Romain Corcolle

A Note on the Effective Magnetic Permeability of Polycrystals

Many classical estimates for the effective behavior of heterogeneous materials can be reinterpreted in terms of inclusion problems. However, in the case of cubic polycrystals, a cubic permeability tensor for single crystals has to be written. In the framework of linear behavior, the description of the cubic symmetry reduces to isotropy. The heterogeneity of polycrystals, which results from single crystal anisotropy, cannot be described, and the classical estimates for the overall behavior of heterogeneous materials cannot be used. In this paper, we propose a particular description of the cubic symmetry for the magnetic permeability. We then derive estimates for the effective permeability of polycrystals from the solution of the basic inclusion problem, for both macroscopically isotropic and anisotropic polycrystals.

Effective Permittivity of Shielding Composite Materials for Microwave Frequencies

Due to mass constraints, composite materials are possible candidates to replace metal alloys for electromagnetic shielding applications. The design of standard metallic shielding enclosures often relies on finite-element calculations. But in the case of composite materials, the strong dependence on the shielding properties to the microstructure makes the finite-element approach almost impossible. Indeed meshing the microstructure would imply a huge number of elements, incompatible with usual computational resources. We propose in this paper to develop homogenization tools to define the effective electromagnetic properties of composite materials at microwave frequencies. The ratio between the characteristic size of the microstructure and the wavelength is shown to be a key parameter in the homogenization process. The effective properties can then be used as an input for electromagnetic compatibility standard tools, designed for homogeneous media.

Modeling of a beam structure with piezoelectric materials: introduction to SSD techniques

Purpose – To provide a model that allows testing and understanding special damping techniques. Design/methodology/approach – The finite element modeling takes into account the piezoelectric coupling. It is used with a non linear electrical circuit. The approach leads to an accurate tool to observe the behavior of the non linear damping techniques such as synchronized switch damping. Findings – The model has been validated by comparison with Ansys® but the CPU time required for the model is around one hundred times shorter. Research limitations/implications – The proposed model is 1D and the assumptions to use it are not verified for all structures. Practical implications – The authors obtain a useful tool for the design of damping structures (for example to find the best localisation of the piezoelectric patches and to test electrical circuits). Originality/value – The model is used for the design and conception of damping as well as for harvesting structures.

A Homogenization Technique to Calculate Eddy Current Losses in Soft Magnetic Composites Using a Complex Magnetic Permeability

Soft magnetic composites (SMCs) are a promising alternative to laminated steel in many electrical engineering applications. This is largely owing to their low level of eddy current (EC) losses. The electromagnetic behavior of SMC in electromagnetic devices cannot be easily predicted using standard numerical techniques, such as the finite-element (FE) method, mostly due to the computational cost required to model the material microstructure. Another difficulty lies in the high contrast between matrix and inclusion properties. In this paper, we propose a homogenization strategy to estimate EC losses in SMC. It is based on the calculation of a homogenized complex magnetic permeability. The imaginary part reflects the EC losses, while the real part describes the standard magnetic permeability. The complex permeability approach is applied to SMC with fiber or spherical inclusions. EC losses obtained from the complex permeability approach are compared with FE calculations, with very satisfying agreement.

Intraphase fluctuations in heterogeneous magnetic materials

The main purpose of homogenization is the determination of the effective behavior (or macroscopic behavior) of heterogeneous materials. Mean fields per phase are generally used in homogenization and represent sufficient information in most cases. However, more information about the field distribution can be necessary, particularly in nonlinear cases. Then, intraphase fluctuations have to be determined. This paper presents a method, based on homogenization tools, for the determination of both estimates and bounds for the intraphase fluctuations. The presented applications deal with magnetic materials and the results obtained with homogenization are compared to those obtained using a finite element modeling.

Influence of skin effect on the effective shielding effectiveness of composite materials

Composite materials are increasingly used to contribute to structure lightening in electromagnetic shielding applications. The interactions between electromagnetic waves and composite materials are highly dependent on their microstructure. This gives rise to challenging modelling issues. Considering details of the microstructure would involve an excessive number of unknowns with standard numerical tools for structural analysis. Homogenisation methods—such as Maxwell-Garnett model—are a possibility to overcome this problem. The equivalent homogeneous medium obtained with such methods can be introduced into numerical tools to model full shielding enclosures. A homogenisation model has been recently proposed to obtain the equivalent homogeneous properties of composite materials subjected to electromagnetic waves. It relies on the introduction of a length parameter into classical non dimensional semi-analytical homogenisation methods—also known as mean field approaches. The model is applicable at microwave frequencies as long as the induced currents in the fibres (or inclusions) of the composite materials remain weak. This paper proposes an extension of the approach to include skin effect in the homogenisation method. This is done by considering Joule losses within the fibres of the composite. This extension significantly broadens the frequency range covered by the model. The results show that the optimization of composite shielding properties relies on a subtle compromise between internal reflections and Joule losses.

Shielding Effectiveness of Composite Materials: Effect of Inclusion Shape

The use of composite materials for electromagnetic shielding applications contributes to the effort of structure lightening in aerospace industry. In these materials the strong interaction between the electromagnetic field and the microstructure makes the standard numerical tools difficult to implement. Indeed these methods would involve an excessive number of degrees of freedom to describe details of the microstructure. An efficient way to overcome this problem is the use of homogenization techniques providing the effective properties of heterogeneous materials. These effective properties can then be introduced in standard numerical tools to estimate the behavior of shielding enclosures. A recent paper proposes an extension to microwave frequencies of quasistatic homogenization methods. It introduces a characteristic length for the microstructure in the case of a square array of circular 2-D conductive phases embedded in a dielectric matrix. In this paper, a method to identify this length parameter is proposed for random microstructures.

Modeling of a Plate Structure With Piezoelectric Patches: Damping Application

Vibrations in thin structures are often not desired, especially because of their harmful effects on lifespan. The addition of piezoelectric materials with appropriate connections can really be useful to reduce this drawback. To study such a damping effect, numerical modeling is necessary and leads to a coupled problem (between mechanics and electricity). This paper presents a 2-D model of a plate with piezoelectric patches. From the coupled behavior laws and with the use of a variational formulation, a finite element model is developed. After a validation process, the influence of the width of piezoelectric patches on damping is studied.

Optimal Design of Magnetostrictive Composites: An Analytical Approach

Giant magnetostriction materials, such as Terfenol-D, have allowed the development of a new class of actuators and sensors based on magnetoelastic properties. However, their mechanical properties are a limiting factor for some applications. Composites, made of Terfenol-D particles in a matrix, can bypass these limitations, improving the overall mechanical properties while maintaining the magnetostriction effect. But, to optimize the design of magnetostrictive composites, advanced modeling tools are needed. This paper proposes a homogenization model based on inclusion problems. It compares modeling results to experimental data from the literature, and it illustrates the use of the model as a tool for optimal design.

Second Order Moments in Linear Smart Material Composites

Homogenization is a mean field approach for the determination of the effective properties of heterogeneous materials. It can provide the average fields per phase but also some information about the field distribution such as second order moments. The use of second order moments of fields can notably improve the estimates of the macroscopic behavior in the nonlinear case. This has been studied mainly in the case of uncoupled behavior. We propose to define second order moments in the case of coupled elasto-magneto-electric behavior using homogenization tools. The results are compared to the field fluctuations obtained from a finite element model.