Assisted generation of complex computational kernels in solid mechanics

The behavior laws used in numerical simulations describe the physical characteristics of simulated materials. As our understanding of these materials evolves, the complexity of these laws increases. Integrating these laws is a critical step for the performance and robustness of scientific computations. Therefore, this step can lead to intrusive and complex developments in the code.

Many digital platforms, such as FEniCS, FireDrake, FreeFEM, and Comsol, offer Just-In-Time (JIT) code generation techniques to handle various physics. This JIT approach significantly reduces the time required to implement new simulations, providing great versatility to the user. Additionally, it allows for optimization specific to the cases being treated and facilitates porting to various architectures (CPU or GPU). Finally, this approach hides implementation details; any changes in these details are invisible to the user and absorbed by the code generation layer.

However, these techniques are generally limited to the assembly steps of the linear systems to be solved and do not include the crucial step of integrating behavior laws.

Inspired by the successful experience of the open-source project mgis.fenics [1], this thesis aims to develop a Just-In-Time code generation solution dedicated to the next-generation structural mechanics code Manta [2], developed by CEA. The objective is to enable strong coupling with behavior laws generated by MFront [3], thereby improving the flexibility, performance, and robustness of numerical simulations.

The doctoral student will benefit from guidance from the developers of MFront and Manta (CEA), as well as the developers of the A-Set code (a collaboration between Mines-Paris Tech, Onera, and Safran). This collaboration within a multidisciplinary team will provide a stimulating and enriching environment for the candidate.

Furthermore, the thesis work will be enhanced by the opportunity to participate in conferences and publish articles in peer-reviewed scientific journals, offering national and international visibility to the thesis results.

The PhD will take place at CEA Cadarache, in south-eastern France, in the Nuclear Fuel Studies Department of the IRESNE Institute [4]. The host laboratory is the LMPC, whose role is to contribute to the development of the physical components of the PLEIADES digital platform [5], co-developed by CEA and EDF.

[1] https://thelfer.github.io/mgis/web/mgis_fenics.html
[2] MANTA : un code HPC généraliste pour la simulation de problèmes complexes en mécanique. https://hal.science/hal-03688160
[3] https://thelfer.github.io/tfel/web/index.html
[4] https://www.cea.fr/energies/iresne/Pages/Accueil.aspx
[5] PLEIADES: A numerical framework dedicated to the multiphysics and multiscale nuclear fuel behavior simulation https://www.sciencedirect.com/science/article/pii/S0306454924002408

Atomistic investigation of the diffusion of small xenon clusters in the metallic nuclear fuel UMo

This project is centered on the application of atomistic methods in order to investigate the stability and diffusion of intra-granular xenon clusters within the metallic nuclear fuel UMo.
Uranium – molybdenum alloys UMo present excellent thermal properties and a good uranium density. For those reasons, they are considered as nuclear fuel candidates for research reactors. It is therefore crucial to deploy new computational methodologies in order to investigate the evolution of their thermophysical properties under irradiation conditions.
During this PhD project, you will be in charge of validating (and, if necessary, recalibrating) the atomistic computational models for UMo that have been published in the literature. You will then apply those to the simulation of the stability and diffusion of small xenon clusters (typically up to 5 xenon atoms) within UMo crystals. Those computations will be performed leveraging accelerated molecular dynamics methods, and systematically compared to the results obtained for the reference nuclear fuel UO2. The results will also be analyzed by comparison to experimental measurements performed within the department, as well as used as reference data for larger-scale nuclear fuel performance codes. The results of your research will be published in scientific journals, and you are expected to attend international conferences to present your findings.
Those different investigations will allow you to acquire a set of competences applicable to many areas of materials science: ab initio calculations, machine-learning adjustment of interatomic potentials, classical and accelerated molecular dynamics, as well as many elements of statistical physics and condensed matter physics, which are among the areas of expertise of the PhD advisors.
The PhD will be based in the Fuel Behavior Modeling Laboratory (IRESNE Institute, CEA Cadarache), a dynamic research environment within which you will have the opportunity to interact with other PhD students. You will also benefit from a rich collaborative network (experimental researchers from the department, ISAS Institute at CEA Saclay, CINAM Laboratory in Marseille), that will allow you to become a member of the nuclear materials research community.

Cohesive powder simulation: link between atomic and grain scale

Nuclear fuel is produced through a powder metallurgy process that involves several stages of the granular medium preparation (grinding, mixing, pressing and sintering). The powders used during these stages exhibit strong cohesion between the grains, making their flow behavior complex. Predicting powder behavior is a critical industrial challenge to quickly adapt to raw material changes, optimize product quality, and enhance production rates.

This thesis aims to establish a link between the properties of powders and their behavior during flow and pressing. Grain cohesion is a key factor that influences both the flow and densification of granular materials. This cohesion is governed by several interparticle forces, such as van der Waals forces, capillary interactions, and electrostatic forces. Understanding these interactions at the atomic scale is essential for accurately predicting and modeling powder behavior. The thesis seeks to address two central questions: How do the surface properties of grains at the atomic level influence the cohesive forces at the grain scale? And how can we scale up from the atomic level to the grain scale to simulate powders more realistically?

Multi-scale simulation approaches are crucial for bridging the gap between microscopic phenomena and the macroscopic behavior of granular materials. Current Discrete Element Method (DEM) simulations rarely incorporate fundamental interactions, such as van der Waals forces, electrostatic forces, and capillary effects, into their contact models. Recent research (1) (2) has explored the impact of cohesion using a simplified approach, treating it as an attractive force or cohesive energy. Simulation methods like Molecular Dynamics (MD) or Coarse-graining enable the modeling of material behavior at finer scales, based on these local structural and chemical properties. A deeper understanding of cohesion at small scales will enhance the predictive capabilities of DEM simulations and clarify the relationship between powder properties and their overall behavior.The main goal of this thesis is to better understand the relationships between atomic-scale interactions and grain-scale cohesion and to assess the consequences for simulations of powder pressing and flow.

The primary goal of this thesis is to make connections between the atomic-scale interactions and grain-scale cohesion and to simulate the powder flow and compaction processes.
One of the main challenges in this project is the development of DEM contact laws that incorporate complex atomic-scale interactions. This will require close collaboration between experts in atomic-level simulations and those working on DEM modeling. Additionally, validating these models through experimental comparisons is essential to ensure their accuracy and relevance for industrial applications.

The PhD candidate will be based at the IRESNE Institute (CEA-Cadarache) within the Laboratory of Numerical Methods and Physical Components on the PLEIADES platform, part of the Department of Fuel Studies. They will collaborate with the Fuel Behavior Modeling Laboratory and will have access to state-of-the-art modeling and simulation tools, as well as a collaborative environment with the Mechanics and Civil Engineering Laboratory at the University of Montpellier.

Bibliography
1. Sonzogni, Max. Modélisation du calandrage des électrodes Li-ion en tant que matériau granulaire cohésif : des propriétés des grains aux performances de l'électrode. s.l. : Thèse, 2023.
2. Tran, Trieu-Duy. Cohesive strength and bonding structure of agglomerates composed. 2023.

Oxide-clad joint and internal corrosion layer modelling in GERMINAL using experimental data provided by different characterisation techniques

This work will be done in the frame of studies on the thermo-mechanical and physico-chemical behaviour behaviour of the « uranium and plutonium mixed oxide fuel » during irradiation currently considered for the future reactors of 4th generation. Because of its particularly hight thermal level during irradiation this kind of fuel is subject to several physical and chemical phenomena duringf its stay in reactor. Those one can have a strong impact on the behaviour of the whole fuel element (pellet and clad), but we can focus on two specific phenomena that take place at middle and high burnup :
- the formation by evaporation-condensation of a fission products layer between the external surface of the fuel pellet and the inner surface of the cladding material at middle burnup, designed as JOG for Joint Oxyde-Gaine;
- the formation of a corrosion layer on the internal surface of the clad, containing fission products and elements constituting the cladding material at high burnup, and resulting from the FCCI (Fuel-Cladding Chemical Interaction),
The occurence of this two phenomena is a limiting factor for increasing the burnup. Thus it is important de be able to estimate quite precisely the chemical composition of the fuel pellet and of the fuel-to-clad gap during irradiation. Previous experimental work had shown that the JOG consisted mainly of caesium, molybdenum and oxygen, with the presence of other elements such as tellurium and barium. Observations have also shown the presence of chromium, iron and nickel, along with other volatile fission products (VFP), in areas of ROG. These observations were backed up by thermodynamic calculations, which led to the assumption that the JOG consisted mainly of caesium molybdate Cs2MoO4. However, until recently, there had been no direct evidence of the presence of this compound. Recently, more detailed characterisation methods carried out as part of a current thesis on (U,Pu)O2 fuel samples confirmed quantitatively that the JOG was mainly made up of Cs, Mo and O, but also of I and Ba distributed in several phases. Other elements were detected and measured in localised areas, namely Te, Zr as well as U and Pu. With regard to corrosion, phases based on Fe, Te and Pd were observed, as well as the joint presence of Cr and O.
At the same time, work was started on modelling the axial redistribution of caesium, with a view to improving the description currently used in GERMINAL. The chemical element inventory at a given axial dimension has a first-order effect on the calculated JOG thickness and ROG thickness.
The aim of this thesis is to improve the description and modelling of JOG and ROG formation in the GERMINAL scientific calculation tool (OCS), which is dedicated to calculating the thermo-mechanical and physico-chemical behaviour of 4th generation reactor fuel irradiated under nominal and/or incidental conditions.
To this end, research will be developed in three areas:
- Further development of the radial migration methodology adopted in the GERMINAL code through comparison with existing and recently obtained experimental results. This is based on a coupling with a thermochemistry module in which several hypotheses for the release of volatile fission products created in the pellet towards the pellet-cladding gap can be considered.
The aim of this PhD subject consists in improving the JOG and FCCI modeling into the fuel performance code (FPC) GERMINAL, dedicated to the calculation of the thermo-mechanical and physico-chemical behaviour of the 4th generation reactors’ fuel irradiated in normal and off-normal conditions. For that purpose, an acurrate experimental caractherization of some irradiated fuel samples, to which the PhD student will contribute, will be elaborated and coupled to a thermodynamic approach. The research will be based on the two items :
- Determination and experimental identification of the chemical elements and phases located into the fuel pellet, into the gap and at the fuel-to-clad interfaces at the end of the irradiation using the implementation of microprobe-SIMS-SEM/FIB techniques, by combining elemental and isotopic analysis results with microscopic observations.
- Comparison of the results with thermodynamic calculations: type and local quantities of the chemical phases formed in the fuel pellet as well as the phases constituting the JOG and those resulting from the FCCI.
Thus, based on those results, it will be possible to evaluate precisely the chemical composition of the irradiated fuel, of the JOG and of the corrosion compounds by using the FPC GERMINAL, from which the input inventory in chemical elements will be estimated in function of burnup at the different radial and axial localisations.
The PhD student will be attached both to a multi-scale modeling group and to an experimental team having sophisticated tools. Furthermore, academic or international collaborations are possible, in particular in the frame of the OECD/NEA with the development of the TAFID database. The student will have the opportunity to enhance the skills learned in the field of nuclear materials characterisation as well as in the field of thermodynamic calculations and irradiated fuel behaviour simulation.
To this end, the research will be developed along three lines:
- Further development of the radial migration methodology adopted in the GERMINAL code through comparison with existing and recently obtained experimental results. This is based on a coupling with a thermochemistry module in which several hypotheses for the release of volatile fission products created in the pellet towards the pellet-cladding gap can be considered.
- Further development of a [simplified] model for the axial redistribution of caesium and, by extension, of volatile fission products, leading to an initial implementation in the GERMINAL code for testing and preliminary validation of the axial inventories estimated by calculation by comparison with experimental results,
- Finally, thermodynamic calculations to determine the nature and local quantity of the chemical phases formed in the fuel pellet and the constituent phases of the JOG and ROG will be carried out on the basis of the axial inventories estimated by the GERMINAL code.
This will enable a more accurate assessment of the chemical composition of the irradiated fuel, the JOG and the ROG products as a function of the burn-up rate using the GERMINAL OCS as a function of time at the various radial and axial locations.
The PhD student will be integrated into the fuel behaviour study and simulation group(IRESNE Institute, CEA CAdarache) which has or is developing various simulation tools, and will also be able to interact with a characterisation laboratory with cutting-edge experimental tools. Academic and international collaborations are also possible, particularly within the OECD/NEA framework with the development of TAFID database. These will enable the PhD student to make the most of the skills he or she has acquired in the field of characterisation of nuclear materials, as well as in thermodynamic calculations and simulation of the physico-chemical behaviour of irradiated nuclear fuel.

Atomic-scale study of dislocation mobility in MOX fuel

The transition to carbon neutrality requires a rapid increase in low-carbon energy sources, including nuclear power, which necessitates a deep understanding of irradiated materials. Mixed oxide (MOX) fuel is particularly important as it optimizes the use of nuclear resources and reduces radioactive waste. The mechanical behavior of MOX under irradiation is crucial for ensuring the integrity of the fuel under various operating conditions.

The objective of this thesis is to perform atomistic simulations to understand dislocation mobility, essential for supporting multiscale modeling of the mechanical behavior of MOX. Molecular dynamics calculations will analyze dislocation mobility under different conditions of temperature, stress, plutonium content, and stoichiometric deviations, with the aim of establishing velocity laws. The results of these simulations will enhance micromechanical modeling within the CEA’s PLEIADES simulation platform, which is dedicated to simulating the complete lifecycle of nuclear fuel, from its fabrication to its storage.

The doctoral student will be based at the Fuel Behavior Modeling Laboratory in Cadarache, a dynamic environment with 11 permanent researchers and an equal number of doctoral students. Located in Provence, this center offers a pleasant working environment between the Verdon and Lubéron natural parks. The thesis will be carried out in collaboration with IM2NP, a leading laboratory in materials physics research.

The candidate should have a strong background in materials physics, ideally with experience in small-scale mechanics. These skills can be further developed during an M2 internship at the laboratory. The doctoral student will have the opportunity to present their work through scientific publications and at international conferences, opening up career opportunities in both research and industry.

Multiphysics modeling of fission gas behavior and microstructure evolution of nuclear fuels

The climate crisis demands urgent action and a rapid shift towards carbon-free technologies. This requires the development of advanced materials for more efficient electricity production and storage, including innovation in nuclear reactor fuels. To enhance the safety and efficiency of both current and future nuclear power plants, it is crucial to understand and predict fuel behavior under operating and accidental conditions.

A critical issue is related to fission gases produced upon nuclear fissions. These gases have low solubility and form small bubbles that grow from nanoscale to microscale during fuel operation, significantly impacting the fuel's overall properties. While experimental characterization is essential, numerical simulations complement this work by modeling bubble formation and growth, as well as the consequences in terms of changes in fuel properties. This approach is key to the design of next-generation, high-performance nuclear fuels.

This PhD project aims to advance simulation models for fission gas behavior within the polycrystalline structure of nuclear fuels, with a particular focus on uranium oxides. The PhD student will develop a physical model using the phase-field method, compute necessary input parameters, and conduct numerical simulations that replicate irradiation experiments performed in our department. Direct comparison between simulation results and experimental data will enable deeper insights into the underlying physics of gas behavior, including bubble formation, gas release, and fuel swelling. Additionally, this project will serve as validation for the INFERNO scientific code that will be used for these simulations on national supercomputers.

The research will be conducted at the Nuclear Fuel Department (DEC) of the IRESNE Institute(CEA-Cadarache), in collaboration with CEA fuel modeling and experimental characterization experts. The PhD student will have opportunities to share their findings through scientific publications and presentations at international conferences. Throughout the project, they will develop expertise in multiphysics modeling, numerical simulations, and scientific computing. These highly transferable skills will prepare them for a successful career in academic research, industrial R&D, or materials engineering.

References :
https://doi.org/10.1063/5.0105072
https://doi.org/10.1016/j.commatsci.2019.01.019

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