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Generalized Kelvin/Voigt models are therefore used to analyze the creep and creep recovery (retardation) functions. A single Kelvin/Voigt model consists of a single spring and a single dashpot in parallel connection (see Figure 5.6). For a generalized Kelvin/Voigt model, however, several Kelvin/Voigt elements are connected in series (see Figure 6.10).

Each one of the individual Kelvin/Voigt elements displays the behavior of an individual polymer fraction having a specific molar mass and molecular structure. Each fraction is represented in the model by a spring and a dashpot which together produce the characteristic values of the viscoelastic behavior of this one fraction. This results in the corresponding individual retardation time Λi.

The following applies to each individual Kelvin/Voigt element:

τi = ηi ⋅ γ ̇ + Gi ⋅ γ

with the individual counting number i = 1 to k; and k is the total number of all Kelvin/Voigt elements available.

The following holds: Λi = ηi/Gi, with the individual retardation time Λi [s]

Thus:

γi(t) = (τ0 / Gi) ⋅ [1 – exp(-t/Λi)]

Dependent on the shear stress step and on its removal, each one of the Kelvin/Voigt elements is showing an individual time-dependent deformation or re-formation behavior, respectively. The resulting total deformation value γ occurs as the sum of all individual deformation values γi:

Equation 6.13

γ(t) = Σi γi(t) = Σi (τ0 / Gi) ⋅ [1 – exp(-t/Λi)]

It is possible to use this calculation since here applies the principle of superposition according to L. Boltzmann (1844 to 1906; see also Chapter 14.2: 1874) [6.7]. According to this principle, for data of the linear viscoelastic range, the ratio of the value pairs of stress/deformation also applies to its multiples and sums (see also Chapter 8.3.2: LVE range) [6.8] [6.9].

Sometimes, an extra spring and an extra dashpot are connected in series as additional components to the generalized Kelvin/Voigt model to enable also analysis, on the one hand of reversible elastic behavior at very low deformations, and on the other hand of purely viscous flow behavior at high deformations (this model is comparable to the Burgers model, see Figure 6.7).