FEM-BEM Modeling of Nonlinear Magnetoelectric Effects in Heterogeneous Composite Structures

This article proposes a multiphysics multimethod model for 3-D nonlinear magnetoelectric (ME) effects in heterogeneous composite structures made of the association of piezoelectric and magnetostrictive materials. Through the coupling of the finite element method (FEM) with the boundary element method (BEM), only the active material is explicitly considered, and thus a single mesh is used for the resolution of all the physics. A mixed formulation combining the vector potential in the volume and a scalar potential in the free space is used to model magnetic phenomena. Nonlinear constitutive laws for the magnetostrictive phase are derived from partial derivatives of a scalar invariant’s formulation of the Helmholtz free energy, while linear relations are used to describe piezoelectric behavior. The coupled problem is solved by iteratively solving single-physics problems, and the full algorithm is used to model a rotating coilless ME device which can operate as an energy harvester or as an actuator.