Module 3: Dynamic Properties and Selection of Materials
  Lecture 13: Advanced Models of Viscoelastic Materials
 

In the last lecture we have discussed about two basic models of VEM Kelvin-Voight (K-V) model and Maxwell model. However, to simulate the complex time dependent behavior of complex VEMs more advanced models are often required. It is easier to establish the constitutive relationship of such systems initially in the frequency domain and then by using inverse Laplace transformation the time-domain relationship could be obtained.

3-Parameter Model of the VEM

Figure 13.1: 3 parameter model

Consider the 3- parameter model as shown in Fig (13.1). Force applied to the system is F(t) and the displacement at the point of application is , spring and damper are in series and the combination in connected in parallel to spring .

The equivalent stiffness of the system in frequency domain could be written as

    where is the Laplace variable