Numerical simulations on the high-frequency dynamic mechanical response of single-crystalline Ni–Mn–Ga samples

In this paper, an efficient numerical scheme is proposed to simulate the high-frequency dynamic mechanical response of single-crystalline Ni–Mn–Ga samples. First, based on a three-dimensional setting, the governing equation system for a single-crystalline Ni–Mn–Ga sample is set up, which is composed of the equation of motion and the twin interface movement criteria. In order to solve the governing system, an iterative numerical algorithm is proposed, in which the finite element method and the NewMark-β method are applied. To demonstrate the efficiency of this numerical scheme, the response of a single-crystalline Ni–Mn–Ga sample under some typical loading conditions are studied. In the numerical simulations, a specific discretisation of the sample is adopted, such that the possible positions of the twin interfaces in the sample can be naturally inherited. With the obtained numerical results, the mechanical behaviours of the sample under the different loading conditions are predicted, which show good consistency with the experimental results. The distribution of variant state and the propagation of twin interfaces in the sample can also be simulated. The numerical scheme proposed in the current work is helpful for the design of novel sensors or actuators based on single-crystalline Ni–Mn–Ga alloys.