Kelvin-Voight model

Figure H3.3.5 The creep response of a food (circles) was fitted to a Burger model with one Kelvin-Voight unit. The goodness of fit is shown as the continuous curve and the standard error. The values of compliance and viscosity of the respective springs and dashpots were outcomes of the fitting process.

The contact force exerted on the tup by the specimen dynamically balances this force. The tup/specimen contact is modelled using a Kelvin-Voight element having stiffness kc and damping coefficient r. Thus the contact force is given by ... 

B. Voight-Kelvin (Creep) Model Superposition Principles... 

The gel layer is treated as a Kelvin-Voight viscoelastic material where the gel shear is acting in parallel. This viscoelastic material stress has both an elastic and viscous component acting in parallel. This viscoelastic material model was substituted into the momentum equation and the resulting gel layer equation of motion is... 

However, various combinations of eiastic and viscous elements have been used to approximate the material behavior of polymer melts. Some models are combinations of springs and dashpots to represent the elastic and viscous responses, respectively. The most common ones being the Maxwell model for a polymer melt and the Kelvin or Voight model for a solid. One model that represents shear thinning behavior, normal stresses in shear flow and elastic behavior of certain polymer melts is the K-BKZ model [28-29]. 

In the last two centuries, a lot of attempts and discussion have been made on the elucidation and development of the various constitutive models of liquids. Some of the theoretical models that can be mentioned here are Boltzmann, Maxwell (UCM, LCM, COM, 1PM), Voight or Kelvin, Jeffrey, Reiner-Rivelin, Newton, Oldroyd, Giesekus, graded fluids, composite fluids, retarded fluids with a strong backbone and fading memory, and so on. Further and deeper knowledge related to the physical and mathematical consequences of the structural models of liquids and of the elasticity of liquids can be found in Ref. [6]. 

FIGURE 11.11 Creep response for (a) Maxwell model, (b) Voight-Kelvin model, and (c) four-parameter model for constant stress applied at r, and removed at if... 

The early stage of development, following the works of Maxwell, Kelvin and Voight, has constituted the starting point for many other researchers. In particular in the mid 40s different modeling strategies have actually been used to describe nonlinear viscoelastic solids. 

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