# Assimilation of transient data and calibration of simulation codes using time series

In the context of scientific simulation, some computational tools (codes) are built as an assembly of (physical) models coupled in a numerical framework. These models and their coupling use data sets fitted on results given by experiments or fine computations of “Direct Numerical Simulation” (DNS) type in an up-scaling approach. The observables of these codes, as well as the results of the experiments or the fine computations are mostly time dependent (time series). The objective of this thesis is then to set up a methodology to improve the reliability of these codes by adjusting their parameters through data assimilation from these time series.

Work on parameter fitting has already been performed in our laboratory in a previous thesis, but using scalars derived from the temporal results of the codes. The methodology developed during this thesis has integrated screening, surrogate models and sensitivity analysis that can be extended and adapted to the new data format. A preliminary step of transformation of the time series will be developed, in order to reduce the data while limiting the loss of information. Machine learning /deep learning tools could be considered.

The application of this method will be performed within the framework of the nuclear reactor severe accident simulation. During these accidents, the core loses its integrity and corium (fuel and structure elements resulting from the reactor core fusion) is formed and can relocate and interact with its environment (liquid coolant, vessel’s steel, concrete from the basemat…). Some severe accident simulation codes describe each step / interaction individually while others describe the whole accident sequence. They have in common that they are multiphysic and have a large number of models and parameters. They describe transient physical phenomena in which the temporal aspect is important.

The thesis will be hosted by the Severe Accident Modeling Laboratory (LMAG) of the IRESNE institute at CEA Cadarache, in a team that is at the top of the national and international level for the numerical study of corium-related phenomena, from its generation to its propagation and interaction with the environment. The techniques implemented for data assimilation also have an important generic potential which ensures important opportunities for the proposed work, in the nuclear world and elsewhere.

# Study of the thermoconversion and de-polymerization mechanisms of plastic wastes in supercritical water conditions

The waste valorization is a hot topic that has attracted great interest in the Circular Carbon Economy. Substantial efforts have been devoted to strengthening sustainable processes in recent years. These are based on the development of systems to improve carbon circularity (material and energy recycling).Global production of plastics doubled from 230 million tons in 2000 to 460 million tons in 2019. This exponential production/consumption has significant consequences on the environment. Despite the existence of recycling methods, only 9% of global plastic production is currently recycled, and the remaining quantity (not valorized) represents a real source of pollution [1].

Mixtures of different types of plastics make sorting stages difficult, which represents the main disadvantage for material recycling systems. An interesting application recently reported in the literature is the use of the hydrothermal gasification process to treat waste (and mixtures of difficult-to-sort) plastics to produce a gas rich in CH4 and H2 [2]. Hydrothermal gasification (HTG) is a thermochemical process which employs the supercritical conditions of water (T > 374 ° C, P > 221 bar), in order to convert the organic carbon contained in the wet feedstock into a gaseous phase (which contains CH4, H2, CO and CO2, mainly). In addition, the flexibility of the process also allows the study of de-polymerization of these wastes in conditions close to the critical point of water, which facilitates the production of chemical intermediates (and their reuse) in the chemical industry.

Thus, the understanding of the conversion mechanisms of different types of plastics (and their mixtures) seems essential to valorize these wastes. However, the identification of reaction pathways is still a major scientific obstacle. The objective of the thesis is the study of the reaction mechanisms of transformation of model plastics (and their mixtures) in supercritical water conditions. Understanding the phenomena will lead to the optimization of the HTG process (with and without catalysts) to facilitate the production of a gas rich in CH4/H2 and the production of intermediates for the chemical industry. The focus of this PhD work will involve: i) the study of thermo-conversion and de-polymerization of plastics; ii) the study of the behavior of catalysts in the supercritical water environment (activation/deactivation); iii) the study of selectivity towards the production of a gas containing CH4/H2 and the production of chemical intermediates.

# Study of fracture toughness - microstructure relationships of new high performance oxide dispersion strengthened steels

ODS steels are considered for the development of components for fourth generation reactors. They offer high tensile and creep strength and good resistance to irradiation [1-3]. This high level of reinforcement is accompanied by a reduction in ductility and toughness. Tube shaping changes the microstructure, so the properties of the material in its final form should be evaluated. The work of B. Rais [4] made it possible to compare the different tests and to develop a test and an analysis method for measuring toughness on thin tubes.

This present PhD will use this new test to evaluate the toughness of various ODS grades. Varied microstructures from historical and recent productions will assessed to identify the mechanisms, the key parameters driving toughness and to identify the microstructural parameters which drive the response of the material. In this work we will be interested in ferritic / martensitic grades, some of which come from a manufacturing process which is the subject of a patent application [5-6] and for which we observe for the first time remarkable properties in resilience, associated with good hot mechanical properties.

The study will be based on a comparison of experience and finite element modeling. This applied research work will allow the student to acquire solid skills in fracture mechanics and fine characterization of materials (SEM, EBSD, etc.). A good understanding of the mechanical properties/microstructure relationships will make it possible to understand the origin of the observed properties and to propose new optimizations on the microstructures to improve the mechanical behavior and/or the shaping of the material.

Student profile: Engineer or M2 Mechanics/Materials

# High-Performance Computing (HPC) resolution of "point-saddle" problems arising from the mechanics of contact between deformable structures

In the field of structural mechanics, simulated systems often involve deformable structures that may come into contact. In numerical models, this generally translates into kinematic constraints on the unknown of the problem (i.e. the displacement field), which are dealt with by the introduction of so-called dual unknowns that ensure the non-interpenetration of contacting structures. This leads to the resolution of so-called "saddle-point" linear systems, for which the matrix is "indefinite" (it has positive and negative eigenvalues) and "sparse" (the vast majority of terms in this matrix are zero).

In the context of high-performance parallel computing, we're turning to "iterative" methods for solving linear systems, which, unlike "direct" methods, can perform well for highly refined numerical models when using a very large number of parallel computing processors. But for this to happen, they need to be carefully designed and/or adapted to the problem at hand.

While iterative methods for solving "positive definite" linear systems (which are obtained in the absence of kinematic constraints) are relatively well mastered, solving linear point-saddle systems remains a major difficulty [1]. A relatively abundant literature proposes iterative methods adapted to the treatment of the "Stokes problem", emblematic of incompressible fluid mechanics. But the case of point-saddle problems arising from contact constraints between deformable structures is still a relatively open problem.

The proposed thesis consists in proposing iterative methods adapted to the resolution of linear "saddle-point" systems arising from contact problems between deformable structures, in order to efficiently handle large-scale numerical models. The target linear systems have a size of several hundred million unknowns, distributed over several thousand processes, and cannot currently be solved efficiently, either by direct methods, or by "basic" preconditioned iterative methods. In particular, we will validate the approach proposed by Nataf and Tournier [2] and adapt it to cases where the constraints do not act on all the primal unknowns.

The work carried out can be applied to numerous industrial problems, particularly in the nuclear industry. One example is the case of fuel pellets, which expand under the effect of temperature and the generation of fission products, and come into contact with the metal cladding of the fuel rod, which can lead to cladding failure [3].

This thesis is in collaboration with the LIP6 laboratory (Sorbonne-université).

An internship can be arranged in preparation for thesis work, depending on the candidate's wishes.

[1] Benzi, M., Golub, G. H., & Liesen, J. (2005). Numerical solution of saddle point problems. Acta numerica, 14, 1-137. (https://page.math.tu-berlin.de/~liesen/Publicat/BenGolLie05.pdf)

[2] Nataf, F., & Tournier, P. H. (2023). A GenEO Domain Decomposition method for Saddle Point problems. Comptes Rendus. Mécanique, 351(S1), 1-18. (https://doi.org/10.5802/crmeca.175)

[3] Michel, B., Nonon, C., Sercombe, J., Michel, F., & Marelle, V. (2013). Simulation of pellet-cladding interaction with the pleiades fuel performance software environment. Nuclear Technology, 182(2), 124-137. (https://hal.science/hal-04060973/document)

# Implicit/explicit transition for numerical simulation of Fluid-Structure Interaction problems treated by immersed boundary techniques

In many industrial sectors, rapid transient phenomena are involved in accident scenarios. An example in the nuclear industry is the Loss of Primary Coolant Accident, in which an expansion wave propagates through the primary circuit of a Pressurized Water Reactor, potentially vaporizing the primary fluid and causing structural damage. Nowadays, the simulation of these fast transient phenomena relies mainly on "explicit" time integration algorithms, as they enable robust and efficient treatment of these problems, which are generally highly non-linear. Unfortunately, because of the stability constraints imposed on time steps, these approaches struggle to calculate steady-state regimes. Faced with this difficulty, in many cases, the kinematic quantities and internal stresses of the steady state of the system under consideration at the time of occurrence of the simulated transient phenomenon are neglected.

Furthermore, the applications in question involve solid structures interacting with the fluid, undergoing large-scale deformation and possibly fragmenting. A immersed boundary technique known as MBM (Mediating Body Method [1]) recently developed at the CEA enables structures with complex geometries and/or undergoing large deformations to be processed efficiently and robustly. However, this coupling between fluid and solid structure has only been considered in the context of "fast" transient phenomena treated by "explicit" time integrators.

The final objective of the proposed thesis is to carry out a nominal regime calculation followed by a transient calculation in a context of fluid/immersed-structure interaction. The transient phase of the calculation is necessarily based on "explicit" time integration and involves the MBM fluid/structure interaction technique. In order to minimize numerical disturbances during the transition between nominal and transient regimes, the calculation of the nominal regime should be based on the same numerical model as the transient calculation, and therefore also rely on an adaptation of the MBM method.

Recent work defined an efficient and robust strategy for calculating steady states for compressible flows, based on "implicit" time integration. However, although generic, this approach has so far only been tested in the case of perfect gases, and in the absence of viscosity.

On the basis of this initial work, the main technical challenges of this thesis are 1) to validate and possibly adapt the methodology for more complex fluids (in particular water), 2) to introduce and adapt the MBM method for fluid-structure interaction in this steady-state calculation strategy, 3) to introduce fluid viscosity, in particular within the framework of the MBM method initially developed for non-viscous fluids. At the end of this work, implicit/explicit transition demonstration calculations with fluid-structure interaction will be implemented and analyzed.

An internship can be arranged in preparation for thesis work, depending on the candidate's wishes.

[1] Jamond, O., & Beccantini, A. (2019). An embedded boundary method for an inviscid compressible flow coupled to deformable thin structures: The mediating body method. International Journal for Numerical Methods in Engineering, 119(5), 305-333.

# Seismic analysis of the soil-structure interface: physical and numerical modelling of global tilting and local detachment

The effect of soil-structure interaction, currently not taken into account in the seismic design of civil engineering structures and their foundations in professional practice, could influence the design of load-bearing structures. Soil-structure interaction effects are linked to inertial interaction (forces in the soil-structure system) and kinematic interaction (influence of the soil-foundation contact surface) (Semblat and Pecker, 2009). A more precise analysis of these two aspects requires three-dimensional (3D) numerical modeling of the soil-foundation-structure system and its temporal response, the definition of relevant constitutive laws for materials in the nonlinear plastic regime and the characterization of their mechanical properties. This makes it possible to consider directly the reduction in soil bearing capacity resulting from loss in soil strength, and the modification over time of the seismic action at the base of the structure. In 3D soil-structure interaction models, the connection between the soil and the embedded part of the footing structure is generally considered to be rigid, and the effects of friction and up-lift are neglected.

A series of tests on the CEA's Azalée shaking table in October 1999 (CAMUS IV, Combescure and Chaudat, 2000) demonstrated the existence of complex phenomena of structural detachment from the ground during seismic shaking. This involved a 1/3 scale model of the structure resting on a sandbox, anchored to the shaking table. Tests revealed up lifting at the foundation level, leading to energy dissipation, as well as significant residual settlement and rotation. Other studies have also highlighted the significant impact of rocking and consequent up-lift at the soil-foundation interface on the seismic response of the structure (Abboud, 2017; Chatzigogos, 2007; Gajan et al., 2021; Gazetas and Apostolou, 2004), as well as the loss of elasticity and nonlinear behavior of the soil, which increases permanent settlement (Pelekis et al., 2021). However, few studies in the literature evaluate the effect of the roughness of the soil-foundation interface and propose contact laws to model settlement and up lifting during rocking of the structure under seismic action.

In the context of interaction effects, understanding the parameters influencing the behavior of the soil-foundation interface and modeling the contact surface remains a challenge. A combined experimental and numerical approach will be developed in the proposed thesis.

The main aim of this thesis is to enable the transition from the modeling of local effects (friction, up lifting) to the simulation of the structure's global response (rocking, settlement, sliding). This is achieved by identifying the experimentally measurable physical parameters that manage the phenomenon locally and, at the same time, the global dynamic parameters altered by interaction effects (change in effective height).

On the one hand, an experimental campaign will be conducted on Vesuve, a single-axis vibrating table. The experimental model will consist of a rigid box containing the reference soil and a structure placed on the surface. The behavior of the system will be monitored using pressure sensors, LVDTs, flexiforce, accelerometers, etc. In addition, a numerical modeling method will be proposed and validated by comparison with experimental results. Finally, a numerical strategy will be proposed for different study cases. The output parameters obtained by the numerical simulations will be correlated with the measured parameters in order to optimize their calibration on the one hand, and to validate the numerical approach on the other.

# Experimental characterisation and numerical simulation of intergranular oxide fracture: Application to Irradiation Assisted Stress Corrosion cracking

Metal alloys used in industrial applications can form oxide layers in the presence of a corrosive environment. These oxides may be distributed on the surface and/or localized at the grain boundaries. In the latter case, the oxidized grain boundaries may experience brittle fracture under mechanical loading, potentially leading to intergranular cracking of the material. This mechanism is, for example, a possible scenario for the failure of austenitic stainless steel bolts used in the internals structure of Pressurized Water Reactors (PWRs). Under the effect of mechanical loading, neutron irradiation and the presence of a corrosive environment, these bolts fail through a phenomenon known as irradiation-assisted stress corrosion cracking. To model this phenomenon, we need to determine the fracture properties of intergranular oxides, and to take into account the coupling between cracking, oxidation and irradiation. In this thesis, experimental and numerical work will be combined. Firstly numerical simulations based on the variational approach to fracture approach will be assessed in order to design micro-beam micromechanics experiments aimed at reliably determining the fracture properties of oxides, and also to study the couplings between cracking, oxidation and irradiation. In particular, the cracking-oxidation coupling that prefigures the transition between initiation and propagation will be investigated in detail. These experiments will then be carried out on model and industry-relevant steels, and interpreted using numerical simulations. Finally, all the results obtained in this work will be incorporated into simulations of polycrystalline aggregates, in order to assess the possibility of quantitatively predicting intergranular cracking in the context of irradiation-assisted stress corrosion.

By the end of the PHD, the doctoral student will have acquired both experimental skills - micromechanical tests - and numerical skills - numerical simulations of fracture - at the cutting edge of the state of the art and applicable to a large number of problems in the mechanics of materials.

A Master's 2 / end-of-studies internship preparatory to the PHD is available in 2024.

# Toward robust simulations of uncertain industrial nonlinear dynamical systems

Vibrations are encountered in many components of nuclear reactors subject to fluid flows (steam generator for example). Resulting impacts and friction contacts can lead to wear of the materials which must be controlled for improved maintenance and to guarantee the lifespan of these industrial components.

Thus, it is necessary to know the solicitation experienced by the structure, define a reliable modeling of the system and implement efficient and accurate numerical methods to obtain the non-linear dynamic responses of the system.

In order to improve the robustness and performance of the numerical methods currently used at Framatome, CEA and EDF, this phD thesis have the following objectives:

- implement an efficient temporal integration algorithm suited for the case of systems with contact and friction, in particular to accurately reproduce “stick-and-slip” regimes and then the wear power of the surfaces in contact.

- demonstrate the ability to simulate both a single tube and a bundle of nearly 5000 interacting tubes,

- study the applicability of fluid-elastic coupling models identified on a single straight tube to a bundle of multi-supported 3D tubes,

- identify the relative influence of physical and numerical parameters by probabilistic approaches.

A Master 2 internship is planned before the phD as an introduction to this work.

Profile required: Final year engineer or Master 2 equivalent. Specialized in mechanics, attracted by numerical methods (both computer development and practical use).

# Detection and diagnosis of anomalies in civil engineering structures using machine learning and numerical simulation

Monitoring reinforced concrete structures is of particular importance when it comes to identifying potential anomalies (cracking or excessive deformation, for example) in relation to nominal operation. These anomalies can have consequences both for the overall behavior (strength, etc.) and the functionality (tightness, etc.) of the structure. To meet this challenge (fault detection and prediction of consequences), a strong coupling between measurement data and simulations is essential. Current methodology relies mainly on initial instrumentation of the structure, based on expert opinion or feedback, but the data is not processed and analyzed using numerical calculation codes. The subject of the proposed thesis falls within the framework of a methodological breakthrough, through the combination of machine learning and numerical simulation tools for the detection and diagnosis of anomalies on civil engineering structures, in order to develop intelligent and adaptive instrumentation for monitoring the life of the structure. The methodology revolves around the following axes: processing of measurement data by machine learning, leading to the identification of potentially faulty zones, reconstruction of suitable boundary conditions around the previously detected anomaly by metamodeling, and identification of the fault and its consequences by numerical simulation. The thesis will be carried out jointly by two CEA laboratories: LM2S, specializing in structural mechanics, and LIAD, a unit specializing in Artificial Intelligence and Data Science.

The desired candidate (M2 level) should have an appetite for advanced numerical methods (including machine learning), as well as knowledge of mechanics and/or civil engineering. By the end of the thesis, the candidate will have developed knowledge and skills in numerical simulation, data assimilation and mechanics that can be effectively exploited in both industrial and academic environments.

The thesis may be combined with a preliminary M2 internship.

# Development of a physically based multi-scale numerical model for the fuel rod cladding of pressurized water reactors

The fuel rods of pressurized water nuclear reactors are made of uranium oxide pellets stacked in zirconium alloy tubes. In reactor, these materials undergo mechanical loading that lead to their irreversible deformation. In order to guarantee the safety and increase the performance of nuclear reactors, this deformation must be modeled and predicted as precisely as possible. In order to further improve the predictivity of the models, the polycrystalline nature of these materials as well as the physical deformation mechanisms must be taken into account. This is the objective of this study, which consists of developing a physically based multi-scale numerical model of the fuel rod cladding.

The mechanical behavior of metallic materials is usually modeled by considering the material as homogeneous. In fact metallic materials are made of many crystalline grains clustered together. The behavior of the material is therefore the result of the deformation of individual grains but also their interactions between each other. In order to take into account the polycrystalline nature of the material, mean-field self-consistent polycrystalline models have been developed for many years. These models are based on the theory of homogenization of heterogeneous materials. Recently, a polycrystalline model, developed in a linear and isothermal framework, has been coupled with an axisymmetric 1D finite element calculation to simulate the in-reactor deformation of cladding tubes. A complex mechanical loading history, mimicking the stresses and strains experienced by the cladding has been simulated.

The objective of this PhD work is to extend the field of application of this model in particular by applying it to a non-linear framework in order to simulate high stress loadings, to extend it to anisothermal conditions but also to carry out 3D finite element simulations with at each element and each time step a simulation using the polycrystalline model. These theoretical and numerical developments will finally be applied to the simulation of the behavior of fuel rods in a power ramp situation thanks to its integration into a software platform used for industrial applications. This approach will allow to better assess the margins available to operate the reactor in a more flexible manner, allowing it to adapt to changes in the energy mix in complete safety.