Uniaxial Electro-Mechanically Coupled Cyclic Deformation of VHB 4905 Dielectric Elastomer: Experiment and Constitutive Model

Abstract

In the uniaxial deformation mode, the electro-mechanically coupled cyclic deformation of VHB 4905 dielectric elastomer (DE) is systematically studied by the experimental observation and constitutive modeling. From a series of uniaxial electro-mechanically coupled cyclic tests, it is found that with applying a constant voltage, the cyclic softening and ratchetting of VHB 4905 DE are more apparent than that without applying any voltage, which indicate that the VHB 4905 DE exhibits an electro-mechanically coupled effect. Also, the uniaxial electro-mechanically coupled cyclic deformation of VHB 4905 DE presents a strong rate-dependence and remarkable stress-level-dependence. Based on the experimental results, an electro-mechanically coupled visco-hyperelastic constitutive model is proposed by considering the remarkable nonlinear viscosity of VHB 4905 DE and the effect of applied voltage on the cyclic deformation. Comparing the predicted results with correspondent experimental data, it is concluded that the proposed constitutive model reasonably reproduces the uniaxial electro-mechanically coupled cyclic deformation of VHB 4905 DE, including the cyclic softening and ratchetting.

Appendix 1

Size design of uniaxial specimen.

In the uniaxial electro-mechanically coupled deformation tests, the size of specimen is set as 100 mm × 50 mm, that is, the aspect ratio is 2:1. Through two tests, it is verified that the uniaxial deformation condition can be satisfied experimentally by using the specimen with a size of 100 mm × 50 mm. The details are provided as follows:

Firstly, the surface of the designed specimen is colored, and then a strain of 3.0 is applied to the specimen. Figure 

Fig. 15

Verification tests for the uniaxial deformation mode: (a) before deformation; (b) after deformation; (c) pixel coordinates and linear fitting

15(a) and (b) give the shapes of the specimen before and after deformation, respectively. The black line in Fig. 15(c) shows the pixel coordinates of the upper and lower edges in the deformed specimen; while the red line is a straight line that linearly fits the homogeneous portion in the middle and extends to the left of the specimen. Note that, only a half of deformed specimen is considered here, because the specimen is symmetrical in the whole deformation stage. As shown in Fig. 15c, the deformation is nonhomogeneous when the longitudinal pixels are located within the region from about 200 to 600, that is, for the specimen with a size of 100 mm × 50 mm and a strain of 3.0, the proportion of the homogeneous deformation part to the whole specimen is about 67%. Moreover, according to the longitudinal pixels, it is found that the longitudinal elongation $\, \lambda_{1}^{{}} = 4$, and the lateral elongation $\, \lambda_{2}^{{}} \approx 0.495$. From the assumption that VHB 4905 DE is an incompressible material, it yields $\, \lambda_{3}^{{}} \approx 0.505$. Thus, the deformation in the middle part of the specimen can be approximately considered as a uniaxial deformation mode.

Secondly, the relationship between the global strain and local strain is investigated. The specimen is first marked in the middle and then loaded at a strain rate of 0.05 s⁻¹ to a strain of 3.0, as shown in Fig. 

Fig. 16

Calibration tests: (a) at the strain of 0; (b) at the strain of 1.0; (c) at the strain of 2.0; (d) at the strain of 3.0

16. In this process, the global and local coordinates are recorded every 3 s, and then are converted into the strains to make the relationship between the global strain and local strain. Finally, a linear relationship is used to fit the obtained data. The results are given in Fig. 

Fig. 17

Calibration of experimental results

17. It is found that the linear relationship between the global strain and local strain is very strong, so the global strain measured by the tests can approximately replace the local strain in the middle part of the specimen.

According to the above analysis, for the specimen with a size of 100 mm × 50 mm, the homogeneous deformation part of the specimen is in a uniaxial deformation mode, and the local strain is basically linear with the global strain. Therefore, the specimen size used in the uniaxial electro-mechanically coupled deformation tests of VHB 4905 DE can be selected as 100 mm × 50 mm.