An Entropy Dynamics Approach for Deriving and Applying Fractal and Fractional Order Viscoelasticity to Elastomers

Entropy dynamics is a Bayesian inference methodology that can be used to quantify time-dependent posterior probability densities that guide development of complex material models using information theory. Here we expand its application to non-Gaussian processes to evaluate how fractal structure can influence fractional hyperelasticity and viscoelasticity in elastomers. We investigate how kinematic constraints on fractal polymer network deformation influences the form of hyperelastic constitutive behavior and viscoelasticity in soft materials such as dielectric elastomers which have applications in the development of adaptive structures. The modeling framework is validated on two dielectric elastomers, VHB 4910 and 4949, over a broad range of stretch rates. It is shown that local fractal time derivatives are equally effective at predicting viscoelasticity in these materials in comparison to non-local fractional time derivatives under constant stretch rates. We describe the origin of this accuracy which has implications for simulating larger scale problems such as finite element analysis given the differences in computational efficiency of non-local fractional derivatives versus local fractal derivatives.