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 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 (Fe 84 Ga 16 ) active layers.
The bidirectionally coupled magnetoelastic model (BCMEM) developed by Mudivarthi et al (2008 Smart Mater. Struct. 17 035005) has been extended to include electric
currents in its magnetic finite element formulation. This enables the model to
capture the magnetoelastic behavior of magnetostrictive materials subjected to
elastic stresses and magnetic fields applied not only using permanent magnets
but also the current carrying coils often used in transducer applications. This
model was implemented by combining finite element solutions of mechanical and
magnetic boundary value problems using COMSOL Multiphysics 3.4 (finite
element modeling software) with an energy-based nonlinear magnetomechanical
constitutive model. The coupling variables are magnetostriction and magnetic
permeability, which are dependent on both the magnetic (magnetic flux density) and
the mechanical (stress) states of a magnetostrictive material. In this research,
the BCMEM was used to simulate actuator load lines for a magnetostrictive
Fe84Ga16
alloy, which were then compared with experimental data (Datta and Flatau 2008
Proc. SPIE 6929 69291Z). Also, the ability of the BCMEM to capture the
ΔE
effect in Galfenol was demonstrated. Finally, the use of the BCMEM as a tool for
transducer design optimization is demonstrated by using the model to visualize
the influence of different magnetic circuit designs on transducer performance.
A non-linear magnetomechanical plate model has been developed to predict the magnetic induction, elastic and magnetostrictive strain and mechanical stress in a laminated structure with magnetostrictive and non-magnetic layers under the simultaneous effect of quasi-static mechanical stress and the magnetic field. This model was obtained by coupling classical laminated plate theory to an energy-based statistical magnetomechanical model. The model was used to study a unimorph structure having a magnetostrictive iron-gallium (Galfenol) patch attached to a non-magnetic aluminum substrate. The sensing responses from the patch were obtained for in-plane axial and shear forces as well as bending and twisting moments acting on the unimorph. The effect of the DC bias magnetic field and the ratio of patch thickness to substrate thickness on the sensor performance was studied. The results demonstrate that the model can capture the non-linearity in the magnetomechanical process and the different structural couplings.
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