Using a Fully Fractional Generalised Maxwell Model for Describing the Time Dependent Sinusoidal Creep of a Dielectric Elastomer Actuator

Actuators made of dielectric elastomers are used in soft robotics for a variety of applications. However, due to their mechanical properties, they exhibit viscoelastic behaviour, especially in the initial phase of their performance, which can be observed in the first cycles of dynamic excitation. A fully fractional generalised Maxwell model was derived and used for the first time to capture the viscoelastic effect of dielectric elastomer actuators. The Laplace transform was used to derive the fully fractional generalised Maxwell model. The Laplace transform has proven to be very useful and practical in deriving fractional viscoelastic constitutive models. Using the global optimisation procedure called Pattern Search, the optimal parameters, as well as the number of branches of the fully fractional generalised Maxwell model, were derived from the experimental results. For the fully fractional generalised Maxwell model, the optimal number of branches was determined considering the derivation order of each element of the branch. The derived model can readily be implemented in the simulation of a dielectric elastomer actuator control, and can also easily be used for different viscoelastic materials.