Identification of Viscoelastic Fractional Complex Modulus

Abstract

An examination is made of a graphical method and derived techniques to characterize the fractional complex modulus of simple and complex viscoelastic materials, by a fit of experimental data, as well as from all of the various states of a material, that is, rubbery, transition, and glassy regions, rather than from that limited just to the sole transition domain, a situation that often occurs in materials investigation. Concrete results of some useful materials are illustrated. Nomenclature D β = fractional derivative of order β Einf = inflexion magnitude E(ω) = magnitude of complex modulus E0 = static Young’s modulus E ∗ (ω) = complex modulus E � (ω) = real part of complex modulus E �� (ω) = imaginary part of complex modulus j 2 = −1 s = Laplace variable t = time z1, z2 = complex numbers (model parameters) α, β, a, b, c = model parameters (real numbers) � =g amma function e(t) = strain e ∗ (ω) =F ourier transform of e(t) ηmax = maximum loss factor