Numerical Techniques to Model Fractional-Order Nonlinear Viscoelasticity in Soft Elastomers

Dielectric elastomers are employed on a wide variety of adaptive structures. Many of these soft elastomers exhibit significant rate-dependencies in their response. Accurately quantifying this viscoelastic behavior is non-trivial and in many instances a nonlinear modeling framework is required. Fractional-order operators have been applied to modeling viscoelastic behavior for many years, and recent research has shown fractional-order methods to be effective for nonlinear frameworks. This implementation can become computationally expensive to achieve an accurate approximation of the fractional-order derivative. In this paper, we demonstrate the effectiveness of using quadrature techniques in approximating the Riemann-Liouville definition for fractional derivatives in the context of developing a nonlinear viscoelastic model.