Viscoelastic constitutive models and their fractional representatives to capture the time-dependent response of DEAs on sinus excitation

Dielectric elastomer actuators (DEAs) are subjected to creep especially in the first few excitation cycles. This paper deals with viscoelastic constitutive models and their fractional representatives to capture time-dependent deformation of DEA on sinus excitation. The sine voltage signal with three different frequencies and the same amplitude was used for deformation of the DEA. Basic constitutive models and their fractional representations of Kelvin-Voigt, Zener, solid linear model (SLM), Burger model and Kelvin-Voigt-Maxwell model were taken into consideration for finding the optimal model describing the behavior of the DEA. The simplicity of forming governing equations of motion derived with the help of Laplace transformation for basic and fractional constitutive models is shown in the work. Electrical force was calculated with the help of Maxwell equation. Responses of constitutive models were calculated with the help of Matlab. Constitutive parameters were optimized with the help of direct search and multiple starting point search method in Matlab. Fractional SLM was found to be the most optimal for describing time-dependent deformation on sinus excitation signal for the DEA. This work can be the basis on which control algorithms can be simulated for control of the DEA or any similar soft actuator.

Automated summary

This study focuses on the creep behavior of dielectric elastomer actuators (DEAs) in the first few excitation cycles. By comparing different constitutive models, the fractional SLM model was found to be the most suitable for describing the time-dependent deformation of DEAs under sinusoidal excitation. Optimization of constitutive parameters using Matlab provides a foundation for simulating control algorithms for DEAs or similar soft actuators.