Raman spectroscopy and microprobe analysis), defect densities (transmission electron microscopy (TEM)), helium release (KEMS), thermal gradient reproduction (CLASH laser) and thermal conductivity (LAF laser). The results will inform simulations modelling the microstructure and thermal properties.
This cross-disciplinary study will improve our understanding of the phenomena involved in the initial power-up of fuels damaged by alpha self-irradiation, particularly the impact of helium produced by decay.

You will be based at the Multi-Fuel Design and Irradiation Laboratory (LECIM) within the Research Institute for Nuclear Systems for Low-Carbon Energy Production at CEA/Cadarache. For the experimental part of the project, you will collaborate with the Chemical Analysis and Materials Characterisation Laboratory (LMAT) at CEA/Marcoule and the European Research Centre (JRC) in Karlsruhe. You will have the opportunity to publish your results through scientific publications and conference presentations. This role offers the chance to develop your expertise in a variety of techniques that can be applied across multiple fields of materials science and engineering.

[1]O. Kahraman, thésis, 2023.[2]M. Kato et al., J Nucl Mater, 393 (2009) 134–140.[3]L. Cognini et al., Nuclear Engineering and Design 340 (2018) 240–244.[4] T. Wiss et al., Journal of Materials Research 30 (2015) 1544–1554.[5]D. Staicu et al., J Nucl Mater 397 (2010) 8–18.[6] T. Wiss et al.,Front. Nucl. Eng. 4 (2025) 1495360.[7]E.P. Wigner, J. Appl. Phys. 17 (1946) 857–863.[8]D. Staicu et al., Nuclear Materials and Energy 3–4 (2015) 6–11.

From optimal control in NMR at 11.7 Tesla to precision imaging of the human brain in vivo

Parallel simulation and adaptive mesh refinement for 3D solids mechanics problems

The challenge of this PhD thesis is to implement adaptive mesh refinement methods for non-linear 3D solids mechanics adapted to parallel computers.

This research topic is proposed as part of the NumPEx (Digital for Exascale) Priority Research Programs and Equipment (PEPR). It is part of the Exa-MA (Methods and Algorithms for Exascale) Targeted Project. The PhD will take place at CEA Cadarache, within the Institute for Research on Nuclear Energy Systems for Low-Carbon Energy Production (IRESNE), as part of the PLEIADES software platform development team, which specializes in fuel behavior simulation and multi-scale numerical methods.

In finite element simulation, adaptive mesh refinement (AMR) has become an essential tool for performing accurate calculations with a controlled number of unknowns. The phenomena to be taken into account, particularly in solids mechanics, are often complex and non-linear: contact between deformable solids, viscoplastic behaviour, cracking, etc. Furthermore, these phenomena require intrinsically 3D modelling. Thus, the number of unknowns to be taken into account requires the use of parallel solvers. One of the current computational challenges is therefore to combine adaptive mesh refinement methods and nonlinear solid mechanics for deployment on parallel computers.

The first research topic of this PhD thesis concerns the development of a local mesh refinement method (of block-structured type) for non-linear mechanics, with dynamic mesh adaptation. We will therefore focus on projection operators to obtain an accurate dynamic AMR solution during the evolution of refined areas.

The other area of research will focus on the effective treatment of contact between deformable solids in a parallel environment. This will involve extending previous work, which was limited to matching contact meshes, to the case of arbitrary contact geometries (node-to-surface algorithm).

The preferred development environment will be the MFEM tool. Finite element management and dynamic re-evaluation of adaptive meshes require assessing (and probably improving) the efficiency of the data structures involved. Large 3D calculations will be performed on national supercomputers using thousands of computing cores.
his will ensure that the solutions implemented can be scaled up to tens of thousands of cores.

Modelling and simulation of convective flows with a mixture approach

Modeling of a non-equilibrium dispersed phase and its fragmentation

In the context of the sustainable use of nuclear energy to produce carbon-free electricity, fourth-generation reactors, also known as "fast neutron" reactors, are necessary to close the fuel cycle.
This thesis falls within the framework of safety studies associated with such sodium-cooled reactors, and more particularly the hypothetical situation of a molten core relocating by gravity towards the core catcher at the bottom of the reactor vessel. A jet of corium (mixture of molten fuel and structural elements of the core) then interacts violently with the coolant, inducing, among other things, the fragmentation of the corium jet into droplets coupled with film boiling of the coolant. Characteristics of the resulting dispersed phase of corium and its fragmentation are crucial for studying the risk of runaway and steam explosion.
The aim of this thesis is to model a dispersed phase and its fragmentation in a surrounding fluid, using an approach that is both efficient and able to account to the scale variations and thermal imbalances between the droplets and the carrier phase. The method considered to meet these objectives is the method of moments, which derives from a kinetic model. It requires adequate closure and numerical schemes that satisfy non-standard constraints, while offering, in return, a crucial cost/accuracy compromise in the context studied. The advancements will be a priori implemented in the CFD software SCONE, built on the CEA's open-source TRUST platform.
The main work location will be based at the LMAG (Laboratory of Severe Accidents Modeling) at the IRESNE Institute of CEA Cadarache. Part of the work will also be carried out at the EM2C Laboratory (Molecular and Macroscopic Energetics, Combustion) – CNRS/CentraleSupélec in Paris.
The future PhD will work in a scientific dynamic environment and will acquire skills enabling to aspire to academic and industrial R&D positions.

Keywords : Dispersed Phase, Fragmentation, Kinetic, Method of Moments, Multiphase, Numerical methods, Severe Accidents.