Modeling the dynamical response of ferromagnetic shape memory alloy actuators using a dissipative Euler–Lagrange equation

A phenomenological dynamical model of ferromagnetic shape memory alloy based actuators is developed. The parameters of effective mass density, viscosity, and elasticity are defined and used in a dissipative Euler–Lagrange equation to determine the martensite variant fraction and strain as a function of time. These three parameters are determined by fitting our simulations to recent experiments on a NiMnGa based actuator. In addition to the simplicity of only three fitting parameters to model martensite variant evolution, the present model is a convenient formulation of the problem because it incorporates self-consistently all stresses and loads in the system.