Chaos in free electron laser oscillators

The chaotic nature of a storage-ring Free Electron Laser (FEL) is investigated. The derivation of a low embedding dimension for the dynamics allows the low-dimensionality of this complex system to be observed, whereas its unpredictability is demonstrated, in some ranges of parameters, by a positive Lyapounov exponent. The route to chaos is then explored by tuning a single control parameter, and a period-doubling cascade is evidenced, as well as intermittence.Comment: Accepted in EPJ

Conditions de bifurcation à l’intérieur et aux frontière pour une classe de matériaux non-standards. (Bifurcation conditions inside and at the boundary for a class of non-standard materials)

International audienc

Phénomènes de localisation à la frontière d’un solide. (Localization phenomena at the boundary of solids)

International audienc

A multiscale model for magneto-elastic couplings

At the macroscopic scale two different phenomena illustrate the couplings between the elastic and magnetic behaviours of ferromagnetic materials : first, magnetisation induces a deformation mechanism called magnetostriction, and, second, stresses have an effect on the magnetic behaviour. The complexity of the non-linear relations between these phenomena is such that few realistic macroscopic constitutive equations have been proposed to model the coupled magneto-elastic behaviour of magnetic materials. Magnetisation and magnetostriction are macroscopic manifestations of the complex magnetic domain structure that is modified by applied mechanic and magnetic loads. Herein, it is proposed to use homogenisation methods to deduce the macroscopic behaviour of single crystals and polycrystals from a statistical description of the magnetic domain structure. Therefore, the macroscopic couplings naturally arise from the expression of the free energy written at the level of the magnetic domains

Continuum damage mechanics and local approach to fracture: Numerical procedures

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Constitutive model for flake graphite cast iron automotive brake disks: From macroscopic multiscale models to a 1D rheological description

International audienceOne of the critical points of the thermomechanical fatigue design process is the correct description of the cyclic behavior of the material. This work focuses on the material of automotive brake disks, namely, flake graphite cast iron. The specificity of this material is its asymmetric behavior under tensile and compressive loadings, which is due to the shape of graphite that acts as small cracks. Multi-scale models inspired from the literature are first presented. They lead to a good description of the material behavior under cyclic loadings. An elasto-viscoplastic constitutive model is then proposed in a one dimensional setting in order to accurately describe cyclic tests from room temperature up to 600 °C

Identification of frequency effect on magnetic hysteresis and modelling with an internal variables model

In this paper, the first magnetisation response experimentally observed on 0.5 nim thick sheets made of a non-oriented silicon-iron alloy is given for different magnetic loading frequencies from 0.05 to 500 Hz. An internal variable magnetic hysteresis model is identified from the quasi-static response (from 0.05 to about 5 Hz). This model is used for finite element analyses performed to predict the electro-magnetic response of the material at higher frequencies. The comparison between the results of these structural analyses and the experimental results proves that in this case the macroscopic eddy currents are sufficient to explain the total frequency effect on the magnetic hysteresis measurements

Influence of the texture of soft magnetic materials on their magneto-elastic behaviour

Magnetisation and magnetostriction are macroscopic manifestations of a complex magnetic doinain structure that is modified by applied mechanic and magnetic loads. In the multiscale model used in this paper this doinain structure is statistically described by a set of internal variables that are defined in each grain. This model is used to predict the evolutions of macroscopic state variables that are related to original partitions of the magnetisation and magnetostriction. This approach is used to predict the influence of the crystallographic texture of the material on its magneto-elastic behaviour

Experimental analysis and multiscale modelling of the anisotropic mechanical and magnetostrictive behaviours of electrical steels

Non-Oriented (NO) iron-silicon laminations are commonly used in electrical engineering. Although these materials are assumed to exhibit a quasi-isotropic behaviour in the sheet plane, some specific coupled properties such as magnetostriction are very sensitive to a weak crystallographic texture. Magnetostriction is the strain mechanism that is induced by a magnetic field. This deformation contributes to the noise emitted by electrical machines. An experimental study of the process-induced anisotropy is presented, for both elastic and magnetostrictive behaviours. A multi-scale approach is then proposed, taking into account two sources of anisotropy: the usual cubic anisotropy at the grain scale, and the heterogeneous orientation of the grains (crystallographic texture) at the macro scale. It is shown that specific surface effects must be taken into account in the description of the anisotropy of industrial iron-silicon laminations