Fractional and fractal order effects in soft elastomers: Strain rate and temperature dependent nonlinear mechanics

Eugenia Stanisauskis, Florida State University
Somayeh Mashayekhi, Kennesaw State University
Basanta Pahari, Florida Agricultural and Mechanical University
Markus Mehnert, Friedrich-Alexander-Universität Erlangen-Nürnberg


Soft dielectric elastomers are commonly used in applications where large deformation is prevalent such as energy harvesters, sensors, and soft actuators. The thermo-mechanical response of these elastomers is important in order to accurately describe the viscoelastic behavior over a broad range of operating conditions. Fractal characteristics of the dielectric elastomer VHB 4905 and their connection to fractional order viscoelasticity are analyzed to better understand viscoelasticity over a range of elevated temperatures starting at room temperature. We extend prior work in viscoelasticity to include excluded volume effects as a function of temperature. A fractal hyperelastic model is combined with a fractional order viscoelastic model and validated experimentally. Bayesian uncertainty methods are used to quantify the material parameters and their influence on temperature dependent viscoelasticity measurements. The model fits are compared to previously collected temperature dependent viscoelastic measurements on VHB 4905 for temperatures ranging from 23 °C to 60 °C. Based on fractional order viscoelasticity, we infer that the excluded volume parameter is negative and initially decreases before reaching a constant value near 50 °C.