This paper addresses a multiscale strategy for the prediction of anhysteretic magneto-elastic behavior and its application to the definition of a magneto-elastic constitutive law for Terfenol-D. The multiscale modeling is based on an energetic procedure at the single crystal scale. Localization and homogenization procedures are then applied to deduce the constitutive law of polycrystalline media from the behavior of the corresponding single crystal. The method is applied first to define the magneto-elastic behavior of single crystals, and the application to polycrystalline samples is then considered. Modeling results are compared to experimental data.PACS. 75.80.+q Magnetomechanical and magnetoelectric effects, magnetostriction -46.25.Hf Thermoelasticity and electromagnetic elasticity (electroelasticity, magnetoelasticity)

In this paper, harvesters coupling magnetostrictive and piezoelectric materials are investigated. The energy conversion of quasi-static magnetic field variations into electricity is detailed. Experimental results are exposed for two macroscopic demonstrators based on the rotation of a permanent magnet. These composite/hybrid devices use both piezoelectric and magnetostrictive (amorphous FeSiB ribbon or bulk Terfenol-D) materials. A quasi-static (or ultra-low frequency) harvester is constructed with exploitable output voltage, even in quasi-static mode. Integrated micro-harvesters using sub-micron multilayers of active materials on Si have been built and are currently being characterized.

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Giant magnetostrictive materials (GMM) can be integrated in actuator or sensor applications. The design of these systems is optimized based on a good knowledge of the material properties and conditions of use. Terfenol-D exhibits the greatest room temperature strain among commercially available GMM, however, its magneto-elastic behavior is very sensitive to prestress level. In this work, the design of an experimental setup dedicated to the characterization of GMM magneto-mechanical behavior under constant stress is described. A major difficulty is to master the mechanical boundary conditions while the sample is subjected to dynamic magnetic loading. The dynamic stress experienced by the sample is connected to the magnitude of the magnetostriction strain, the stiffness of the sample and the stiffness of the characterization setup. Results show that an appropriate setup is able to reduce the dynamic stress variations induced by magnetic excitation variations below 0.1 MPa, while this dynamic stress can reach up to 20 times the magnitude of the applied stress when the control system is not used. With the boundary conditions being controlled, magnetic and magnetostrictive behavior of Terfenol-D are characterized under various uniaxial compressive stress levels, from the stress-free conditions to 90 MPa. By comparing the results obtained under controlled and non-controlled stress conditions, it is shown that uncontrolled boundary conditions can be responsible for errors of several percent on the magnetic induction measurement. The measurement of strain is even more sensitive to the boundary conditions, with errors up to 40% and 30% on the longitudinal and transverse strains, respectively. This work highlights the utmost importance to control the boundary conditions in order to characterize the magneto-mechanical behavior of GMM.

An integral method using the magnetic scalar potential to solve nonlinear magnetostatic problems is developed. This method uses the range interactions between magnetizable elements and it is particularly well suited to compute field in the air domain which do not need to be meshed. The collocation and Galerkin approaches are presented and compared to solve the nonlinear magnetostatic equation. Both methods need the construction of full interaction matrices which may be computed with analytical formulae. A Newton-Raphson method, in which the interaction matrix must be built at each solver iteration, is used to solve the nonlinear formulation. A modified fixed point scheme, in which the interaction matrix is built only once, is also proposed. 3-D numerical examples are given and results of the different methods are compared.

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SUMMARYMagnetic forces are computed in the scope of magnetostatic problems solved by a volume integral method. This method uses the range interactions between magnetizable elements and is particularly well suited to compute the fields without meshing the air domain. This paper proposes an adaptation of the virtual work principle to the framework of the volume integral method in order to compute the magnetic forces. First, its application for electromagnetic devices in the nonlinear case allows to compute the global magnetic force. Second, its local application in the linear case provides a magnetic force density. 3D numerical examples are given, and the results are compared with the analytical solution and the finite element method.

This article deals with the use of the Volume Integral Method (VIM) to compute the magnetic anomaly created by a non-conductive ferromagnetic thin shell placed in a static inductor field. An original facet integral formulation considering the magnetic induction as unknowns is presented. The use of thin shell element assumption leads to a surface mesh decreasing highly the number of elements so the computation cost. The method is very performant in terms of speed and accuracy. Index Terms-Magnetostatic, volume integral method, thin shell element, shielding modeling.