Figure 3
From: Exactly solvable model for a velocity jump observed in crack propagation in viscoelastic solids
Three types of dynamic responses of a Zener element: soft-elastic, viscoelastic, and hard-elastic responses. (a) Dynamical response of a Zener element to adequately slow or fast stretch (see, text). (b) Dynamic modulus E(ω) = ReE(ω) + iImE(ω) as a function of an angular frequency of strain oscillation ω in a Zener element. Here, ReE(ω) and ImE(ω) are the storage and loss moduli, respectively. We plot E(ω) = E 0(1 + iωt slow)/(1 + iωt fast) obtained from the stress-strain relation in equation (4), with \({t}_{{\rm{fast}}}\simeq \eta /{E}_{\infty }\) and \({t}_{{\rm{slow}}}\simeq \eta /{E}_{0}\). In the (rubbery) soft-elastic and (glassy) hard-elastic regimes, the dynamics are elastic and characterized by E 0 and E ∞, respectively, whereas in the viscoelastic regime the dynamics is governed by η, E 0, and E ∞.
