Analytical 3D model for coupled magneto-mechanical behaviors of ferromagnetic shape memory alloy

Abstract

Ferromagnetic shape memory alloys (FSMA), a type of smart material, are promising for engineering applications due to their large, high-frequency, and reversible magnetic-field-induced-strain (MFIS). However, the magneto-mechanical behaviors of FSMA are still not well understood due to the intrinsically coupled and cross-scale magneto-mechanical responses, limiting the design and optimization of FSMA-based devices such as sensors and actuators. In this work, a fully-analytical 3D model containing only basic material parameters and incorporating all key mechanisms for the magneto-mechanical performances of FSMA is developed based on a new magneto-mechano-decoupled energy minimization approach. It is shown that the coupled magneto-mechanical responses of FSMA-based sensors (cyclic stress with constant magnetic field) and actuators (cyclic magnetic field with constant stress) predicted by the model are in excellent agreement with existing experimental measurements. Based on these analytical predictions, the optimal ranges for the constant field and demagnetization factor are determined to achieve simultaneous complete strain recovery and considerable magnetization change as required by the FSMA-based sensors. In addition, the dependences of switching and saturating fields of MFIS on the constant stress and demagnetization factor are quantified for the FSMA-based actuators. Finally, a phase diagram is constructed to quantitatively determine the critical magnetic fields and stresses for predicting the strain induction and recovery under various loading conditions. The analytical model provides a simple, reliable, and versatile tool to reveal the comprehensive mechanisms for the coupled magneto-mechanical behaviors of FSMA and to guide the design of FSMA-based sensors and actuators with customized and on-demand performances.