
Nicolas FavriePolytech Marseille · Civil Engineering
Nicolas Favrie
PhD
After 18 years in Aix Marseille University, I'm looking for a new position in a research lab or university.
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57
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Introduction
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September 2006 - present
Publications
Publications (57)
Phase transition in compressible flows involves capillarity effects, described by the Euler–Korteweg (EK) equations with nonconvex equation of state. Far from phase transition, that is, in the two convex parts of the equation of state, the dispersion terms vanish and one should recover the hyperbolic Euler equations of fluid dynamics. However, the...
Phase transition in compressible flows involves capillarity effects, described by the Euler-Korteweg equations. Far from phase transition, the dispersion terms vanish and one should recover the hyperbolic Euler equations of fluid dynamics. However, the solution of Euler-Korteweg equations does not converge towards the solution of Euler equations wh...
In this paper, two Eulerian and Lagrangian variational formulations of non-linear kinematic hardening are derived in the context of finite thermoplasticity. These are based on the thermo-mechanical variational framework introduced by Heuzé et al. [37], and follow the concept of pseudo-stresses introduced by Mosler [48]. These formulations are deriv...
This study provides a new formulation of gradient damage model which allows an efficient explicit numerical solution of dynamics problems. The proposed methodology is based on an ”extended Lagrangian approach” developed by one of the authors for the nondissipative and dispersive shallow water equation. By using this strategy, the global minimizatio...
A macroscopic model describing nonlinear viscoelastic waves is derived in Eulerian formulation, through the introduction of relaxation tensors. It accounts for both constitutive and geometrical nonlinearities. In the case of small deformations, the governing equations recover those of the linear generalized Zener model (GZM) with memory variables,...
The post-doctoral work concerns the mechanism of mass transfer induced by evaporation-condensation under a thermal gradient. In nuclear fuels, the presence of porosities, the very high temperatures combined with the strong thermal gradient activate this evaporation-condensation phenomenon. This results in a displacement of porosities towards the ce...
When simulating multiphase compressible flows using the diffuse‐interface methods, the test cases presented in the literature to validate the modellings with regard to interface problems are always textbook cases: interfaces are sharp and the simulations therefore easily converge to the exact solutions. In real problems, it is rather different beca...
An Eulerian, hyperbolic, multiphase-flow model for dynamic and irreversible compaction of porous materials is constructed. A reversible model for elastic, compressible, porous material is derived. Classical homogenization results are obtained. The irreversible model is then derived in accordance with the following basic principles. First, the entro...
When simulating multiphase compressible flows using the diffuse-interface methods, the test cases presented in the literature to validate the modellings with regard to interface problems are always textbook cases: interfaces are sharp and the simulations therefore easily converge to the exact solutions. In real problems, it is rather different beca...
This paper is on arbitrary high order fully discrete one-step ADER discontinuous Galerkin schemes with subcell finite volume limiters applied to a new class of first order hyperbolic reformulations of nonlinear dispersive systems based on an extended Lagrangian approach introduced by Dhaouadi et al. (Stud Appl Math 207:1–20, 2018), Favrie and Gavri...
In its original formulation by Forest & Sab (Math. Mech. Solids, 2017), stress gradient elastodynamics incorporate two inner-lengths to account for size effects in continuum theory. Here, an extended one-dimensional stress gradient model is developed by means of Lagrangian formalism, incorporating an additional inner-length and a fourth-order space...
The motivation of this work is to better understand the dynamic behaviour of bistable structures presenting an analogy with regularized Ericksen bars. The archetype of such structures is the bistable tape spring, which exhibits a particular scenario of deployment, from the stable coiled configuration to the straight stable configuration: at each ti...
In its original formulation by Forest & Sab (Math. Mech. Solids, 2017), stress gradient elastodynamics incorporate two inner-lengths to account for size effects in continuum theory. Here, an extended one-dimensional stress gradient model is developed by means of Lagrangian formalism, incorporating an additional inner-length and a fourth-order space...
The motivation of this work is to better understand the dynamic behaviour of bistable structures presenting an analogy with reguralized Ericksen bars. The archetype of such structures is the bistable tape spring, which exhibits a particular scenario of deployment, from the stable coiled configuration to the straight stable configuration: at each ti...
The reference fuel design for french Sodium nuclear Fast Reactor (SFR) consists of fuel pins made of (U,Pu)O2 pellets inserted in a steel alloy cladding tube. Fuel pin behaviour under irradiation is complex and simulated with SFR fuel performance codes through the world. Concerning the thermal behaviour, the pellet-to-cladding gap evolution has a s...
This presentation proposed a new model for the numerical treatment of granular materials and porous material in the isotropic case. The model is compatible with the multiphase flow model framework. Numerical results are compared with loading unloading experiment on powder HMX, Hugoniot curve of aluminium.
Presentation made in Shark FV conference on how to make parabolic or dispersive equation hyperbolic
Propagation of elastic waves in damaged media (concrete, rocks) is studied theoretically and numerically. Such materials exhibit a nonlinear behavior, with long-time softening and recovery processes (slow dynamics). A constitutive model combining Murnaghan hyperelasticity with the slow dynamics is considered, where the softening is represented by t...
Propagation of elastic waves in damaged media (concrete, rocks) is studied theoretically and numerically. Such materials exhibit a nonlinear behavior, with long-time softening and recovery processes (slow dynamics). A constitutive model combining Murnaghan hyperelasticity with the slow dynamics is considered, where the softening is represented by t...
In the literature, two classes of models for the high‐strain dynamics of solids can be found: hypoelastic and hyperelastic ones. Hypoelastic models are widely used in industrial and military numerical codes. For this class of models, an empirical partial differential equation for the deviatoric part of the stress tensor is formulated to close the g...
This chapter introduces bases of nonlinear mesoscopic elasticity and presents a novel approach to model and numerically simulate the dynamical behavior of this class of material. Under dynamical solicitation, these so-called nonclassical materials exhibit two different time-dependent nonlinear mechanisms termed “fast” (nonlinear elasticity) and “sl...
We study the defocusing nonlinear Schrödinger (NLS) equation written in hydrodynamic form through the Madelung transform. From the mathematical point of view, the hydrodynamic form can be seen as the Euler–Lagrange equations for a Lagrangian submitted to a differential constraint corresponding to the mass conservation law. The dispersive nature of...
Rocks and concrete are known to soften under a dynamic loading, i.e. the speed of sound diminishes with forcing amplitudes. To reproduce this behavior, an internal-variable model of continuum is proposed. It is composed of a constitutive law for the stress and an evolution equation for the internal variable. Nonlinear viscoelasticity of Zener type...
A numerical method for longitudinal wave propagation in nonlinear elastic solids is presented. Here, we consider polynomial stress-strain relationships, which are widely used in nondestructive evaluation. The large-strain and infinitesimal-strain constitutive laws deduced from Murnaghan's law are detailed, and polynomial expressions are obtained. T...
We study the defocusing Non-Linear Schrödinger (NLS) equation written in hydrodynamic form through the Madelung transform. From the mathematical point of view, the hydrodynamic form can be seen as the Euler-Lagrange equations for a Lagrangian submitted to a differential constraint corresponding to the mass conservation law. The dispersive nature of...
The mathematical model of shear shallow water flows of constant density is studied. This is a 2D hyperbolic non-conservative system of equations that is mathematically equivalent to the Reynolds-averaged model of barotropic turbulent flows. The model has three families of characteristics corresponding to the propagation of surface waves, shear wave...
A model for longitudinal wave propagation in rocks and concrete is presented. Such materials are known to soften under a dynamic loading, i.e. the speed of sound diminishes with forcing amplitudes. Also known as slow dynamics, the softening of the material is not instantaneous. Based on continuum mechanics with internal variables of state, a new fo...
A multiphase Eulerian formulation for the interaction of visco-plastic compressible solids and compressible fluids is proposed. The plasticity effects in solids are described by relaxation terms in the governing equations which are compatible with the Von Mises yield criterion. The visco-plastic model is validated on experimental data in a range of...
The equations of 1D elastodynamics write as a 2×2 hyperbolic system of conservation laws. The solution to the Riemann problem (i.e. piecewise constant initial data) is addressed, both in the case of convex and nonconvex constitutive laws. In the convex case, the solution can include shock waves or rarefaction waves. In the nonconvex case, compound...
In heterogeneous solids such as rocks and concrete, the speed of sound diminishes with the strain amplitude of a dynamic loading (softening). This decrease known as " slow dynamics " occurs at time scales larger than the period of the forcing. Also, hysteresis is observed in the steady-state response. The phenomenological model by Vakhnenko et al....
A new numerical method for solving the Serre–Green–Naghdi (SGN) equations describing dispersive waves on shallow water is proposed. From the mathematical point of view, the SGN equations are the Euler–Lagrange equations for a 'master' lagrangian submitted to a differential constraint which is the mass conservation law. One major numerical challenge...
In heterogeneous solids such as rocks and concrete, the speed of sound diminishes with the strain amplitude of a dynamic loading (softening). This decrease known as "slow dynamics" occurs at time scales larger than the period of the forcing. Also, hysteresis is observed in the steady-state response. The phenomenological model by Vakhnenko et al. is...
The aim of this article is the construction of a multiphase hyperelastic model. The Eulerian
formulation of the hyperelasticity represents a system of 14 conservative partial differential
equations submitted to stationary differential constraints. This model is constructed with
an elegant approach where the specific energy is given in separable for...
A new numerical method for solving the Serre-Green-Naghdi (SGN) equations describing dispersive waves on shallow water is proposed. From the mathematical point of view, the SGN equations are the Euler-Lagrange equations for a 'master' lagrangian submitted to a differential constraint which is the mass conservation law. One major numerical challenge...
Hypoelastic models are widely used in industrial and military codes for numerical simulation of high strain dynamics of solids. This class of model is often mathematically inconsistent. More exactly, the second principle is not verified on the solutions of the model, and the initial state after a reversible cycle is not recovered. In the past decad...
We extend the model of diffuse solid-fluid interfaces developed earlier by authors of this paper to the case of arbitrary number of interacting hyperelastic solids. Plastic transformations of solids are taken into account through a Maxwell type model. The specific energy of each solid is given in separable form : it is the sum of a hydrodynamic par...
Heterogeneous materials, such as rocks and concrete, have a complex dynamics
including hysteresis, nonlinear elasticity and viscoelasticity. It is very
sensitive to microstructural changes and damage. The goal of this paper is to
propose a physical model describing the longitudinal vibrations of this class
of material, and to develop a numerical st...
A material is hyperelastic if the stress tensor is obtained by variation of the stored energy function. The corresponding 3D mathematical model of hyperelasticity written in the Eulerian coordinates represents a system of 14 conservative partial differential equations submitted to stationary differential constraints. A classical approach for numeri...
The piston problem for a hyperelastic hyperbolic conservative
model where
the stored energy is given in separable form is studied. The eigenfields
corresponding to the hyperbolic system are of three types : linearly
degenerate fields (corresponding to the contact characteristics), the fields
which are genuinely
nonlinear in the sense of Lax (corres...
We consider the equations of hyperelasticity for isotropic solids in the Eulerian coordinates in a special case where the specific stored energy is a sum of two functions. The first one, the hydrodynamic part of the energy, depends only on the solid density and the entropy, and the second one, the shear energy, depends on the invariants of the Fing...
An Eulerian hyperbolic multiphase flow model for dynamic and irreversible compaction of granular materials is constructed. The reversible model is first constructed on the basis of the classical Hertz theory. The irreversible model is then derived in accordance with the following two basic principles. First, the entropy inequality is satisfied by t...
An Eulerian hyperbolic diffuse interface model for elastic–plastic solid–fluid interaction is constructed. The system of governing equations couples Euler equations of compressible fluids and a visco-plastic model of Maxwell type materials (the deviatoric part of the stress tensor decreases during plastic deformations) in the same manner as models...
The Maxwell type elastic-plastic solids are characterized by decaying the absolute values of the principal components of the deviatoric part of the stress tensor during the plastic relaxation step. We propose a mathematical formulation of such a model which is compatible with the von Mises criterion of plasticity. Numerical examples show the abilit...
A macroscopic model describing elastic-plastic solids is derived in a special case of the internal specific energy taken in separable form: it is the sum of a hydrodynamic part depending only on the density and entropy, and a shear part depending on other invariants of the Finger tensor. In particular, the relaxation terms are constructed compatibl...
This work deals with the building of a discrete model able to describe and to predict the evolution of complex gas flows in heterogeneous media. In many physical applications, large scales numerical simulation is no longer possible because of a lack of computing resources. Indeed the medium topology may be complex due to the presence of many obstac...
Un modèle Eulérien multiphasique hyperbolique à une vitesse pour la résolution de problèmes à interfaces entre solides et fluides est proposé. Ce type de modélisation est bien adapté aux grandes déformations. Les interfaces matérielles correspondent à une zone de mélange où les conditions d’interfaces (égalité des contraintes et des vitesses normal...
A multiphase hyperbolic model for dynamic and irreversible powder compaction is built. Four important points have to be addressed in this case. The first one is related to the irreversible character of powder compaction. When a granular media is subjected to a loading–unloading cycle, the final volume is lower than the initial one. To deal with thi...
Dans ce rapport, on présente un modèle hyperbolique d'écoulement multiphasique incluant la com- paction dynamique irréversible de poudres. Ce modèle doit être capable de remplir quatre principaux objectifs. Le premier objectif concerne le caractère irréversible de la compaction des poudres. Quand un lit de poudres est soumis à un cycle de charge-dé...
Diffuse interface methods have been recently proposed and successfully used for accurate compressible multi-fluid computations Abgrall [1]; Kapila et al. [20]; Saurel et al. [30]. These methods deal with extended systems of hyperbolic equations involving a non-conservative volume fraction equation and relaxation terms. Following the same theoretica...
An Eulerian conservative hyperbolic model of isotropic elastic materials subjected to finite deformation is addressed. It was developed by Godunov [S.K. Godunov, Elements of continuum mechanics, Nauka, Moscow, 1978 (in Russian) and G.H. Miller, P. Colella, A high-order Eulerian Godunov method for elastic–plastic flow in solids, J. Comput. Phys. 167...
Résumé : Un modèle d'hyper élasticité en coordonnées Eulérienne est rappelé. Un modèle multiphasique hyperbolique à une pression et une vitesse mais plusieurs températures pour la résolution de problèmes à interfaces entre solides et fluides est proposé. La formulation de ce modèle est Eulérienne, ce type d'approche étant plus adapté aux grandes dé...