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Communication Dans Un Congrès Année : 2021

A FEM-BEM multiphysics coupling for the modeling of magnetoelectric composite structures

Résumé

This study concerns the modeling of structures made of composite materials with magnetoelectric effects arising from the combination of magnetostrictive and piezoelectric materials. Modeling these effects requires consideringan electro-magneto-mechanical problem derived bycoupling equations describing active materialssuch asTerfenol-D for the magnetostrictive phaseand PZT for the piezoelectric phase. A typicalmethod used for the resolution of this kind of problemis the finite element method(FEM). Although this method is general and has proven to be effective in many instances, it can becomecomputationally expensive, particularlyfor electromagnetic problems whereactive materials and coils are distantfromeach otherthus necessitating a huge mesh of air. In our case, the FEMis well adapted to the modeling of electro-mechanical coupling. Indeed, the large permittivity of piezoelectric materials makes the electric field leaks negligible.For magneto-mechanical coupling involving a small volume of active magnetic materials compared to air, FEM becomes expensive. Coupling between finite element method and boundary element method offers the possibility to not have to mesh the air while still providing excellent results(G. Meunier, J. Coulomb, S. Salon, and L. Krahenbul, “Hybrid finite element boundary element solutions for three dimensional scalar potential problems,” IEEE Transactions on Magnetics, vol. 22, no. 5, pp. 1040–1042, Sep. 1986). In this work an approach coupling FEM, for the electric and mechanicalfields, and BEM, for the magnetic field, is proposed to solve problems involving a reduced volume of active materials.The magnetostrictive phenomenon is strongly nonlinear, but it will be consideredlinear as a first approximation.Two dual formulations of the magneto-mechanical problemwill be presented, based on total magnetic vector potential and reduced magnetic scalar potential formulations respectively.The electro-mechanical problem is solvedby a classical FEM formulation. The electro-magneto-mechanical coupling isthen expressed by a matrix block system with sparse matrices for the mechanical and electrical problemsand full matrices for the magnetic problem. The resulting system is solved using theblockGauss-Seidel methodwith linear solvers adapted to the type of matrix, i.e, MUMPS used for sparse matrices and GMRES used for full matrices.Results of the two formulations and their performance will be compared.
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Dates et versions

hal-03264866 , version 1 (18-06-2021)

Identifiants

  • HAL Id : hal-03264866 , version 1

Citer

A Urdaneta-Calzadilla, O Chadebec, N Galopin, I Niyonzima, G Meunier. A FEM-BEM multiphysics coupling for the modeling of magnetoelectric composite structures. EMF'2021 - The 12th International Symposium on Electric and Magnetic Fields, Jul 2021, Online, France. ⟨hal-03264866⟩
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