A Variational Continuum Model for Variant Reorientation of Ni–Mn–Ga Alloys Under Dynamic Mechanical Loading

Abstract

In this paper, a variational continuum model is proposed to investigate the dynamic mechanical properties of Ni–Mn–Ga alloy samples. Two continuous internal variables, i.e., the variant state and the lattice rotation angle, are introduced to characterize variant reorientation in Ni–Mn–Ga samples. Hamilton’s action integral for a dynamically loaded Ni–Mn–Ga sample is formulated, which incorporates a misfit energy term to account for the incompatibility of lattice structures. Through variational calculations, the weak forms of the governing equations are derived, which are further simplified by specifying the orientation of lattice structures. Both the full-form and the simplified governing equations are implemented in a commercial FE software. To demonstrate the efficiency of the present model, it is applied to simulate the dynamic behavior of a Ni–Mn–Ga sample in uniaxial compression tests. Based on the numerical solutions, the global response of the sample can be predicted, which shows good consistency with the experimental results. Furthermore, the configurations and variant state evolutions of the Ni–Mn–Ga sample during variant reorientation are properly simulated. The effects of loading rates and parameter values on the dynamic response of Ni–Mn–Ga samples are also discussed.