Investigation on a segment linearized super-elastic constitutive model of magnetic shape memory alloy considering the influence of magnetic field

Magnetic Shape Memory Alloy (MSMA), as a new smart material, has both shape memory effect and super-elastic effect as traditional temperature-controlled Shape Memory Alloy. Most of the existing MSMA constitutive models have some problems, e.g., theoretically oriented, complex forms, and multiple parameters, which may affect their engineering application. The segment linearized stress-strain relationship of super-elastic MSMA is established using the linear method. The segment linearized super-elastic constitutive model is established based on the plasticity theory frame for the MSMA, which considers the volume fraction of the stress-preferred orientation martensite variants. The Logistic function is proposed to predict the relationship between critical stress and environment magnetic field, and the parameters of this function are fitted using experimental data. The constitutive model is used to simulate the super-elasticity of MSMA considering the influence of magnetic field, and the results are compared with the experimental results in terms of hysteretic curve shape and hysteretic energy consumption. The results show that the goodness of fit, which reflects the relationship between critical stress and environmental magnetic field, can reach 0.993. The proposed model results are close to the test results, and the average error between theoretical energy consumptions and test results is 11.9%. Therefore, the proposed model can accurately simulate the super-elastic deformation and energy dissipation capacity of MSMA, and can provide a simple method to predict MSMA's super-elastic characteristics considering the magnetic field's influence. Copyright ©2022 Engineering Mechanics. All rights reserved.