Transient response, nonlinear viscoelasticity

Transient Response Constant Rate of Deformation. The constant rate of deformation response of the linear viscoelastic material was discussed above. From that discussion, the stress-deformation response looks nonlinear even when the material is linear viscoelastic. For the nonlinear material the response will not be simply described by the linear viscoelastic laws. However, the curves will look similar at low strain rates. At higher strain rates, a stress overshoot is observed. 

Transient Response Creep. The creep behavior of the polsrmeric fluid in the nonlinear viscoelastic regime has some different features from what were found with the linear response regime. First, there are no ready means of relating the creep compliance to the relaxation modulus as was done in the linear viscoelastic case. In fact, the relationship between the relaxation properties and the creep properties depends entirely on the exact constitutive relationship chosen for the response of the material, and numerical inversion of the specific constitutive law is ordinarily necessary to predict creep response from the relaxation... 

Behavior of Entangled Polymer Melts and Solutions Transient Response. While the steady-state response of polymers in shear and elongational flows is of much interest, there are also many instances in which the transient response is important because not all processes attain steady state. There are two important transient responses in the nonlinear regime of behavior. These are the stress relaxation response in which the deformation is held constant and the stress evolution with time is followed. This was discussed above for the linear viscoelastic case. In addition, the response to a constant rate of deformation can be an important transient response to study. Also note that creep experiments are sometimes used to characterize the nonlinear response of polymeric fluids and these will also be discussed briefly. 

Transient Response Constant Rate of Deformation. The constant rate of deformation response of the linear viscoelastic material was discussed above. Prom that discussion, the stress-deformation response looks nonlinear even when the material is linear viscoelastic. For the nonlinear material the response will not be simply described by the linear viscoelastic laws. However, the curves will look similar at low strain rates. At higher strain rates, a stress overshoot is observed, which cannot occur for the linear viscoelastic material. Figure 26 shows the effect of increasing the strain rate on the transient stress-time response (which is related to the strain) for a polymer solution (81). As seen, the stress overshoot becomes weaker with decreasing strain rates (when the material response may be linearly viscoelastic) however, as strain rate increases, there is an onset of... 

The utility of the K-BKZ theory arises from several aspects of the model. First, it does capture many of the features, described below, of the behavior of polymeric melts and fluids subjected to large deformations or high shear rates. That is, it captures many of the nonlinear behaviors described above for steady flows as well as behaviors in transient conditions. In addition, imlike the more general multiple integral constitutive models (108,109), the experimental data required to determine the material properties are not overly burdensome. In fact, the information required is the single-step stress relaxation response in the mode of deformation of interest (72). If one is only interested in, eg, simple shear, then experiments need only be performed in simple shear and the exact form for U I, /2, ) need not be obtained. Furthermore, because the structure of the K-BKZ model is similar to that of finite elasticity theory, if a full three-dimensional characterization of the material is needed, some of the simplilying aspects of finite elasticity theories that have been developed over the years can be applied to the behavior of the viscoelastic fluid description provided by the K-BKZ model. One such example is the use of the VL form (98) of the strain energy function discussed above (110). The next section shows some comparisons of the material response predicted by the K-BKZ theory with actual experimental data. 

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