| A search for connecting fractal structure and fractional properties in polymers William Oates1; 1FLORIDA CENTER FOR ADVANCED AERO-PROPULSION, , United States; PAPER: 337/Mathematics/Plenary (Oral) SCHEDULED: 18:15/Wed. 30 Nov. 2022/Arcadia 3 ABSTRACT: In this talk, we explore a method to uncover fractal structure and fractional property relations in thermomechanical and electromechanical polymeric materials. The methodology is based on entropy dynamics where Shannon’s entropy is combined with fractional order constraints to obtain Bayesian posterior probability densities. This results in fat-tailed posterior densities where their maximum likelihood is evaluated using localized fractal and non-local fractional order operators. We argue that the entropy dynamic approach provides a means to identify the appropriate fractal and/or fractional order operators as a function of (multi)fractal material structure. We give examples in hyperelastic energy functions based on underlying multifractal structure and fractional order viscoelasticity. The modeling framework is compared to experiments on dielectric elastomers and auxetic foams where the uncertainty in the constitutive properties and the fractional order are quantified. |
