Entropy Dynamics Approach To Fractional Order Mechanics With Applications To Elastomers

Entropy dynamics is a Bayesian inference methodology that quantifies posterior probability densities and associated phases as a sequence of snap-shots in time to estimate the most likely material particle positions as a function of external stimuli (e.g., heat, traction, electromagnetic fields, chemicals, etc.). The inference method provides a means to create models at the continuum and quantum scales purely based on probability inference. Here we explore its application to fractal structure and fractional properties for polymer mechanics. We investigate how fractal polymer network structure influences the hyperelastic constitutive behavior for a broad class of polymers such as auxetic foams, dielectric elastomers, and liquid crystal elastomers which can exhibit fractal structure and have applications in the development of adaptive structures.