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Behavior of VE solids becomes clear when using the differential equation according to Kelvin/Voigt (see Chapter 5.2.2.1b): τ = η ⋅ γ ̇ + G ⋅ γ

UsingΛ = η/Gorη = Λ ⋅ Gthen:

Equation 6.11

τ = (Λ ⋅ G) ⋅ γ ̇ + G ⋅ γorτ/G = Λ ⋅ γ ̇ + γ

Here, the symbol Λ is taken for the retardation time. Some authors choose the symbol λK (or τκ) to show the correlation between the Kelvin/Voigt model – which is used to characterize the rheological behavior of VE solids – and this specific time [6.1]. The retardation time determines the time-dependent deformation and re-formation behavior of the parallel connected components spring and dashpot of the Kelvin/Voigt model for both intervals, as well for the stress phase as well as for the rest phase. The solution of the differential equation leads to the following time-­dependent exponential function:

Equation 6.12

γ = (τ / G) ⋅ [1 – exp(-t/Λ)]

1 At the time point t = Λ, the following applies to the creep phase:

γ(Λ) = (τ / G) ⋅ [1 – (1/e)] = 63.2 % ⋅ (τ / G) = 63.2 % ⋅ γmax

Therefore counts for the creep phase: The retardation time Λ of the Kelvin/Voigt model is reached if the γ-value has increased to 63.2 % of the maximum deformation γmax which will finally occur at the end of the stress interval (see also Chapter 6.3.3a).

1 At the time point t = Λ, the following applies to the creep recovery phase:

γ(Λ) = γmax – (τ / G) ⋅ [1 – (1/e)] = γmax – 63.2 % ⋅ (τ / G) = (100 % – 63.2 %) ⋅ γmax

and thus: γ(Λ) = 36.8 % ⋅ γmax

Therefore counts for the creep recovery phase: The retardation time Λ of the Kelvin/Voigt model is reached if the γ-value has decreased to 36.8 % of γmax (see also Chapter 6.3.3b).