## 2 Magnetstrictive Mechanism of the Giant Magnetostrictive Material and Its Modeling Method
### Comparative Study of Hysteresis Models of Giant Magnetostrictive Actuators  
At present, there are two types of models mainly used to study the hysteresis phenomenon of giant magnetostrictive actuators [33]: hysteresis models based on mathematical methods (Preisach model) and hysteresis models based on physical methods (Jiles-Atherton model, free-energy hysteresis model).  
(1) Preisach model  
The Preisach hysteresis model [33] is a model for calculating magnetostrictive deformation by studying the hysteresis model of iron material proposed by [PERSON] and [PERSON]. Subsequently, [PERSON] proposed a Preisach hysteresis model describing frequency hysteresis behavior at 200 Hz working range, which shows the dynamic characteristics of hysteresis behavior with increasing operating frequency [34]. At present, the research on the Preisach model has become comprehensive [35; 36; 37]. Because the model can only reflect the relationship between input and output, it cannot explainthe magnetostrictive mechanism inside the giant magnetostrictive material, and it cannot reflect the relationship between magnetostriction and the external thermal and machinery fields, moreover, a large number of complex equations and nonphysical parameters need to be identified and processed in the model, which leads to low flexibility and a long processing cycle for the Preisach model in the actual application process.  
(2) Jiles-Atherton model  
The Jiles-Atherton hysteresis model [38] is founded based on the domain wall theory of ferromagnetic materials, this model is applied to build the dynamic hysteresis model of Terfenol-D by [PERSON] [39]. The Jiles-Atherton model is quite limited for the capture of hysteresis, and many physical causes of hysteresis have not been explored. It can only be applied to research a small number of ferromagnetic functional materials such as giant magnetostrictive material and shape memory alloys.  
(3) Free energy hysteresis model  
In 2003, [PERSON] and [PERSON] [40] proposed a free energy hysteresis model based on the Jiles-Atherton model, the model is combined Helmholtz-Gibbs free energy and statistical distribution theory to simulate the hysteresis model at medium or high driving strengths, and its main input and output parameters are included with magnetic field strength, magnetization, and mechanical strain. The Boltzmann statistical theory is adopted in the model, and the related energy relation function of the external thermal field and the mechanical field is substituted into the telescopic deformation of the material, furthermore, an intrinsic nonlinearity three-field model coupled by magnetic field, machanical field and thermal field is established, and it can be built a model accurately for the functional materials such as Terfenol-D and piezoelectric ceramics [41; 42; 43].  
Since the free energy hysteresis model is a new hysteresis model proposed in recent years, it has the advantages of being a simple model, easily modifiable external influence factors (such as eddy current, temperature, etc.), and less parameters, and it is the main theoretical basis for studying the magnetic coupling model of giant magnetostrictive microactuators.