# Field-Dependent Stiffness of a Soft Structure Fabricated from Magnetic-Responsive Materials: Magnetorheological Elastomer and Fluid

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## Abstract

**:**

## 1. Introduction

## 2. Fabrication of Soft Structures

#### 2.1. Characteristics of MRE

#### 2.2. Characteristics of MRF

#### 2.3. Sample Fabrication

## 3. Experimental Apparatus

## 4. Results and Discussion

_{b}and n denote the distance, bifurcation within large and small deformation and the order of polynomial expression, respectively. F(d) was fitted to order 3 and 1 for the samples with and without MRF, respectively. The order of the samples was chosen based on the tensile force-displacement curves given in Figure 10. Specific formulae and R-square values in the magnetic field intensity range were obtained and given in Figure A1 of Appendix A and the field-dependent stiffness for the large deformation region in Figure A2 of Appendix A. The stiffness was based on an instantaneous sloped force-displacement curve calculated by differentiating the values given in Figure A1. According to Figure A2, the stiffness of the sample without MRF did not change with displacement and was not affected by the magnetic flux density in the large displacement region. On the other hand, the stiffness of the sample with MRF changed according to displacement and was affected by the magnetic flux density. Notably, a 0.3 T magnetic flux density caused a 330.9% increase in stiffness at 5.0 mm deformation. The stiffness of the samples with MRF was higher than in samples without regardless of the amount of deformation, and a change in stiffness was noted even across a large deformation. The stiffness behavior of the soft structure proved that the use of a magnetic-responsive skin layer and core was very effective in controlling stiffness across a wide displacement or deformation range.

## 5. Conceptual Applications

## 6. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Force-displacement relationships approximated by polynomial expression in the large deformation region of the soft structure.

**Figure A2.**Stiffness approximated by polynomial expression in the large deformation region of the soft structure.

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**Figure 1.**A typical smart structure using controllable magnetorheological fluid (MRF)/ electrorheological fluids (ERF) for vibration control.

**Figure 2.**Applications of the proposed soft structures produced using two different magnetic-responsive materials.

**Figure 3.**Material characterization of magnetorheological elastomer (MRE) presented as a (

**a**) SEM image and (

**b**) shear modulus vs. magnetic flux density plot.

**Figure 4.**Material characterization of the MRF presented as an (

**a**) SEM image and (

**b**) yield stress vs. magnetic flux density plot.

**Figure 5.**The two soft structure samples, namely (

**a**) filled with MRF and (

**b**) without MRF, and (

**c**) their identical geometric dimensions.

**Figure 7.**The sample and its components during production, namely the (

**a**) mold, (

**b**) skin layers and (

**c**) assembled structure.

**Figure 8.**Experimental apparatus and set-up; (

**a**) the universal tensile testing machine (KDPI-205 Series, KD PRECISION Co., capacity 1 kN), (

**b**) top and front view of permanent magnet (PM) jig (

**c**) the schematic diagram for the measuring distance and magnetic flux density, (

**d**) the mean magnetic flux density simulation of the PMs based on FEM analysis, (

**e**) the reference measurement of magnetic flux density using a gauss meter (F.W. BELL Co., 5100 series).

**Figure 10.**The tensile force-displacement curves in a range of magnetic flux density for the soft structures (

**a**) without MRF and (

**b**) with MRF.

**Figure 11.**SEM image of the interface between the MRE skin layer and MRF core in the soft structure.

**Figure 12.**The stiffness was dependent on mean magnetic flux density for small displacement in the soft structures without MRF (blue) and with MRF (red).

**Figure 14.**Schematic diagrams of a smart braille watch, specifically its (

**a**) braille display actuator components and (

**b**) operating principle.

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**MDPI and ACS Style**

Song, B.-K.; Yoon, J.-Y.; Hong, S.-W.; Choi, S.-B.
Field-Dependent Stiffness of a Soft Structure Fabricated from Magnetic-Responsive Materials: Magnetorheological Elastomer and Fluid. *Materials* **2020**, *13*, 953.
https://doi.org/10.3390/ma13040953

**AMA Style**

Song B-K, Yoon J-Y, Hong S-W, Choi S-B.
Field-Dependent Stiffness of a Soft Structure Fabricated from Magnetic-Responsive Materials: Magnetorheological Elastomer and Fluid. *Materials*. 2020; 13(4):953.
https://doi.org/10.3390/ma13040953

**Chicago/Turabian Style**

Song, Byung-Keun, Ji-Young Yoon, Seong-Woo Hong, and Seung-Bok Choi.
2020. "Field-Dependent Stiffness of a Soft Structure Fabricated from Magnetic-Responsive Materials: Magnetorheological Elastomer and Fluid" *Materials* 13, no. 4: 953.
https://doi.org/10.3390/ma13040953