# Construction and Numerical Realization of a Magnetization Model for a Magnetostrictive Actuator Based on a Free Energy Hysteresis Model

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## Abstract

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## Featured Application

**This study constructs and analyzes the constitutive model of the giant magnetostrictive material actuator,**

**which provides a theoretical basis for the development of a new intelligent structure of giant magnetostrictive material.**

## Abstract

## 1. Introduction

## 2. Magnetostrictive Mechanism of the Giant Magnetostrictive Material and Its Modeling Method

#### 2.1. Ferromagnetic Properties of Material and Their Magnetostrictive Mechanisms

#### 2.2. Factors Affecting Magnetic Coupling Characteristics of Giant Magnetostrictive Material

#### 2.3. Comparative Study of Hysteresis Models of Giant Magnetostrictive Actuators

## 3. Construction of a Hysteresis Model of a Giant Magnetostrictive Microactuator Based on Free Energy

#### 3.1. Research Process Based on the Free Energy Hysteresis Model

#### 3.2. Theoretical Basis for the Establishment of the Free Energy Hysteresis Model

## 4. Numerical Implementation of a Magnetization Model Based on the Free Energy Hysteresis Model

#### 4.1. Discretization of Integrals

#### 4.2. Kernel Function Implementation

#### 4.3. Verification Based on the Free Energy Hysteresis Model

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**The magnetization process of plane $\left(1\overline{1}0\right)$ of the Terfenol-D single crystal under the magnetic field in the [$11\overline{2}$] direction. (

**a**) Non-zero spontaneous magnetization state; (

**b**) Magnetization caused by the reversible domain wall motion when the input field is low; (

**c**) Two irreversible magnetization mechanisms appearanced when the input field increases gradually; (

**d**) The magnetization saturation state of the material.

**Figure 8.**Simulation and experimental comparison curves of magnetization and magnetic field strength.

**Figure 9.**Simulation and experimental comparison curves of output displacement and magnetic field strength.

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**MDPI and ACS Style**

Yu, Z.; Zhang, C.-y.; Yu, J.-x.; Dang, Z.; Zhou, M.
Construction and Numerical Realization of a Magnetization Model for a Magnetostrictive Actuator Based on a Free Energy Hysteresis Model. *Appl. Sci.* **2019**, *9*, 3691.
https://doi.org/10.3390/app9183691

**AMA Style**

Yu Z, Zhang C-y, Yu J-x, Dang Z, Zhou M.
Construction and Numerical Realization of a Magnetization Model for a Magnetostrictive Actuator Based on a Free Energy Hysteresis Model. *Applied Sciences*. 2019; 9(18):3691.
https://doi.org/10.3390/app9183691

**Chicago/Turabian Style**

Yu, Zhen, Chen-yang Zhang, Jing-xian Yu, Zhang Dang, and Min Zhou.
2019. "Construction and Numerical Realization of a Magnetization Model for a Magnetostrictive Actuator Based on a Free Energy Hysteresis Model" *Applied Sciences* 9, no. 18: 3691.
https://doi.org/10.3390/app9183691