Comparison between the dynamic moduli of fully non-linear and quasilinear viscoelastic materials

This paper deals with the non-linear viscoelastic model with multiple hereditary integrals (MHI) in the frequency domain and the conditions that it reduces to single hereditary integral or the quasilinear viscoelastic (QLV) model. It is shown that when the higher order complex moduli are related to the first-order modulus as En(ω1,…,ωn)=αnqE1(ω1+⋯+ωn) the MHI model reduces to the QLV model. The coefficients of quasilinearity αnq should be real and independent of amplitude and frequency.