Numerical analysis of the magnetic shape memory effect based on the absolute nodal coordinate formulation

Abstract

In this paper, the absolute nodal coordinate formulation (ANCF) is applied to simulate the magnetic shape memory effect. Using the absolute nodal coordinate formulation makes it possible to describe complicated or large deformation cases. The nonlinear bidirectional coupling terms between the mechanical and magnetic field are taken into account in the analysis of the single-crystalline Ni-Mn-Ga sample. A two-loop iteration procedure with variable steps is implemented to predict the magnetic-field-induced strain (MFIS) in the specimen under a changing external magnetic field and a constant auxiliary compression. In addition, the proposed approach is used to track the superelastic behavior of the magnetic shape memory alloy when subjected to a constant magnetic field. The approach effectively describes the hysteresis and superelastic phenomenon of the shape memory effect. The solution is compared here with solutions obtained using classical linear and quadratic quadrilateral elements. The deviation observed in the solution is discussed, and its cause is further clarified from a two-domain pure magnetostatic analysis of a permanent magnet. It is found that the accurate solution of such problems is associated with discontinuity of the normal component of the magnetic potential gradient across the domain interface. Special measures must be taken to make the absolute nodal coordinate formulation element compatible with the discontinuity. A mixed FEs strategy, which adopts ANCF FE in the displacement field solver and classical FE in the magnetic field solver, is proposed as an alternative option to rectify the problem, which is verified by predicting the MFIS and the dynamic mechanical response of a sample under cyclic compression.