Conference Agenda

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Session Overview
PC-A2: Material Modelling, Multi-Scale Modelling and Homogenization
Thursday, 18/Jul/2019:
2:20pm - 4:10pm

Session Chair: Lin Li
Session Chair: Paavo Rasilo
Location: Patio 44-55

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Finite Element Modeling of Magnetic Properties Degradation Due to a Plastic Deformation

Nabil M'Zali1,2, Thomas Henneron1, Abdelkader Benabou1, Floran Martin2, Anouar Belahcen2, Ravi Sundaria2

1Univ. Lille, Arts et Metiers ParisTech, Centrale Lille, HEI, EA 2697 - L2EP - Laboratoire d’Electrotechnique et d’Electronique de Puissance, F-59000 Lille, France; 2Department of Electrical Engineering and Automation, Aalto University, Aalto FI-00076, Finland

In this work the anhysteretic Sablik model is identified from measurements and implemented in a finite element code. The model takes into account the effect of the plastic deformation through the dislocation density and thus enables it to account for the degradation of the magnetic properties. Experiment data are used to identify the parameters of the model and simulations were carried out on a steel sheet impacted by a plastic deformation. Results of the simulations carried out on an electric machine and some further improvement in the Sablik model will be presented in the full version

A Temperature and Stress-Dependent Hysteresis Model with Experimental Validation

Weijie Xu1, Nana Duan2, Yongjian Li3, Shuhong Wang2, Jianguo Zhu4

1State Grid Shaanxi Electric Power Company, Construction Branch, China; 2School of Electrical Engineering, Xi’an Jiaotong University, China; 3School of Electrical Engineering, Hebei University of Technology, China; 4Faculty of Engineering and Information Technologies, The University of Sydney, Australia

The magnetic properties of magnetic material under work conditions will be influenced by some non-magnetic factors, such as temperature and stress. In this paper, based on the microscopic magnetization mechanisms of magnetic materials, a hysteresis elemental operator has been presented. Besides, by taking into account the differences between the laboratory conditions and the practical engineering manufacturing and operation, the temperature-depended saturation magnetization, temperature-depended anisotropy, and stress-depended distribution function are introduced to the hysteresis elemental operator. With the employment of the Gaussian-Gaussian distribution function and the interaction field, a temperature and stress dependent hysteresis model is proposed to simulate the magnetic properties under different temperature and stress conditions. Besides, with the help of the energy minimum principle, the octagonal law which can determine the orientation of the magnetization has been introduced. Finally, by comparing the simulation results with the experimental measurement results, the effectiveness and viability of this proposed hysteresis model have been confirmed.

3D modelling of the thermal runawway in ceramic flash sintering

François Henrotte1, Jean-François Fagnard1, Christophe Geuzaine1, Philippe Vanderbemden1, Laurent Boilet2, Jean-Pierre Erauw2, Caroline Gajdowski2

1ULiege, Belgium; 2BRC, Belgium

This paper presents the 3D multi-physics finite element modelling of the thermal runaway associated with the flash sintering ceramics. With appropriate linearization, whose validity is discussed, and a specific time integration scheme,

the model is shown to be able to capture effectively the thermal instability.

Investigation of surface induced-residual stresses due to hammer peening using needle probes technique

Yves Armand Tene Deffo1, Pierre Tsafack1, Benjamin Ducharne2

1Faculty of Engineering and Technology of the University of Buea, CAMEROON; 2LGEF INSA Lyon, FRANCE

Hammer peening is an important surface work hardening process widely used in industries for fatigue retardation of mechanical parts. It is a shot peening process based on the principle of preventing dislocation movement in the surface layer either by creating substantial levels of compressive residual stress or by reducing the surface roughness in thin near-surface layers of material. The constructive effect extent of hammer peening process on material properties and the residual stresses inherited from the processing history of the component, however, are dimmed by the degree of favorable compressive residual stresses or dislocation density introduced in the material. Investigating the extent to which hammer peening process may result in positive compressive residual stresses via experimental evidence will be the purpose of the present study. Then, a magneto-mechanical model of the subject material due to shot peening surface induced-residual stresses will be introduced based on the Jiles-Atherton-Sablik (JAS) model. The needle probe method was used for local measurement of magnetic properties.

Computation of transformer iron losses under saturation using the Fourier method - Part 1: Spectra for core loss calculation

Wei Wang1, Arne Nysveen1, Niklas Magnusson2, Robert Nilssen1

1Norwegian University of Science and Technology, Norway; 2SINTEF Energy Research

Computation of iron losses in transformers requires significant numerical efforts, particularly under magnetic saturation when the magnetic non-linearity needs to be considered. This paper proposes a Fourier method for calculation of the magnetic flux density and the core loss in transformers under saturation. The proposed method has the advantage of easy implementation and short calculation time. It includes pre-processing of the non-linear material. A permeability frequency spectrum is obtained from Fourier analysis, where the fundamental part is used as magnetization definition and the harmonic components are used for loss calculation. The results obtained by this method are compared to those given by a corresponding time domain calculation.

Computation of transformer iron losses under saturation using the Fourier method - Part 2: Stray loss

Wei Wang1, Arne Nysveen1, Niklas Magnusson2, Robert Nilssen1

1Norwegian University of Science and Technology, Norway; 2SINTEF Energy Research

Computation of iron losses is a heavy numerical task, and the problem is further complicated by magnetic non-linearity when saturation is considered. In an accompanying paper, a Fourier method for calculation of the transformer core loss under saturation is presented. In this paper, the influence of the definition of the core material on leakage field and the associated stray loss calculation is studied. Based on a frequency domain field-current scan, a waveform correction factor is introduced which enables stray loss estimation of non-sinusoidal excitation. The results obtained by this method are compared to those given by a time-domain calculation to evaluate the accuracy of the method.

Homogenization of lamination stacks based on the vector potential formulation

Mohammad Issa1, Laurent Krähenbühl2, Clair Poigard3, Jean-René Poirier1, Ronan Perrussel1

1LAPLACE, Université de Toulouse, CNRS, INPT, UPS; 2Université de Lyon, Ampère CNRS, Ecole centrale de Lyon; 3Université de Bordeaux, INRIA CNRS

We present an effective modelling of a lamination stack in 1d using classical homogenization and a correction for the interface between the air and the lamination stack. We consider the case where the skin depth is kept less than or equal to the thickness of one metal sheet.

Non-local Third Boundary Conditions and its Application in Multi-scaled Modelling

Miaosong Gu, Xiang Cui, Xuebao Li, Zhibin Zhao, Mingyang Li

North China Electric Power University

This paper proposes a novel non-local third boundary condition (NLBC), applicable to linear partial differential equations, to describe the relationship between the electric field and the potential on the boundary of a single connected domain. The information inside the non-uniform dielectric sphere, such as geometry and parameter distribution, is reflected by this boundary condition so that the multi-scaled modelling and decoupling of the electric field calculation inside and outside the dielectric sphere can be realized. To illustrate this method in detail, a special kind of inhomogeneous dielectric ball is calculated whose permittivity changes continuously in a radial direction. The results show that the method can significantly save computing resources in a system containing multiple particles.

Effect of bending stress on the magnetic properties of electrical steel using needle probe method

Yves Armand Tene Deffo1, Pierre Tsafack1, Benjamin Ducharne2, Minh Quyen Le2, Pierre-Jean Cottinet2

1Faculty of Engineering and Technology of the University of Buea, CAMEROON; 2LGEF INSA Lyon, FRANCE

The changes in magnetic hysteresis of electrical steel due to the effect of surface stress-induced magnetic flux leakage around bends is investigated. This paper deals with the bending angle impact on magnetic properties of electrical steels subjected to bending stress. Test samples are five equal strips extracted from a single wrought iron sheet, four of which subjected to bending stresses to create 130°, 150°, 160° and 170° bending angles respectively, and a reference strip at 180°. Hysteresis patterns of the test samples were compared for response to bending angles. Also, a graphical relation between magnetic flux leakage and bending angles at the top and bottom bending tips is deduced from the earlier pattern. Measurements of magnetic properties was carried out using the needle probe method. Bending stress results in significant magnetic flux leakage observed at the bottom bending tip of each sample due to uniform distribution of magnetic flux around tips. This effect was observed to increase with bending stress and angle.

Reduce vector dynamic hysteresis model, for lump model applications or for integration in space discretized simulations

Benjamin Ducharne1, Bin Zhang2, Yves Armand Tene Deffo3, Gael Sebald4

1LGEF INSA Lyon, FRANCE; 2SHANDONG University, CHINA; 3Faculty of Engineering and Technology of the University of Buea, CAMEROON; 4ELyTMaX, Tohoku University Sendai, Japan

Even if vector dynamic hysteresis models have been proposed and studied since many years, the so-called ideal model (accurate, fast, and based on less parameters and memory allocation …) is still missing. Even if progresses in computer science have allowed large improvement in the numerical simulation domain, high non-linearity property of vector dynamic hysteresis is still a challenge. In this article, we described a non-congruent vector dynamic hysteresis model based on a dry-friction type equation quasi-static contribution extended to the dynamic behavior using fractional derivatives. The model is fast, accurate and particularly well adapted to space discretized simulations.

Study of Inter-Ply Electrical Percolation Phenomena in CFRP Composite Materials

Banda Kane, Guillaume Wasselynck, Didier Trichet, Gerard Berthiau

IREENA, Université de Nantes, Saint-Nazaire Cedex, France

In this paper, a predictive homogenization model that takes into account electrical percolation is used to predict the electrical properties of a unidirectional carbon-epoxy composites. A calculation of the tensor of electrical conductivities is proposed for different sequences of ply of a stratified composite material in order to highlight the phenomena around the interface between the plies.

A New Dynamical Magnetic Model for the Transient Computation of Eddy Current Losses in Laminated Iron Cores

Maxime Tousignant1,2,3, Gérard Meunier1, Frédéric Sirois2

1Univ. Grenoble Alpes, CNRS, Grenoble INP, G2Elab, 38000 Grenoble, France; 2Polytechnique de Montréal, Montréal, Canada; 3Altair Engineering France, 38240 Meylan, France

In this paper, we present a new transient dynamical model to accurately take into account the eddy current losses in laminated iron cores. The model is based on a medium frequency approximation of the analytical solution to the linear 1-D eddy current problem that is accurate up to 5 kHz in the linear case. We also developed an extension of the model that can be applied in the nonlinear case and is accurate up to approximately 1 kHz.

Eddy Current Non Destructive Evaluation Model of Composite Materials with Considering of Capacitive Effect

Samir Bensaid1, Omar Adib Safer1,3, Didier Trichet2, Guillaume Wasselynck2, Javad Fouladgar2, Gerard Berthiau2

1Laboratoire des Matériaux et du Développement Durable (LM2D), Université de Bouira, Algeria; 2Institut de Recherche en Energie Electrique de Nantes Atlantique,Saint-Nazaire, France; 3Laboratoire de Génie Electrique (LGE), University de M'sila, Algeria

This paper presents a modeling approach of eddy current Non Destructive Evaluation of Unidirectional Carbon Fiber Reinforcement Composite (UD-CFRC) rods with taking into account of capacitive effect. To construct the model, the following three steps must be respected. In the first step, the multilayer solenoidal air coil is modeled with an axisymmetric eddy current model formulated with a coupled finite element model (FEM) and equivalent electrical circuit model (EECM), without taking into account the capacitive effect. The complex impedance of each coil layer is computed for several frequencies, then it is introduced into the EECM with considering the equivalent capacitors of each layer and between all neighboring layers. After that, the total impedance of the coil is computed for each frequency. The difference between computed and measured impedances is minimized until reaching the convergence criterion of the goal function using the simulated annealing optimization algorithm. All capacitances of the coil are thus identified. In the second step, the transverse conductivity of the homogenized UD-CFRC rod is identified using a coil with a low number turns at the frequency less then 2MHz, where the capacitive effect is neglected. The last step, consists to introduce the UD-CFRC rod, in the FEM coupled to EECM, as a homogenized conductive material with the identified transverse conductivity. Finally, the coil with a presence of the UD-CFRC rod is modeled as a transformer with secondary short-circuited on a capacitor. This latter, allows to take into account the displacement current in the UD-CFRC rod. Its value is determined manually by the FEM-EECM. All the identified parameters are then introduced in the coupled FEM-EECM to compute the impedance. The curves of the computed impedance, real and imaginary parts, are confronted to those obtained with experiment.

Modelling of Anomalous Eddy Current Loss Due to Movement of Domain Wall in Particle of Soft Magnetic Composite

Yanhui Gao1, Yusuke Araki1, Hiroshi Dozono1, Kazuhiro Muramatsu1, Weimin Guan2, Jiaxin Yuan2, Cuihua Tian2, Baichao Chen2

1Saga University, Japan; 2Wuhan University, P. R. C.

Soft magnetic composite (SMC) is composed of ferromagnetic particles surrounded by electrical insulation. SMC has advantages such as three-dimensional (3D) isotropic magnetic characteristics, low eddy current loss, and easy to be manufactured into complex shapes compared with electrical steel sheets. To establish a homogenization technique for the magnetic field analysis of an electrical machine using SMC, we have already proposed a method to evaluate the effective permeability and iron loss taking account of nonlinear magnetic characteristics and eddy currents by using a cell model composed of one particle of SMC. However, the measured eddy current loss cannot be represented by using the proposed method. The reason seems to be the neglect of anomalous eddy current loss in the proposed method. In this paper, a method of modeling the anomalous eddy current loss due to the movement of the domain walls in the cell model is developed using 3-dimensional eddy current analysis of the Pry and Bean magnetic domain model. Then, the anomalous eddy current loss obtained from the developed method is compared with the classical eddy current loss. It is shown that the anomalous eddy currents due to the movement of the domain walls are 30-45 % of the classical one at 0.1-100 kHz.

Coupled Numerical and Experimental Identification of Geometrical Parameter for Predicting the Electrical Conductivity of CFRP layers

Banda Kane1, Antoine Pierquin1,2, Guillaume Wasselynck1, Didier Trichet1

1IREENA, Université de Nantes, Saint-Nazaire Cedex, France; 2Institut de Recherche Technologique (IRT Jules Verne), Chemin de Chaffault, 44340 Bouguenais, France

The analysis of the local structure of a unidirectional (UD) composite material sample requires a lot of resources and measurement techniques. To get around this constraint, the real composite material is replaced by a virtual material having the same overall behavior. However, some parameters still must be defined based on measurement results. In this paper an approach to determine the parameters to generate a virtual material is presented in order to mimic the behavior of a real UD material in the three spatial directions.

Piezoelectric Constitutive Relations for Ferroelectric Materials Considering the Effect of Stress

Romain Corcolle1,2, Laurent Daniel2

1NYU Shanghai, People's Republic of China; 2GeePs, France

This abstract presents a model for the determination of piezoelectric coefficients of ferroelectric materials. When large levels of stress are applied to such materials, a change in the piezoelectric coefficients is induced. This effect has been observed experimentally, but no predictive model actually exists for that effect. The proposed model is based on an anhysteretic multiscale model for ferroelectric materials and the predicted effect of stress on piezoelectric coefficients shows a good qualitative agreement with experiments.

A Multiscale FEM for the Eddy Current Problem \\ with $\boldsymbol{T},\Phi - \Phi$ in Laminated Conducting Media

Karl Hollaus, Markus Schöbinger

Vienna University of Technology, Austria

To avoid the necessity of modeling each laminate in iron cores of electrical devices for the eddy current problem a novel multiscale finite element method based on a current vector potential $\boldsymbol{T}$ and a reduced magnetic scalar potential $\Phi$ is presented for three-dimensional problems. Material properties are assumed to be linear. Hence, the methods are developed for the frequency domain. External currents are represented by the Biot-Savart-field serving as excitation. Planes of symmetry are exploited. Numerical simulations are presented showing very satisfactory results.

Magnetostriction simulation for EMAT signal analysis

Katsuhiko Yamaguchi1, Yoshiro Ueno1, Yuma Morii1, Tsugiko Takase1, Tetsuya Uchimoto2, Toahiyuki Takagi2

1Fukushima university, Japan; 2Tohoku university, Japan

The effect of magnetostriction on the intensity of ultrasonic wave generated in the iron based structural material by electromagnetic acoustic transducer (EMAT) was analyzed by Monte Carlo simulation. The orientation of the spin placed at each atom site of the body-centered cubic structure of iron was given a distortion effect by pseudo-dipole interaction, and the lattice coupling force was given by Morse potential. The calculation result shows good agreement with the direction dependence of the bulk iron magnetostriction. Furthermore, the magnetostriction effect was calculated when a magnetic field was applied in an arbitrary direction to the crystal orientation. As a result, it is shown that there is a possibility that the magnetostriction is canceled and the ultrasonic amplitude intensity is weakened when there are many regions where the crystal grain orientation is random.

Modelling of multiferroic nanoparticle composites with an analytical multiscale approach

Hakeim Talleb, Tuan-Anh Do, Aurélie Gensbittel, Zhuoxiang Ren

L2E/Sorbonne Université, France

An analytical mulitscale approach on the ferroelectric and ferromagnetic phases is proposed to modelling multiferroic artificial magnetoelectric composites constituted of piezoelectric and magnetostrictive nanoparticles under a volume fraction . The proposed approach is applied to the practice case of CoFe2O4n-(1-n)BaTiO3 composite. The homogenized material properties are incorporated in macroscopic scale to model a magnetoelectric device by using the finite element method.

The Heterogeneous Multiscale Method Applied to Two-dimensional and Three-dimensional Problems

Innocent Niyonzima1, Gérard Meunier1, Ruth Vazquez Sabariego2, Christophe Geuzaine3

1Univ. Grenoble Alpes, CNRS, Grenoble INP, G2ELab, F-38000 Grenoble, France; 2KU Leuven, Dept. Electrical Engineering (ESAT), Leuven & EnergyVille, Genk, Belgium; 3University of Liège, Dept. Electrical Engineering and Computer Science, Montefiore Institute B28, B-4000 Liège, Belgium

This paper explores the use of the heterogeneous multiscale method to model 2D and 3D nonlinear magnetoquasistatic problems. This method consists in solving a macroscopic problem defined on a coarse macroscopic mesh, and multiple mesoscale problems defined at the Gauss points of the macroscale mesh and that allow to upscale the unknown homogenized law. The cost of the method can be dramatically reduced by carrying out massive parallel resolution of the independent mesoscale problems.

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