Due to high environment adaptability and low pressure impedance characteristics, soft robot has broad application prospects in the fields of biology, medicine, etc. The adoption of electro active polymer (EAP) material has become a hot research topic these years. Electrochemical actuator has been further developed in the last decades due to their desired mechanical properties exhibited in intelligent robots, which has been an alternative to air and fluid deriving equipment.^[1–4] The flexible ionic conductivity of the ILG is more suitable building blocks for the evolution of actuators due to its chemical stability, thermal stability and simpler ion transport.^[5–7]

Non-covalent interactions provide the gels with very high mechanical strength and excellent self-healing ability of supramolecular materials.^[8–10] On the basis of these studies, we use TiO₂ nanoparticles to fabricate supramolecular nanocomposites with electrochemical behavior of mechanical strength ionogel polymer and ionic liquid.

With the good development of numerical means, finite element analysis has been one of the most effective and abundant information extraction methods to evaluate and optimize robot design. Analytical model can therefore be greatly simplified, hence the computational efficiency is greatly increased. The most critical drawback is that the ignorance of the nonlinear and constitutive model and simplification of the computational model lead to a coarse solution.^[11,12] The numerical simulations offer a sufficient insight for every single case during the general soft robot approach.

To reduce the experimental cost and time consumption,we perform a systematic analysis of the ILG based on numerical simulations, and verify the accuracy of the finite element calculation, and also make some contribution to the development of the ILG in soft robot. The numerical simulation results are matched with the corresponding experiments, and hence the validity of the finite element model is proved.

This single behavior can be directly applied to some simple geometric numerical method, which takes into consideration some specific features of analysis process, and the finite element method has therefore become one of the most effective tools for process modeling, including ILG.^[13–15]

In our experiments, the ILGs are composed of1-butyl-3-methylimidazolium tetrafluoroborate (BMIMBF₄), hydroxyethyl methacrylate (HEMA) and TiO₂ nanoparticles, with mass of 890 mg, 100 mg, and 10 mg, respectively. The mixed solution is then placed into a magnetic stirrer to stir, forming a suspension. Following that the sample was placed on the ML-3500C Maxima-type cold light source, i.e., an ultra high intensity UV curing lamp, for polymerization.

Figure 1(a) shows a comparison between the morphologies of the ionic liquid before and after the gel is formed, the right figure shows the liquid state, and the left figure shows the solid state formed after polymerization. The schematic diagram of the generating principle is illustrated in Figs. 1(b)–1(d). Under the irradiation of UV light, the polymerization reaction occurs in HEMA, polymer matrix cross-linked with each other, and thus a porous network structure is formed.^[16]

Fig. 1.

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	Fig. 1. (color online) Proposed mechanism of the BMIMBF4-based ionogel under UV light. (a) ILG solution and ILG respectively. (b) The ILG solution inclusion BMIMBF4, HEMA, and TiO2 nanoparticles. (c) Polymerization initiated by the TiO2 nanoparticles. (d) HEMA and TiO2 nanoparticles cross coupled to form a three-dimensional (3D) network.

The morphology analysis of freeze-dried sample using scanning electron microscopy (SEM) shows that the porous microstructure occurs in the ubiquitous ionogels. Distilled water was used to replace the ILG internal ionic liquid, after the freeze-drying treatment, S4800 Hitachi type high resolution field emission scanning electron microscope was used to scan the section. Figure 2 shows that under a magnification of 5000, the spatial structure of the ionic liquid carrier HEMA is the typical 3D porous structure, and its matrix is cross-linked to each other to form a 3D support skeleton, offering good mechanical strength and self-repair performance.

Fig. 2.

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	Fig. 2. SEM image of a freeze-dried BMIMBF4-based gel after replacing the ionic liquid with water.

Fig. 3.

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	Fig. 3. Stress in each direction.

From the image of the ILG under the SEM, it can be seen that the material possesses an irregular network structure, which is a nonlinear material. The nonlinear properties of the material are also validated by stress-strain curves of the experimental results and simulation results.

The main purpose of the numerical simulations is to seek an effective analytical tool for studying the ILGs in detail to support the design of soft robots. The details of the whole finite element model including ILG elements are depicted in Fig. 4, corresponding to its geometric model.^[21–23]

Fig. 4.

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	Fig. 4. (color online) (a) Geometric model; (b) Finite element model.

The model size is 30 mm× 5 mm× (0.5 mm or 1.0 mm), and the stress–strain curves are computed under various values of TiO₂ content, and the force-displacement curves are thus can be calculated.

4.1. Geometry, materials, program settings

The geometric model shown in Fig. 4 has an ILG size of 25-mm long, 5-mm wide, and 0.5-mm or 1-mm thick.

The first analysis of the finite element model required for the deformation must be globally acceptable hyperelastic model, and the general characteristics of the ILG hyperelastic model can therefore be captured.

According to the uniaxial tensile tests, the values of C₁₀, C₀₁, C₂₀, C₁₁, C₀₂, C₃₀, C₂₁, C₁₂, and C₀₃ are obtained and summarized in Table 1.

Table 1.

Table 1.

Table 1. Mechanical properties of the BMIMBF4-based ionogels with different TiO2 concentrations. . TiO2/wt% C10 C01 C20 C11 C02 C30 C21 C12 C03 0.2 −12.2807 18.3417 3.0927 0.5 −18.5854 27.8485 0.0218 4.6449 1.0 36.3521 −53.9507 0.0122 −9.0515 1.5 660.293 −986.710 0.0272 −4.3149 −158.571 1.0694

Table 1. Mechanical properties of the BMIMBF4-based ionogels with different TiO2 concentrations. .

Due to nonlinear hyperelastic calculation, maximum ILG deformation strain turns to be as high as approximately 430%. For better convergence, in the analysis of the ANSYS finite element simulations, the load step is set to be 2000, the minimum load step is set to be 100, the maximum load step is set to be 1000, and the maximum iteration is set to be 100.

In Fig. 5, when the content of TiO₂ is 0.2 wt%, the simulation results are analyzed: when f = 1.49 mN, the deformation is 6.72 mm; when f = 8.56 mN, the deformation is 28.56 mm; when f = 12.68 mN, the deformation is 59.32 mm; when f = 13.92 mN, the deformation is 93.94 mm; when f = 13.02 mN, the deformation is 130.16 mm.

Fig. 5.

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	Fig. 5. (color online) Calculation results for TiO2 content of 0.2 wt% and ILG thickness of 0.5 mm.

Figure 6(a) shows that the ILG is thick and short before the load is applied. As the tensile load increases, the ILG becomes longer and thinner, which is shown in panels (b) and (c). Figure 5(a)–5(e) are the simulation results of ILG under different loads, showing that with the tensile load increasing, the simulation results are consistent with the experiment results, too. It can be seen in Figs. 5 and 6 that the ILG is consistent with the assumption that the material is incompressible, as shown in Eq. (9).

Fig. 6.

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	Fig. 6. (color online) Change of the ILG.

Table 2.

Table 2.

Table 2. Calculation results for TiO2 content of 0.2 wt% and ILG thickness of 0.5 mm. . Force/mN 1.49 8.56 12.68 13.92 13.02 Deformation/mm 6.72 28.56 59.32 93.94 130.16

Table 2. Calculation results for TiO2 content of 0.2 wt% and ILG thickness of 0.5 mm. .

In Fig. 8, when the content of TiO₂ is 0.2 wt%, the simulation results are analyzed: when f = 4.34 mN, the deformation is 5.92 mm; when f = 15.12 mN, the deformation is 24.57 mm; when f = 24.41 mN, the deformation is 51.11 mm; when f = 26.55 mN, the deformation is 81.57 mm; when f = 27.93 mN, the deformation is 113.72 mm.

Fig. 8.

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	Fig. 8. (color online) Calculation results for TiO2 content of 0.2 wt% and ILG thickness of 1.0 mm.

Table 3.

Table 3.

Table 3. Calculation results for TiO2 content of 0.2 wt% and ILG thickness of 1.0 mm. . Force/mN 4.34 15.12 24.41 26.55 27.93 Deformation/mm 5.92 24.57 51.11 81.57 113.72

Table 3. Calculation results for TiO2 content of 0.2 wt% and ILG thickness of 1.0 mm. .

In Fig. 10, when the content of TiO₂ is 0.5 wt%, the simulation results are analyzed: when f = 7.21 mN, the deformation is 6.01 mm; when f = 25.32 mN, the deformation is 25.10 mm; when f = 35.49 mN, the deformation is 52.62 mm; when f = 37.56 mN, the deformation is 84.43 mm.

Fig. 10.

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	Fig. 10. (color online) Calculation results for TiO2 content of 0.5 wt% and ILG thickness of 0.5 mm.

Table 4.

Table 4.

Table 4. Calculation results for TiO2 content of 0.5 wt% and ILG thickness of 0.5 mm. . Force/mN 7.21 25.32 35.49 37.56 Deformation/mm 6.01 25.10 52.62 84.43

Table 4. Calculation results for TiO2 content of 0.5 wt% and ILG thickness of 0.5 mm. .

In Fig. 12, when the content of TiO₂ is 0.5 wt%, the simulation results are analyzed: when f = 11.62 mN, the deformation is 4.86 mm; when f = 40.70 mN, the deformation is 19.39 mm; when f = 69.44 mN, the deformation is 40.42 mm; when f = 74.42 mN, the deformation is 65.54 mm; when f = 76.14 mN, the deformation is 92.74 mm.

Fig. 12.

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	Fig. 12. (color online) Calculation results for TiO2 content of 0.5% and ILG thickness of 1.0 mm.

Table 5.

Table 5.

Table 5. Calculation results for TiO2 content of 0.5 wt% and ILG thickness of 1.0 mm. . Force/mN 11.62 40.70 69.44 74.42 76.14 Deformation/mm 4.86 19.39 40.42 65.54 92.75

Table 5. Calculation results for TiO2 content of 0.5 wt% and ILG thickness of 1.0 mm. .

It can be seen that the ILGhas a TiO₂ content value of 0.2 wt% in Figs. 7 and 9, and the value is 0.5 wt% in Figs. 11 and 13. Both the length and the width of the ILG are fixed, the ILG thickness is 0.5 mm in Figs. 7 and 11, and the value is 1.0 mm in Figs. 9 and 13. The simulation results show that the stress-strain curve in Fig. 7 is substantially the same as the stress-strain curve in Fig. 9, and the stress-strain curve in Fig. 11 is substantially the same as the stress-strain curve in Fig. 13. The thickness of the ILG therefore has no effect on the hyperelastic nonlinear calculation and affects the magnitude of the load only.

Fig. 7.

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	Fig. 7. (color online) Comparison of experimental data with calculated data, for TiO2 content of 0.2 wt% and ILG thickness of 0.5 mm.

Fig. 9.

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	Fig. 9. (color online) Comparison of experimental data with calculated data for TiO2 content of 0.2 wt% and ILG thickness of 1.0 mm.

Fig. 11.

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	Fig. 11. (color online) Comparison of experimental data with calculated data for TiO2 content of 0.5 wt% and ILG thickness of 0.5 mm.

According to Figs. 7,9,11, and 13, it can be seen that the calculated thickness has no effect on the nonlinearity of the finite element. The ILG with a thickness of 0.5 mm is then calculated.

Fig. 13.

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	Fig. 13. (color online) Comparison of experimental data with calculated data for TiO2 content of 0.5 wt% and ILG thickness of 1.0 mm.

In Fig. 14, when the content of TiO₂ is 1.0 wt%, the simulation results are analyzed: when f = 11.90 mN, the deformation is 4.61 mm; when f = 40.35 mN, the deformation is 18.14 mm; when f = 73.60 mN, the deformation is 37.56 mm; when f = 79.69 mN, the deformation is 60.82 mm; when f = 80.01 mN, the deformation is 86.05 mm.

Fig. 14.

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	Fig. 14. (color online) Calculation results for TiO2 content of 1.0 wt% and ILG thickness of 0.5 mm.

Table 6.

Table 6.

Table 6. Calculation results at TiO2 content for 1.0 wt% and ILG thickness of 0.5 mm. . Force/mN 11.90 40.35 73.60 79.69 80.01 Deformation/mm 4.61 18.14 37.56 60.82 86.05

Table 6. Calculation results at TiO2 content for 1.0 wt% and ILG thickness of 0.5 mm. .

In Fig. 16, when the content of TiO₂ is 1.5 wt%, the simulation results are analyzed: when f = 23.67 mN, the deformation is 2.64 mm; when f = 74.56 mN, the deformation is 9.43 mm; when f = 136.13 mN, the deformation is 18.65 mm; when f = 164.13 mN, the deformation is 30.41 mm; when f = 169.05 mN, the deformation is 44.31 mm.

Fig. 16.

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	Fig. 16. (color online) Calculation results for TiO2 content of 1.5 wt% and ILG thickness of 0.5 mm.

Table 7.

Table 7.

Table 7. Calculation results for TiO2 content of 1.5 wt% and ILG thickness of 0.5 mm. . Force/mN 23.67 74.56 136.13 164.13 169.05 Deformation/mm 2.64 9.43 18.65 30.41 44.31

Table 7. Calculation results for TiO2 content of 1.5 wt% and ILG thickness of 0.5 mm. .

It can be seen in Figs. 7,11,15, and 17 that the content values of TiO₂ are 0.2 wt%, 0.5 wt%, 1.0 wt%, and 1.5 wt%, respectively. From the stress-strain curve, during the initial period (with a strain less than 100%), the error between the experimental results and the finite element simulation results is less than 10%, and both the errors of the remaining experimental results and the errors of the finite element calculation results are less than 5%.

Fig. 15.

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	Fig. 15. (color online) Comparison of experimental data with calculated data for TiO2 content of 1.0 wt% and ILG thickness of 0.5 mm.

Fig. 17.

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	Fig. 17. (color online) Uniaxial tensile test.

Figure 18 shows a series of pictures for TiO₂ content of 1.5 wt% from the applied load to the fracture process. Before the load is applied in Fig. 18(a), a material deformation under a load in Fig. 18(b), and the material is broken in Fig. 18(c). Figure 19 shows the stress-strain curves for TiO₂ content values of 0.2 wt%, 0.5 wt%, 1.0 wt%, and 1.5 wt%, respectively. According to the analysis results summarized and illustrated above, it can be seen that the simulation results are consistent with the experimental results.

Fig. 18.

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	Fig. 18. (color online) Uniaxial tensile test.

Fig. 19.

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	Fig. 19. (color online) ILG tensile test.

The ionogel BMIMBF₄ shows a high level of hyperelastic toughness when the maximum deformation and a tensile limit is close to 430%. Tensile tests show that the tensile properties of the gel can be enhanced by increasing the TiO₂ content. In the tensile tests, Young’s modulus is an optimum mechanical index for the synthesis condition. Increasing the quantity of TiO₂ nanoparticles will generate more cross-linking sites and higher conversion, which will contribute to the final mechanical properties.^[24] The optimized quantity of TiO₂ nanoparticles is 1.0 wt%, considering the data that have been collected so far and the relatively large tensile deformation and tensile strength.

In the analysis of ILG, SOLID186 element with finer mesh sizes can be used to achieve better simulation results. At the beginning of the simulation analysis, a small time step is necessary for system convergence. An appropriate macro or user subroutine is built up in the form of the parameters of the table and allows the restart of analysis at every time step.

The simulation results show that the finite element model has a good correlation with the corresponding experimental data. It is pointed out that the average error between the finite element calculation and the experimental data is small, showing the design potential of this method for soft robots.^[25,26] The finite element model requires the input of some mechanical properties of the ILG. In this paper, a standard uniaxial stretch method is used to measure the required ILG properties.

As shown in Fig. 2, the ILG is a network structure. However, in the process of finite element simulations, it is assumed that the ILG is a hyperelastic nonlinear network structure. The simulation results of the finite element are almost the same as the experimental results, and the result of the finite element simulation is therefore credible.

ANSYS structure program can be used to model the formation process of the soft robot by hyperelastic nonlinear calculation of the ILGs. In this paper, the model of the ILG is built up based on the hyperelastic nonlinear finite element model, and the results show that Mooney–Rivlin model can be well adapted to the constitutive relation of the material.^[27] The main advantage of the ILG is that it can obtain stress-strain curve, which can therefore obtain the performance parameters of the material in a relatively short time.

In the future, the investigations on the generalized algorithm to recognize the mechanical properties of ILGs are carried out. Finally, it is pointed out that all the results in this work show a good correlation between the 3D theoretical assumptions and the experimental conditions. The achievements made in this work will contribute to the design of future soft robot actuator.