Identification of the viscoelastic properties of soft materials at low frequency: performance, ill-conditioning and extrapolation capabilities of fractional and exponential models

We report about the experimental identification of viscoelastic constitutive models for frequencies ranging within 0-10Hz. Dynamic moduli data are fitted forseveral materials of interest to medical applications: liver tissue (Chatelin et al., 2011), bioadhesive gel (Andrews et al., 2005), spleen tissue (Nicolle et al., 2012) and synthetic elastomer (Osanaiye, 1996). These materials actually represent a rather wide class of soft viscoelastic materials which are usually subjected to low frequencies deformations. We also provide prescriptions for the correct extrapolation of the material behavior at higher frequencies. Indeed, while experimental tests are more easily carried out at low frequency, the identified viscoelastic models are often used outside the frequency range of the actual test. We consider two different classes of models according to their relaxation function: Debye models, whose kernel decays exponentially fast, and fractional models, including Cole-Cole, Davidson-Cole, Nutting and Havriliak-Negami, characterized by a slower decay rate of the material memory. Candidate constitutive models are hence rated according to the accurateness of the identification and to their robustness to extrapolation. It is shown that all kernels whose decay rate is too fast lead to a poor fitting and high errors when the material behavior is extrapolated to broader frequency ranges.