Modeling G vs. Strain

Extracting data Strain (%) N660G (MPa) N330G (MPa) NllOG (MPa) 

Guess parameters for nonlinear fitting algorithm (GenFit function) Finding max G and corresponding y 

The Kraus model fits reasonnably well the experimental G data but cannot meet the asymmetric shape of G vs. strain data. 

Note the results of the nonlinear algorithm are very sensitive to the initial guess values, particularly for y using the strain position of somewhat reduces this problem. 

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As can be seen, the model fits reasonably well the experimental G data but cannot meet the asymmetric shape of G" vs. strain data. The exponent m is depending on the reinforcing character of the filler, as well as the critical strain y. A similar assessment of the Kraus equations with a silica (40 phr) filled polydimethylsiloxane composite yielded the same conclusions regarding the low strain deficiencies of Equation 5.39. For such a silica filled material, fit parameter values were as expected different, i.e., 0.02 and m 0.45 for G (Yo) Yc 0.01 and m 0.35 for G"(Yo)-... 

Due to its starting hypotheses, the Maier and Goritz model has a mathematical form that leads to symmetries in both the G vs. strain and the G" vs. strain functions the former exhibits an horizontal symmetry with respect to a mid- modulus value, the latter shows vertical symmetry with respect to a critical strain=l/c. 

A related issue is that the modulus is a viscoelastic property, as evidenced by the temperature/strain-rate dependence, and that for most poljnners (at least those without a large beta transition near the alpha transition) time-temperature superposition of, for example, the shear relaxation modulus is valid (80). Further, G Sell and McKenna (81) have shown that the 5neld stress vs strain rate also seems to obey time-temperature superposition. Hence there is a correlation between the viscoelastic properties and the yield response of pol5uners, though one that is not generally stated explicitly. We note that some of the models mentioned previously, such as those of Caruthers group (41,42), Tervoort and co-workers (40), and Knauss and Emri (35), are (nonlinear) viscoelastic models that have yield arising due to the nonlinear response induced by the material clock (see Viscoelasticity). 

As indicated earlier the ER particle may form a network structure instead of the nbrillaled chain structure once the particle volume fraction exceeds the critical volume fraction 162,83], due to the percolation transition. Under a large amplitude shear field the formation and destruction of network junctions may happen one after the other, and thus the type III LAOS behavior may best describe ER suspensions. Figure 43 shows the simulated storage and loss moduli vs. strain amplitude at different frequencies, using an idealized electrostatic polarization model of ER fluids that was implemented in the particle-level dynamics simulation. Tlie storage modulus G and loss modulus G" remain constant up to a certain strain amplitude (/() 0.4), which defines the linear response region. With further increase... 

In Fig. 13.18 the strain of a Burgers element, after applying a constant stress cr0 at time zero, is plotted vs. time. It clearly shows the various contributions and how the various model constants can be determined there is an instantaneous strain mom equal to time dependent part belonging to the Voigt-Kelvin part. For long times (e.g. t 10t) the strain becomes a linear function of time, with a slope equal to crQ/pM. 

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