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Finite element simulation of ferromagnetic shape memory alloys using a revised constitutive model

In this article, a previously developed constitutive model for ferromagnetic shape memory alloys is phenomenologically enhanced using experimental observations. A modified phase diagram along with a method for calibration of the required model parameters is further presented. The model is implemented into a user material subroutine to equip commercial finite element software ABAQUS with the capability of simulating magneto-mechanical behaviors of ferromagnetic shape memory alloys. A combined convergence scheme is employed to solve the implicit equations. The proposed model together with the presented numerical solution is shown to be able to study shape memory effect and pseudoelasticity at different constant magnetic fields. The simulated magnetic loading/unloading cycles at different constant stresses are found to be well-fitted to the experimental findings. As a practical application of the ferromagnetic shape memory alloy coupled magneto-mechanical response, a spring actuator (a bias spring serially connected to one ferromagnetic shape memory alloy element) is investigated, and the numerical predictions are shown to be in a good agreement with available experimental results. As a novel case, geometrically graded NiMnGa elements are also introduced and are simulated with the use of this approach.