Dielectric elastomers are commonly implemented in adaptive structures due to their unique capabilities for real time control of a structure’s shape, stiffness, and damping. These active polymers are often used in applications where actuator control or dynamic tunability are important, making an accurate understanding of the viscoelastic behavior critical. This challenge is complicated as these elastomers often operate over a broad range of deformation rates. Whereas research has demonstrated success in applying a nonlinear viscoelastic constitutive model to characterize the behavior of Very High Bond (VHB) 4910, robust predictions of the viscoelastic response over the entire range of time scales is still a significant challenge. An alternative formulation for viscoelastic modeling using fractional order calculus has shown significant improvement in predictive capabilities. While fractional calculus has been explored theoretically in the field of linear viscoelasticity, limited experimental validation and statistical evaluation of the underlying phenomena have been considered. In the present study, predictions across several orders of magnitude in deformation rates are validated against data using a single set of model parameters. Moreover, we illustrate the fractional order is material dependent by running complementary experiments and parameter estimation on the elastomer VHB 4949 as well as an auxetic foam. All results are statistically validated using Bayesian uncertainty methods to obtain posterior densities for the fractional order as well as the hyperelastic parameters.
Hannah Solheim, Eugenia Stanisauskis, Paul Miles, and William Oates, "Fractional viscoelasticity of soft elastomers and auxetic foams," Proc. SPIE 10596, Behavior and Mechanics of Multifunctional Materials and Composites XII, 1059604 (Presented at SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring: March 05, 2018; Published: 22 March 2018); https://doi.org/10.1117/12.2296666.
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