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.
Shape optimization for innovation in nuclear fuels
Nuclear industry is currently developping enhanced Accident Tolerant Fuels" (ATF) [1]. These fuels feature enhanced physical properties; in particular, thanks to the addition of thermal conductors inside the fuel, they tend to be colder in standard as well as in accident conditions.
This thesis aims at developping numerical strategies (that will be programmed into a semi-industrial code) in order to propose new "shapes" of fuels (by "shape", we mean internal structures or microstructures), and to optimze already existing concepts. It will take advantage of recent numerical and mathematical techniques related to the so-called "shape optimization" [2]. Based on the previous work [3], more and more complex physical phenomena will be taken into account : first, thermal conductivity and mechanical behaviour in standard conditions, then gaz diffusion... Discussion with experts and modelization will be necessay in order to reformulate these physical behaviours into forms amenable to numerical simulation.
This thesis will take place at the CEA center of Cadarache in the fuel research department, in a laboratory devoted to modelling and numerical methods. The latter is affiliated to the Institute IRESNE for the research low-carbon energy production.
This project will be in collaboration with Nice University offering so an environment both academic and connected to application.
It also takes part in the PEPR DIADEM called Fast-in-Fuel, a national research project.
We search for excellent candidates with a solid background in scientific computing, analysis and numerical analysis of partial differential equations, as well as in optimization. Skills in physics (mechanics and thermics) will also be considered. The proposed subject aims at a concrete application at the intersection of various scientific fields, and it is largely exploratory. Hence, curiosity and creativity will also be highly appreciated.
[1] Review of accident tolerant fuel concepts with implications to severe accident progression and radiological releases, 2020.
[2] G. Allaire. Shape optimization by the homogenization method, volume 146 of Applied Mathematical Sciences. Springer-Verlag, New York, 2002.
[3] T. Devictor. PhD Manuscript, 2025 (in preparation)
Constrained geometric optimization of immersed boundaries for thermal-hydraulic simulations of turbulent flow in a finite-volume approach
The technical issue underpinning this thesis topic is the mitigation of the consequences of a loss of primary coolant accident in a pressurized water reactor with loops. It is of the utmost importance to minimize the flow of water leaving the vessel and to manage the available cold water reserves for safety injections as effectively as possible, in order to prevent or delay core flooding, overheating, and possible core degradation. To this end, the use of passive devices operating on the principle of hydraulic diodes, such as vessel flow limiters or advanced accumulators, is being considered. The subject of this thesis is the geometric optimization of this type of device, described by an immersed boundary, in order to maximize its service efficiency.
Several recent theses have shown how to introduce the Penalized Direct Forcing (PDF) immersed boundary method into the TRUST/TrioCFD software, under various spatial discretizations and for laminar and turbulent regimes. Similarly, they have ruled on the possibilities of deterministic geometric optimization in the finite-element context during simulations, based on the use of the PDF method.
After a bibliographic study of this kind of method, we will focus on the possibilities of implementation in finite volume discretization, the consideration of constraints, and the comparison to reference calculations. The latter will be carried out on academic and industrial configurations (accumulators and flow limiters).
The doctoral student will work in a R&D unit on innovative nuclear system within the IRESNE Institute (CEA Cadarache. He will develop skills in fluid mechanics and numerical methods.
Experimental Investigation and DEM Simulation of Actinide Powder Segregation During Transfer Processes
The fabrication of nuclear fuels based on actinide oxides (UO2, PuO2) involves numerous powder-handling operations, during which segregation phenomena may occur. These phenomena—arising from differences in particle size, shape, density, or surface condition—directly affect the homogeneity of the mixtures and, consequently, the quality and consistency of the resulting fuel pellets. Controlling these effects is therefore a major industrial challenge to ensure both process robustness and final product conformity.
This PhD project aims to deepen the understanding of the mechanisms driving powder de-mixing of UO2 during transfer stages, particularly during vibratory conveyor transport and gravitational discharge. The main scientific objective is to establish the relationship between the physical and rheological properties of the powders, the process operating conditions, and the intensity of the observed segregation phenomena. The work will combine experimental studies and numerical simulations using the Discrete Element Method (DEM) to identify the material and process parameters influencing segregation. Experimental setups will be developed to characterize the powders and quantify the degree of de-mixing, while simulations will serve to validate and extrapolate the experimental observations.
Conducted at CEA Cadarache, within the Uranium Fuel Laboratory (LCU) of the Institute for Research on Nuclear Systems for Low-Carbon Energy Production (IRESNE), and in collaboration with the TIMR laboratory at UTC, this project will provide recommendations to limit segregation during industrial operations and improve the prediction of segregation tendencies in powder mixtures, particularly in cohesive actinide powders.
The PhD candidate will disseminate their findings through publications and conference presentations. They will also have the opportunity to learn and refine several transferable techniques applicable to a wide range of materials science and engineering contexts.In particular, the issues related to the physics of granular materials, which form the core of this thesis, are of significant industrial relevance and are shared by many other sectors handling powders, such as the pharmaceutical, food processing, and powder metallurgy industries.
Development of machine learning algorithms to improve image acquisition and processing in radiological imaging
The Nuclear Measurements Laboratory at the LNPA (Laboratory for the Study of Digital Technologies and Advanced Processes) in Marcoule consists of a team specializing in nuclear measurements in the field. Its activities are divided between developing measurement systems and providing technical expertise to CEA facilities and external partners (ORANO, EDF, IAEA).
The LNPA has been developing and using radiological imagers (gamma and alpha) for several years. Some of the developments have resulted in industrial products, while other imagers are still being developed and improved. Alpha imaging, in particular, is a process that allows alpha contamination zones to be detected remotely. Locating the alpha source is an important step in glove boxes, whether for a cleanup and dismantling project, for maintenance during operation, or for the radiation protection of workers. The alpha camera is the tool that makes alpha mapping accessible remotely and from outside glove boxes.
The objective of the thesis is to develop and implement mathematical prediction and denoising solutions to improve the acquisition and post-processing of radiological images, and in particular alpha camera images.
Two main areas of research will be explored in depth:
- The development of real-time or post-processing image denoising algorithms
- The development of predictive algorithms to generate high-statistics images based on samples of real images.
To do this, an experimental and simulation database will be established to feed the AI algorithms.
These two areas of research will be brought to fruition through the creation of a prototype imager incorporating machine learning capabilities and an image acquisition and processing interface, which will be used in an experimental implementation.
Through this thesis, students will gain solid knowledge of nuclear measurements, radiation/matter interaction, and scientific image processing, and will develop a clear understanding of radiological requirements in the context of remediation/decommissioning projects.
Nucleate boiling within porous deposits: study of the coupling between coolant composition and capillary vaporization
In the search of the optimal combination of low-carbon energy sources to address the challenge of climate change, nuclear energy plays a crucial role alongside intermittent renewable energies. In this context, the performance and safety of Pressurized Water Reactors (PWRs), which make up the French nuclear fleet, remain an active and high-value research area.
In these reactors, a subcooled nucleate boiling regime can occur, particularly when the local temperature of the coolant exceeds its saturation temperature. This wall boiling promotes the formation of porous deposits of metallic oxides. Within the porosities of these deposits, gas nuclei can be trapped and lead to the onset of nucleate boiling on these surfaces. The vapor formed through a wick boiling or capillary vaporization mechanism then escapes through the chimneys of the deposit. The chemistry of the coolant affects not only the thermodynamic properties of the fluid (such as saturation temperature and latent heat) but, more importantly, its interfacial properties (surface tension and solid/liquid/gas contact angles). These interfacial properties directly control the capillary forces within the deposits, and thus the onset and dynamics of subcooled boiling. As of today, the influence of coolant chemistry on the initiation and development of subcooled nucleate boiling within porous heated surfaces remains poorly understood.
The objective of this PhD is therefore to systematically study the coupled influence of coolant composition and capillary vaporization on nucleate boiling within porous substrates heated by conduction.
The research will follow an experimental approach to investigate how coolant chemistry affects surface tension and contact angles, in order to characterize fluid wetting on idealized porous substrates. Subcooled convective boiling experiments will also be conducted, with the phenomena characterized by shadowgraphy and fiber-optic thermometry.
The PhD will take place within the Thermal Hydraulics of Core and Circuits Laboratory (LTHC) and the Contamination Control, Coolant Chemistry and Tritium Management Laboratory (LMCT) at CEA IRESNE (Cadarache, France). The work will be supervised by Prof. Benoît Stutz of the University of Savoie Mont Blanc. Throughout this project, the doctoral student will develop expertise in interfacial physico-chemistry and two-phase thermohydraulics through the observation, characterization, and modeling of complex multiphysics phenomena.
Three-Dimensional Fine Measurements of Boundary Layers in Turbulent Flows within PWR Fuel Assemblies
The production of electricity through nuclear energy is a key pillar of the energy transition due to its low carbon footprint. In a continuous effort to improve safety and performance, the development of new knowledge and tools is essential.
Fuel assemblies, which are components of a reactor core, face various challenges involving thermo-hydraulic phenomena. These include flow-induced vibrations, power transmission associated with critical fluxes, and fluid-structure interactions in cases of assembly deformation or seismic excitation. In all these situations, the behavior of the fluid near the wall plays a crucial role. The use of Computational Fluid Dynamics (CFD) allows for the simulation of these phenomena with the goal of obtaining predictive tools. The experimental validation needs required by today's simulations push classical measurement techniques to their limits. There is a strong need for refined experimental data in both time and space on complex geometries.
This doctoral project aims to address this need by leveraging the latest advancements in optical measurements for turbulent flows. By combining index matching techniques, panoramic cameras, and Particle Tracking Velocimetry (PTV), it is possible to measure the velocity field in a representative volume (approximately 1 cm³) with a spatial density of around 10 micrometers. This allows for the simultaneous measurement of flow in the boundary layer and the hydraulic channel.
The thesis will primarily be conducted at the Hydromechanics Laboratory (LETH) at the IRESNE Institute (CEA Cadarache) and will involve collaboration with the Thermo-Fluids Lab at George Washington University. Travel to the USA will be required.
Instrumented PCB for predictive maintenance
The manufacturing of electronic equipment, and more specifically Printed Circuit Boards (PCBs), represents a significant share of the environmental impact of digital technologies, which must be minimized. Within a circular economy approach, the development of monitoring and diagnostic tools for assessing the health status of these boards could feed into the product’s digital passport and facilitate their reuse in a second life. In a preventive and prescriptive maintenance perspective, such tools could extend their lifespan by avoiding unnecessary periodic replacement in applications where reliability is a priority, as well as adapting their usage to prevent premature deterioration.
This PhD proposes to explore innovative instrumentation of PCBs using ‘virtual’ sensors, advanced estimators powered by measurement modalities (such as piezoelectric, ultrasonic, etc.) that could be integrated directly within the PCBs. The objective is to develop methods for monitoring the health status of the boards, both mechanically (fatigue, stresses, deformations) and electronically.
A first step will consist of conducting a state-of-the-art review and simulations to select the relevant sensors, define the quantities to be measured, and optimize their placement. Multi-physics modeling and model reduction will then make it possible to link the data to PCB integrity indicators characterizing its health status. The approach will combine numerical modeling, experimental validations, and multiparametric optimization methods.
Numerical modelling of large ductile crack progagation and assessment of margins comparing to engineering approach
Predicting failure modes in metal structures is an essential step in analyzing the performance of industrial components where mechanical elements are subjected to significant stress (e.g., nuclear power plant components, pipelines, aircraft structural elements, etc.). To perform such analyses, it is essential to correctly simulate the behavior of a defect in ductile conditions, i.e., in the presence of significant plastic deformation before and during propagation.
Predictive numerical simulation of ductile tearing remains an open scientific and technical issue despite significant progress made in recent years. The so-called local approach to fracture, notably the Gurson model (and its modified version GTN), is widely used to model ductile tearing. However, its use has limitations: significant computation time, simulation stoppage due to the presence of completely damaged elements in the model, and non-convergence of the result when the mesh size is reduced.
The aim of this thesis is to develop the ductile tear simulation model used at LISN so that it can be applied to large crack propagation on complex structures. It also aims to compare the results obtained with engineering methods that are simpler to implement.