Modeling the Coupled Strain and Magnetization Response of Magnetic Shape Memory Alloys under Magnetomechanical Loading

Abstract

This article is concerned with the modeling of the magnetic shape memory alloy (MSMA) constitutive response caused by the reorientation of martensitic variants under mechanical and magnetic fields. The presented model is able to better capture the complexity of the magnetomechanical MSMA behavior by accounting not only for the mechanism of field-induced variant reorientation, but also the magnetization rotation away from magnetic easy axes and the magnetic domain wall motion at low stress and magnetic field levels. Following the general formulation of the model, reduced versions of the constitutive equations are derived for three specific loading cases: (1) magnetic-field-induced variant reorientation at constant stress; (2) stress-induced variant reorientation at constant magnetic field; (3) variant reorientation under collinear magnetic field and stress with perpendicular bias field. For each of these cases the nonlinear and hysteretic strain and magnetization response of MSMAs are predicted and compared to experimental data where available. The relation of critical stresses and magnetic fields for the activation of the reorientation process are visualized in a variant reorientation diagram. The captured loading-history-dependent macroscopic material response is explained in detail by connecting it to the evolution of the crystallographic and magnetic microstructure as represented by a set of internal state variables.

Modelling Shape-Memory Effects in Ferromagnetic Alloys

“…1). As pointed out by Kiefer and Lagoudas [39], such magnetization rotation inside the martensitic variants is known to be an important feature that favours the magnetic field-induced twin reorientation.…”

“…[13,14,22,[38][39][40][41][42]). Most of them include explicitly dissipation terms occurring in twin reorientation to account for hysteresis in strainmagnetic field loops and deal with magnetostatic effects by means of approximate calculations of demagnetizing factors.…”

“…In particular, Wang et al [38] proposed a phenomenological constitutive model based on a variational approach of a pseudo-free energy that neglects exchange interactions. Kiefer and Lagoudas [39] introduced a micromechanical model aimed at studying magnetostrain curves under the effect of an additional bias magnetic field. Auricchio et al [40] considered a simple model, which is restricted to the limit of very strong magnetocrystalline anisotropy, so that no magnetization rotation is allowed inside each variant.…”

Magnetic Shape Memory Microactuators

“…Different simulation models have been developed to predict the strain and force output of MSM actuators as a function of external magnetic field [46][47][48][49][50][51]. Here, we present a brief sketch of a thermodynamic model that considers three possible variants of a Ni-Mn-Ga single crystal with tetragonal 10M martensite structure [52,53].…”

A three‐dimensional phenomenological model for Magnetic Shape Memory Alloys

“…Some alternative phenomenological modeling of MSMAs are proposed in [4] and [5]. The referred papers, albeit taking their origin from the same basic principles, differ from the present approach as they are essentially restricted to two dimensions (or two martensitic variants), and they feature a scalar internal variable (local proportion of one martensitic variant with respect to the others) and a different choice of the relevant potentials.…”