Schapery model parameters

The Schapery Model. One of the earliest models of the nonlinear viscoelastic response of pol5nners to use the concept of a reduced time is due to Schapery (147-149). The model is based on thermodynamic considerations and has a form similar to the Boltzmann superposition principal described previously. The model time dependences, except for the shift factors, are the same as those obtained in the linear response regime. Hence, the model is relatively easy to implement and to determine the relevant material parameters. It results in a generalization of the generalized superposition principal developed by Leaderman (150). 

The creep and recovery behaviour of an UHMWPE was studied in the region of small xmiaxial deformations by Zapas and Crissman [152]. These results are used to illustrate the capability of the Schapery model to represent the viscoelastic/viscoplastic behaviour of UHMWPE. Creep and recovery experiments were carried out on specimens under creep stresses in the range 1-8 MPa. In Figure 7.9 are plotted the creep compliances obtained, showing to be stress dependent above 1 MPa. Using the appropriate values for the model parameters, the strain under creep and creep-recovery loading conditions were very well captured as shown in Figure 7.10. 

The Schapery-Zapas-Crissman (SZC) model described in an earlier section was used to model the constitutive behavior of a [90]i6 specimen. All material parameters used in this benchmark verification are listed in Table 12.2. 

Consider a nonlinear viscoelastic material which is well modeled by the Schapery approach. Would it be possible to determine all seven (7) material parameters only using creep tests That is, not using recovery (unloading) data or a multiple steps in stress Give a detailed explanation for your answer. 

The finite element description of the nonlinear viscoelastic behavior of technical fabric was presented by Klosowski et al. [65]. The technical fabric called Panama used in this model was made of two polyester thread families woven perpendicularly to each other with the 2/2 weave. The long term uniaxial creep laboratory tests in directions were conducted at five different constant stress levels. The dense net model [66] together with the Schapery one-integral viscoelastic constitutive model [67] was assumed for the fabric behavior characterization and the least square method in the Levenberg-Marquardt variant was used for the parameters identification. 

Figure 60 illustrates two-step creep and recovery data at different stresses for a reinforced polymer along with the predictions finm the Schapery creep formulation and those obtained from simply applying a modified form of the Boltzmann superposition principle. Without going into the details of the procedures of obtaining all the parameters, it is clear that the model captures much of the observed nonlinear response, while the modified Boltzmann rule does not. (Note that the modified Boltzmann rule simply assumes additivity of responses, but without the linearity assumptions.) Figure 61 shows the creep and recovery data... 

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