Mooney-Rivlin model

The true stress in the Mooney-Rivlin model can be obtained from the free energy density ... 

In uniaxial extension, the Mooney-Rivlin model predicts Eq. (2) to hold, where Q and C2 are two material constants. 

Fig. 22.13 Reduced stress representation of the stress-strain curves for the four adhesives. The broken line is an illustrative fit of the data with the Mooney-Rivlin model.

Fig. 22.14 Experimental data (O) and best fit (full line) with the Mooney-Rivlin model in uniaxial extension.

The nonlinear elastic properties can be described by both the Mooney-Rivlin model and the molecularly based slip-tube model. Both of these models stress the fact that the low-strain modulus of the adhesives is controlled by the entanglement structure of the isoprene -i- resin phase, while the high-strain modulus is controlled by the physical crossHnk structure. The incorporation of diblocks in the adhesive dramatically reduces the density of crossHrrks and causes a more pronounced softening in the high-strain part of the stress-strain curve. 

The preceding equations provided a reasonable foundation for predicting DE behavior. Indeed the assumption that DEs behave electronically as variable parallel plate capacitors still holds however, the assumptions of small strains and linear elasticity limit the accuracy of this simple model. More advanced non-linear models have since been developed employing hyperelasticity models such as the Ogden model [144—147], Yeoh model [147, 148], Mooney-Rivlin model [145-146, 149, 150] and others (Fig. 1.11) [147, 151, 152]. Models taking into account the time-dependent viscoelastic nature of the elastomer films [148, 150, 151], the leakage current through the film [151], as well as mechanical hysteresis [153] have also been developed. 

Plot of tensile and compressive data for a silicone rubber sample (replotted from Gottlieb, Macosko, and Lepsch, 1981) compared with predictions of the neo-Hookean (C s 101 kPa) and Mooney-Rivlin models (Ci = 17.5 kPa.C2 = 16.5kPa). 

Example 1.6.1 shows that both the neo-Hookean and Mooney-Rivlin models are of the Valanis-Landel form. 

Mooney—Rivlin model would describe the behaviors exhibited (89—91). The reader is referred to reviews of various proposed strain energy functions (89,92,93) for further information. 

Comparison with values of and of the NAST model described earlier supports this hypothesis [36]. However, unlike the NAST model, the Mooney-Rivlin model fails to predict compression data as the linearity shown in Figure 9.21 continues for a > 1, whereas the experimental data show a maximum and a decrease in the function plotted in Figure 9.21. There have been many other constitutive relations for rubbers based on different representation of the strain energy function... 

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