Kelvin-Voigt test

In the Kelvin-Voigt test, emax is imposed almost instantly and maintained, while a declining t is measured from its corresponding maximum (Fig. 2b Kaelble, 1971) ... 

To model the flexural dynamics of the test specimen, two masses and a Kelvin-Voigt element are used. The first mass, Wjc, represents the inertia of the central part of the specimen and it is also the mass first involved in the local interaction at the contact point. The second mass, Wj,., represents the inertia of the wings of the specimen. 

The most direct way to study arterial viscoelasticity is to determine the response of the test tissue to oscillatory stresses. If the arterial wall is conceived to be represented by a simple Kelvin-Voigt model consisting of a spring and a dashpot in parallel, the dynamic elastic component and the viscous component of a vessel can be expressed as... 

If a creep test is performed on a Kelvin-Voigt model, the strain gradually builds up to a constant value as described by... 

If we now stress the Burgers model in a creep test, it is easy to see what will happen, see figure 3 first, the unrestrained spring Gi will instantaneously deform to its expected extent, while the isolated dashpot will start to deform at its expected rate. However, the spring in the Kelvin-Voigt element cannot immediately respond, being hindered (i.e. retarded) by its dashpot. Nevertheless, it does begin to deform, and eventually comes to its expected steady-state deformation. It is possible to show that the overall deformation can be written down as ... 

Recently Bonner et al. [135] have shown that the recovery behaviour of a lactide based copolymer can be predicted by a Kelvin-Voigt model (see Chapter 5, Section 5.2.5) where the recovery stress in the spring and the dashpot viscosity can be determined using the transient stress dip test of Fotheringham and Cherry [70]. The recovery stress ory is... 

This means in the Kelvin-Voigt model, the stress is constant during the stress relaxation test (Figure 16.22B), which is not trae for real polymer fibers. 

Figure 16.22. Behavior of the Kelvin-Voigt model in (A) creep and (B) stress relaxation tests.

Basis for the planned investigation are the creep curves of plastics under the influence of media. To describe the material behaviour of the plastics in the creep test the material models of Kelvin-Voigt and Maxwell are used. The combination of these two models can be seen in Figure 9. They are formed by a parallel and a serial use of a spring and a damper. According to this model the strain can be described as a function of the constant stress gq and the properties of the springs and dampers as follows ... 

The static tests considered in Chapter 8 treat the rubber as being essentially an elastic, or rather high elastic, material whereas it is in fact viscoelastic and, hence, its response to dynamic stressing is a combination of an elastic response and a viscous response and energy is lost in each cycle. This behaviour can be conveniently envisaged by a simple empirical model of a spring and dashpot in parallel (Voigt-Kelvin model). 

For creep tests, a generalized Voigt-Kelvin model is used (Figure 15.11). The creep response of an individual Voigt-Kelvin element is given by... 

Example 15.1 analyzes the response of a Maxwell element in an engineering stress-strain test. Do the same thing for a Voigt-Kelvin element. Illustrate the effect of strain rate with a sketch. Do not expect great realism. 

---