Two-Dimensional Versus Three-Dimensional Finite-Element Method Simulations of Cantilever Magnetoelectric Sensors

This paper investigates the suitability of two-dimensional (2D) finite-element method (FEM) simulations to model the quasi-static bending-mode response of cantilever magnetoelectric (ME) sensors. We compute the deformation of the cantilever due to an applied magnetic field across the magnetostrictive (MS) layer as well as the generated voltage across the piezoelectric (PE) layer by solving a system of coupled linear elastostatic/elastodynamic and electrostatic/magnetostatic equations. In the 2D FEM formulation a plane-stress boundary condition is employed. Both 2D and 3D FEM results are compared for varying cantilever length and width. For cantilevers with length >> height >> width good agreement is obtained between 2D and 3D results. For cantilevers obeying the condition length >> width >> height, a systematic deviation occurs between 2D and 3D results as the plane-stress condition does not model the situation in the center of the cantilever. For a length:width:height ratio of 25:5:1, a difference in generated voltage of ~12% is obtained for the Terfenol-D-PZT-Si material system. Especially for cantilevers with high aspect ratios, we show that 2D FEM simulations are sufficient to investigate the ME properties.