Fractional calculus in describing the viscoelastic response of PVB foil

Abstract

To address the response of a PVB foil, both traditional and fractional viscoelasticity based formulations are described and compared in this paper. Traditional viscoelasticity uses models consisting of elastic springs and viscous dashpots. Fractional viscoelasticity is based on the principles of fractional calculus (derivatives and integrals of non-integer order) and introduces another rheological element, the springpot, which behaves as viscoelastic on its own and allows us to construct even more complex models. While limiting attention to the Maxwell chain model, both formulations are compared in light of approximation of experimental data provided by rheometer measurements. This is illustrated by plotting the storage modulus derived experimentally as well as computationally, which in turn promotes application of fractional calculus as an efficient tool for smoothing out and storing the experimental data.