A FEM-BEM coupling for the modeling of linear magnetoelectric effects in composite structures

International audienceThe aim of this study is to model magnetoelectric effects involved in laminate composites made of magnetostrictive and piezoelectric materials. We therefore have to consider an electro-magneto-mechanical problem derived by coupling equations describing active materials, as Tefenol-D for magnetostrictive layers and PZT for piezoelectric layers [1]. The reference method for the resolution of this type of problems is the finite element method. Although this method is general and largely proven, it can be computationally expensive, especially for low-frequency electromagnetic problems where the resolution may require meshing the air and considering an infinite box to simulate the decay of electromagnetic fields at infinity. In our case, this method is well adapted to the modeling of electro-mechanical coupling. Indeed, the large permittivity of piezoelectric materials makes the electric field leaks negligible. It may become expensive for the modeling of the magneto-mechanical coupling especially if the volume of the active magnetic materials is very small compared to the volume of the air leading to a huge mesh with a lot of air. To solve this type of problem without having to mesh the air, coupling between finite element method for the active material and boundary element method for the air region have already been used with excellent results [2]. We will therefore use this type of method in the modeling of the magnetic problem. Although the magnetostrictive phenomenon is strongly nonlinear, we will consider it as linear as a first approximation. This approximation makes it dual to the piezoelectric phenomenon. The electro-magneto-mechanical coupling is therefore expressed by a linear matrix block system with sparse matrices for the mechanical and electrical problem and full matrices for the magnetic problem. The resulting linear system is solved using the Gauss-Seidel method with linear solvers adapted to the type of matrix, i.e, MUMPS used for sparse matrices and GMRES used for full matrices