Modeling and experimental validation of the hysteretic dynamics of shape memory alloy springs

Abstract

In this work, the hysteretic dynamics of a pseudoelastic shape memory alloy (SMA) spring is modeled and tested. A constitutive model of SMA spring is constructed by combining the theory of mechanical spring and the derived SMA constitutive relation. The SMA spring recovery force is modeled by employing the Euler-Lagrange equation based on a non-convex potential function. A macroscopic differential model is formulated to describe the hysteretic dynamics and the pseudoelasticity of the SMA spring. A theoretical method for estimating the equivalent stretch ratio at a specific temperature of SMA spring is given. Numerical simulations were presented in studying the influence of the stretch ratio at a temperature of 50, 70, and 90°C. The experimental tests are performed and presented together with their numerical counterparts. The comparison is made between numerical and experimental results to validate the proposed model for SMA spring.