A discrete twin-boundary approach for simulating the magneto-mechanical response of Ni–Mn–Ga

Abstract

The design and optimization of ferromagnetic shape memory alloys (FSMA)-based devices require quantitative understanding of the dynamics of twin boundaries within these materials. Here, we present a discrete twin boundary modeling approach for simulating the behavior of an FSMA Ni–Mn–Ga crystal under combined magneto-mechanical loading conditions. The model is based on experimentally measured kinetic relations that describe the motion of individual twin boundaries over a wide range of velocities. The resulting calculations capture the dynamic response of Ni–Mn–Ga and reveal the relations between fundamental material parameters and actuation performance at different frequencies of the magnetic field. In particular, we show that at high field rates, the magnitude of the lattice barrier that resists twin boundary motion is the important property that determines the level of actuation strain, while the contribution of twinning stress property is minor. Consequently, type II twin boundaries, whose lattice barrier is smaller compared to type I, are expected to show better actuation performance at high rates, irrespective of the differences in the twinning stress property between the two boundary types. In addition, the simulation enables optimization of the actuation strain of a Ni–Mn–Ga crystal by adjusting the magnitude of the bias mechanical stress, thus providing direct guidelines for the design of actuating devices. Finally, we show that the use of a linear kinetic law for simulating the twinning-based response is inadequate and results in incorrect predictions.