A bidirectionally coupled magnetoelastic model and its validation using a Galfenol unimorph sensor

This paper describes a bidirectionally coupled magnetoelastic model, BCMEM. BCMEM is a 3D nonlinear finite element-based model comprising magnetic and elastic boundary value problems (BVPs) that are bidirectionally coupled through stress and field dependent coupling variables-magnetostriction and magnetization. The coupling variables are calculated using an energy-based magnetomechanical model. The BVPs are solved iteratively using the finite element method with values of coupling variables updated every iteration to account for the bidirectional coupling. Such an approach is effective in incorporating the apparent variation in modulus of elasticity (the Delta E effect) and permeability with changing stress and magnetic field, as well as modeling their effects on stress and field distributions. Thus, BCMEM allows the prediction of both nonlinear sensing and actuating behaviors of magnetostrictive materials. Moreover, the use of the finite element method provides the model with the ability to incorporate demagnetizing fields due to shape anisotropy and hence the capability to predict the response of magnetostrictive materials in complex 3D structures. The model predictions of magnetic flux density and bending strain for an aluminum-Galfenol unimorph cantilever structure showed good correlation when compared against experimental results obtained from both magnetically unbiased and biased single-crystal Galfenol (Fe84Ga16) active layers.