Use of single and double fractional Kelvin–Voigt model on viscoelastic elastomer

Abstract

Dielectric elastomer actuators also known as DEAs are widely used as soft actuators. In order to control such actuators its mechanical properties are needed. Since viscoelastic materials are mainly used as a base for DEAs, an appropriate mathematical model is needed to get appropriate control parameters. Viscoelastic elastomers have very complex mechanical characteristics. They exhibit a combination of behaviors of solid material and liquid. Usually, solid materials exhibit elasticity up to a certain point. Liquids exhibits viscosity. They change their shape regardless on the stress applied on it and do not regain their original shape. Viscoelastic materials exhibit both behaviors at once. However, the ratio between elasticity and viscosity depends on the material being used. The use of fractional Kelvin–Voigt model can be of great help in determining the elastic and/or viscous material properties. Even more, a comparison between single and double fractional Kelvin–Voigt models will be given for low frequency strain ranges. It will be shown that viscoelastic mechanical properties are frequency dependent. At the end a least-square method is introduced for determination of optimal parameters for both models. This study can be used as a guidance for viscoelastic material parameter identification either for single or double fractional Kelvin–Voigt model. Both models can be further used in control theory with fractional derivatives to obtain proper control parameters since they are easily transferable to Laplace domain.