Magnetic Shape Memory Alloys (MSMAs) are promising high-frequency active materials for actuation, sensing,
shape control, vibration suppression and energy harvesting applications. The macroscopic functionality of MSMAs
originates from the coupled evolution of highly heterogeneous magnetic and elastic domain microstructures.
Microstructure dependence of phase transformations in MSMAs introduces internal variables into the model to
account for strong effects of domain microstructure processes on MSMA properties and varying elastic and magnetic
coupling. Selection of internal variables and their incorporation into constitutive modeling has been done
for the problem of field-induced martensite reorientation. Introducing a new internal variable, the austenitic
volume fraction, the study of field induced phase transformation between the parent and martensitic phases is
This paper is concerned with the development of a finite element model for fully-coupled magnetomechanical
boundary value problems, which allows the implementation of nonlinear, anisotropic and hysteretic material
models. The formulation is based on a vector-valued magnetic potential and a small strain setting. The derivation
of the numerical algorithm is considered in detail. In order to test its implementation the case of piezomagnetism
is considered, for which a thermodynamically-consistent formulation is presented. The results of the finite element
analysis that have been obtained for two different boundary value problems, which involve the mechanical
and magnetic loading of an elastic matrix material with a transversely isotropic piezomagnetic inclusion, are
A major complication in measuring material properties of ferromagnetic materials is the influence of the demagnetization effect. The resulting difference between the internal and applied magnetic field depends on the specimen geometry and the distribution of the magnetization inside the sample. This phenomenon also affects the interpretability of magnetic-field induced strain and magnetization data measured for magnetic shape memory alloys, which in turn makes the formulation of reliable constitutive models for these materials difficult. To solve this problem, the approximation of uniform magnetization is usually adopted, in which case a tabularized demagnetization factor can be used to correct the data. In this paper, the validity of this simplification is tested by explicitly solving the magnetostatic problem for relevant geometries, while taking the nonuniform magnetization of a magnetic shape memory alloy specimen into account. In addition to comparing the relation between the volume averaged internal and applied magnetic field, the local variation of the magnetic field and magnetization is analyzed.
This work is concerned with the magnetic field-induced rearrangement of martensitic variants in magnetic shape memory alloys (MSMAs). In addition to the variant reorientation, the rotation of the magnetization and magnetic domain wall motion are considered as the microstructural mechanisms causing the macroscopically observable constitutive response. The considered free energy terms are the elastic strain energy, the Zeeman energy and the magnetocrystalline anisotropy energy. It is shown how thermodynamic constraints on the magnetization rotation lead to only partial reorientation of the martensitic variants under higher stresses. A straightforward methodology has been devised for the calibration of model parameters based on experimental data. The presented model predictions indicate an improvement of the predictability of the nonlinear strain hysteresis and in particular the magnetization hysteresis.
A thermodynamically consistent phenomenological model is presented which captures the ferromagnetic shape memory effect, i. e. the large macroscopically observable shape change of magnetic shape memory materials under the application of external magnetic fields. In its most general form the model includes the influence of the microstructure for both the volume fraction of different martensitic variants and magnetic domains on the described macroscopic constitutive behavior. A phase diagram based approach is taken to postulate functions governing the onset and termination of the reorientation process. A numerical example is given for an experiment
on a NiMnGa single crystal specimen reported in the literature, for which the model is reduced to a two-dimensional case of an assumed magnetic domain structure.