Finite element simulation of the magneto-mechanical response of a magnetic shape memory alloy sample

Abstract

In this paper, the stress-and magnetic field-induced variant reorientation in a magnetic shape memory alloy (MSMA) sample is simulated by using the finite element method. This model is set up based on a three-dimensional setting with the whole sample and the surrounding space taken into account. A typical loading pattern is proposed on the sample. The unknowns of the model governing system include the spatial displacement vector, the scalar magnetic potential and some internal variables related to the effective magnetization vector. By considering the different properties of the unknowns, an iterative computational scheme is proposed to derive the numerical solutions. With the obtained solutions, the magneto-mechanical response of the MSMA sample under different field and stress levels can be predicted. The distributions of the variant state and the effective magnetization in the sample can also be determined. By comparing with the experimental results, it is found that the numerical solutions obtained in this model can predict the response of the MSMA sample at a quantitative level.

Modelling and simulation of multi-physics applications in case of sudden transformations of material properties

“…Additionally, all three possible crystal orientations are taken into account instead of the two-dimensional simplification. [10] gives a more comprehensive overview of the different models available.…”

A variational approach towards the modeling of equilibrium twin interfaces in a single‐crystalline magnetic shape memory alloy sample

“…The governing PDE system of the current model can be explicitly solved by using an iterative numerical algorithm [4]. To show the validity of the current model, we consider a MSMA sample with cuboid shape and subject to perpendicularly applied magnetic and mechanical loadings (cf.…”

3-D Meso-Scale Finite Element Calculations of Free Energy on Twin Boundaries in Magnetic Shape Memory Alloys

“…Phenomenological models have been developed to predict macroscopic behaviors of MSM alloys based on the idea of moving TBs as well as domain wall boundaries. In many cases that is done by introducing internal variables that describe alloy microstructures: the volume ratio of different variants, the volume ratio of the magnetic domains, and the orientations of the magnetization vectors [31], [32], [33], [34], [35], [36], [37]. Many of these models were successfully implemented using numerical finite element techniques [34], [37], [38], including non-conventional ones, such as the absolute nodal coordinate formulation [39].A development of the model to study the quasi-static movement of TBs based on internal variables was reported in [40], and recent work [41] presents a numerical algorithm for studying the dynamic magnetomechanical response of MSM alloys.…”