Thermodynamic Modelling of Ferromagnetic Shape Memory Actuators

Abstract

We present a thermodynamic Gibbs free energy model for the finite element simulation of the coupled thermo-magneto-mechanical behavior of ferromagnetic shape memory alloys (FSMAs). Starting from a free energy model for the conventional shape memory effect, additional terms are included to take into account the magnetic anisotropy and the geometry-dependent magnetostatic energy. Different functions are considered for the strain dependence of the anisotropy energy in order to describe the experimentally found strong dependence of the anisotropy energy on the ratio of short and long crystallographic axis c/a. The resulting energy landscape is used to calculate the transition probabilities between three martensite variants and the austenite state under applied stress and external magnetic field. The magnetic shape memory effect is simulated for different loading conditions and sample geometries. We demonstrate the influence of the c/a dependence of the anisotropy energy as well as the influence of twinning strain and elastic modulus on the transition between martensite variants. The model calculations are compared with experimental results on Ni-Mn-Ga single crystals.

Magnetic Shape Memory Microactuators

“…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]. The model has been implemented into a FEM (Finite element method) code to predict the MIR effect in linear actuators based on MSMA foils that are subjected to different loading conditions and mechanical constraints [53][54][55][56][57]. The finite element software includes an integral magnetic solver and applies classical beam theory for solid mechanics.…”

A novel foil actuator using the magnetic shape memory effect

“…MSM actuation is simulated by adopting a free-energy model of the shape memory effect [17] combined with a Stoner-Wohlfarth model of magnetic anisotropy [18][19][20]. Taking into account the crystallographic evidence that the magnetic shape memory effect results from a collective action of many individual unit cells arranged in layers, the model considers the mean properties of these layers at the mesoscopic scale.…”

“…The transition probabilities enter into a set of rate equations to determine the time-dependent fractions of martensite variants in each energy state. From the variant fractions, the total strain ε, stress σ and magnetization M are derived [18][19][20].…”

Phase Transformations in Electrically Conductive Ferromagnetic Shape-Memory Alloys, Their Thermodynamics and Analysis

“…The first term on the right-hand side of (17) incorporates temperature-dependent magnetoelastic coupling; specific choices for NiMnGa may be found in [24,52]. The second term takes into account interfacial energy between twin boundaries through the positive-definite sixth-order tensor C hpr .…”

“…Our next task is to establish, in a manner consistent with (24), appropriate constitutive restrictions on (q, j, p di , P di ). To this aim, we introduce the total dissipation potential…”