Accurate evaluation of the configurational forces in single-crystalline NiMnGa alloys under mechanical loading conditions

Abstract

To properly predict the mechanical response of a single-crystalline NiMnGa sample, the configurational forces on the twin interfaces in the sample have to be calculated accurately. However, the conventional displacement-based finite element (DB-FE) method usually yields large numerical errors in calculating the contact stress values on the twin interfaces, which will further influence the evaluations of the configurational forces. In this paper, an interface element (IE) method is incorporated into the conventional FE framework. Through this FE-IE method, the contact stress is treated as one of the primary unknowns on the twin interfaces. By solving the governing system of the model numerically, the contact stresses on the twin interfaces can be directly obtained, based on which the configurational forces can be calculated. The obtained results are further used to predict the global mechanical response of the NiMnGa sample. For a simple example, the theoretical values of the resultant contact forces and the configurational forces on the twin interfaces can be determined. By comparing the numerical results obtained from the DB-FE method and the FE-IE method with the theoretical values, it is found that the FE-IE method can generate more accurate numerical solutions. Furthermore, the influence of the cross-sectional shapes of NiMnGa samples on their mechanical response is investigated.