Kelvin or Voigt model

This is the governing equation for the Kelvin (or Voigt) Model and it is interesting to consider its predictions for the common time dependent deformations. 

In the parallel coupling of the Kelvin or Voigt model, the applied stress, (Tq, is simply the sum of the stresses of the individual components ... 

In the Kelvin or Voigt model the spring and dashpot elements are connected in parallel, as shown in Figure 3.13a. This model roughly approximates the behavior of rubber. When the load is applied at zero time, the elastic deformation cannot occur immediately because the rate of flow is limited by the dashpot. Displacements continue until the strain equals the elastic deformation of the spring and it resists further movement. On removal of the load the spring recovers the displacement by reversing the... 

FIGURE 3.13 (a) The Kelvin or Voigt model, (b), (c) Responses of the model under time-dependent modes... 

The Kelvin (or Voigt) model therefore gives an acceptable first approximation to creep and recovery behavior but does not predict relaxation. By comparison, the previous model (Maxwell model) could account for relaxation but was poor in relation to creep and recovery. It is evident therefore that a better simulation of viscoelastic materials may be achieved by combining tbe two models. 

Fig. 7.8 The Kelvin or Voigt model spring and dashpot in parallel.

Maxwell bodies are obtained if Hookean and Newtonian bodies are connected in series (Figure 11-11). The Kelvin or Voigt model, on the other hand, contains Hookean and Newtonian bodies in a parallel arrangement (Figure 11-11). The Maxwell body is a model for relaxation phenomena and the Kelvin body is a model for retardation processes. 

The equation represents one of the simple models for linear viscoelastic behaviour, the Kelvin or Voigt model, and is discussed in detail in Section 4.2.3 below. 

Note that this definition does not subtract the instantaneous or elastic strain to obtain creep. This is due to the difficulty in separating the two components of the time-dependent strain required by the Kelvin or Voigt model of viscoelasticity. 

The simplest models consist of a single spring and a single dashpot either in series or in parallel and these are known as the Maxwell model and the Kelvin or Voigt models respectively. 

Finally, one should bear in mind that the Maxwell model does not describe creep phenomena, such as those displayed in Figure 1.11b. Putting a constant stress, Go, in Equation (1.15) simply leads to a constant shear rate, y = ao t]p, as in a Newtonian liquid, without reproducing any real viscoelastic behavior. For describing creep, one has to use other approaches, such as the Kelvin or Voigt model. 

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