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.

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.

Modelling and simulation of convective flows with a mixture approach

Fluid–structure interaction in mixtures: theory, numerical simulations and experiments

This PhD project is part of research on fluid–structure interactions (FSI) in complex media, particularly fluid mixtures involving multiple phases (liquid/liquid or liquid/gas) and/or suspended particles. The objective is to develop a thorough, multi-scale understanding of the coupled mechanisms between deformable structures (such as droplets, interfaces, or flexible walls) and the flows of complex mixtures, by combining theoretical modelling, advanced numerical simulations, and comparison with experimental data.

Chemical and mechanical properties of N-A-S-H aluminosilicates of geopolymer

Management of low- and medium-level nuclear waste relies primarily on cements, but their limitations with regard to certain types of waste (reactive metals, oil) require the exploration of new, more effective materials. Geopolymers, particularly those composed of hydrated sodium aluminosilicates (Na2O–Al2O3–SiO2–H2O, or N–A–S–H), appear to be a promising alternative thanks to their chemical compatibility with certain types of waste.
However, despite the growing interest in geopolymers, scientific obstacles remain: 1) The available thermodynamic data on N-A-S-H is still incomplete, making it difficult to predict their long-term stability via modeling, 2) The role of their atomic structure in regard to their reactivity remains unclear, and 3) The links between chemical composition (in terms of Si/Al ratio) and mechanical properties are not established, limiting the representativeness of the models created.
By combining experimentation and modeling in order to link atomic structure and properties, this thesis aims to obtain robust and novel data on the chemical and mechanical properties of N-A-S-H. The thesis is organized around three major objectives: 1) determining the impact of N-A-S-H composition on dissolution and establishing thermodynamic solubility constants, 2) characterizing their atomic structure (aluminols, silanols, and hydrated environments) using advanced NMR spectroscopy, and 3) linking their mechanical properties, measured by nanoindentation, to their structure and composition using molecular dynamics modeling.

Study of oxygen and hydrogen diffusion processes in pre- and post-transitional oxide layers formed on zirconium alloys

The corrosion mechanisms of zirconium alloys in pressurised water reactors are still a subject of debate more than half a century after the first research on this material. The literature reports two distinct mechanisms for the transport of diffusing species in oxide layers: one favours the molecular diffusion of oxygen and hydrogen through interconnected nanopore channels during the pre-transient regime, while the other favours diffusion via short circuits (grain boundaries, etc.) in the oxide layer. In the latter case, the oxide layer is considered to be relatively homogeneous and impermeable to the oxidising medium, in this case the water in the primary circuit. On the other hand, the first interpretation is based on the principle that there is a layer that is permeable to the medium due to an interconnected network of nanopores, even during the pre-transient regime, with the density of percolated nanopores increasing over time.
Technically speaking, how can we decide between these two divergent interpretations in terms of the diffusion mechanism, which consequently leads to different solutions for protection against degradation? What is the reaction mechanism that ultimately leads to the hydration of Zr alloys and their oxidation?
To address this challenge, we will explore diffusion processes by studying the dissociation-recombination rates of molecular species at different temperatures in equi-isotopic gas mixtures such as H2/D2, 18O2/16O2, H218O/D216O, H218O/D2, etc., using an experimental device equipped with a mass spectrometer that tracks the molecular species of interest in real time.

Development and Calibration of an Hyperbolic Phase-Field Model for Explicit Dynamic Fracture Simulation

The numerical simulation of the mechanical behavior of structures subjected to dynamic loads is a major challenge in the design and safety assessment of industrial systems. In the nuclear industry, this issue is particularly critical for the analysis of severe accident scenarios in Pressurized Water Reactors (PWRs) such as the Loss of Coolant Accident (LOCA), during which the rapid depressurization of the primary circuit can lead to pipe rupture. Developing physically representative models and robust, efficient numerical methods to simulate such phenomena with high fidelity remains an active area of research.

Among the existing non-local approaches, phase-field methods have emerged as a interesting framework for simulating crack initiation and propagation. However, most current studies are limited to quasi-static or low-rate dynamic problems, where wave propagation effects can be neglected. In contrast, high-rate dynamic regimes - relevant to accidental loads - require explicit time integration schemes for the mechanical equations, which are sensitive to the stability condition. The classical elliptic formulation of the damage evolution equation is therefore not ideally suited to this context. To address these limitations, recent works have proposed and assessed hyperbolic phase-field formulations, which are naturally more compatible with explicit dynamics and allow better control of crack propagation kinetics.

The objective of this PhD thesis is to advance this emerging modeling strategy through three main research directions:
- Extend the theoretical framework of the hyperbolic phase-field formulation for damage within the context of generalized standard materials, which is suitable for ductile fracture;
- Propose solutions to the negative impact of damage evolution on the critical time step;
- Rely on an dynamic fracture experimental test campaign to calibrate simulations, with a focus on the identification of damage-related parameters

This research is to be conducted in collaboration between CEA Paris-Saclay, ONERA Lille, and Sorbonne Université, with CEA as the main host institution.

Dislocation glide in body-centered-cubic high-entropy alloys

High entropy alloys are single-phase multi-component solid solutions, all elements being present in high concentrations. This class of materials has significant improvements in mechanical properties over "conventional" alloys, particularly their high strength at high temperature. It is commonly accepted that good mechanical performance comes from the interactions of dislocations with the alloying elements and that at high temperature interstitial impurities or interstitial doping, such as oxygen, carbon or nitrogen, play a preponderant role. The study of plasticity in concentrated alloys with a body-centered cubic crystal structure in the high temperature range therefore constitutes the objective of this PhD thesis. The associated technological challenges are important, these alloys being promising structural materials, notably for nuclear applications where operating temperatures above room temperature are targeted.
This work aims to understand and model the physical mechanisms controlling the mechanical strength of these alloys at high temperature, by considering different concentrated alloys of increasing complexity and by using atomistic simulations, in particular ab initio electronic structure calculations. We will first focus on the binary alloy MoNb before extending to the ternary alloys MoNbTi and MoNbTa and studying the impact of oxygen impurities on plastic behavior of these alloys. We will model the dislocation cores and analyze their interaction with interstitial and substitutional elements in order to determine the energy barriers controlling their mobility. Based on these ab initio results, we will develop strengthening models notably allowing us to predict the yield strength as a function of temperature and alloy composition.
This work will be carried out within the framework of the DisMecHTRA project funded by the French National Research Agency, allowing in particular to compare our strengthening models with the data from the experiments which are planned in the project (mechanical tests and transmission electron microscopy), and which will be carried out by the other partners (CNRS Toulouse and Thiais). The PhD thesis, hosted at CEA Saclay, will be co-supervised by a team from CEA Saclay and MatéIS (CNRS Lyon).