Mooney-Rivlin solid

The elastic free energy of the so-called Mooney-Rivlin solid is obtained from Equation (46) as... 

AAei = Cioo(Ji -3) -H Coio(l2 -3) is called the Mooney-Rivlin solid. 

The reduced force is obtained for the Mooney-Rivlin solid as... 

Figure 28 41 depicts the isochronal Mooney-Rivlin plots for SBR-1, where the extrapolated values of bW/bli and X lbW/bI2 are represented by solid lines and the sum of them by broken lines. As above, these sums are equivalent to the Mooney-Rivlin plot of uniaxial data. We again find that the slope of the sum curves depends mainly on the Xj dependence of bW/dli and therefore the slope is not equal to... 

Figure 6-6. Simulated Mooney-Rivlin plot, equation (6-82), for C2/C = 2. Solid line is the undistorted response of the material "data" are the results with a 1% (standard deviation) random error incorporated into both the force and length "measurements."...

An alternative model which also describes stress-strain data for larger deformation is presented by the Mooney-Rivlin equation [40, 41], The equation describes the rubber elasticity of a polymer network on the basis that the elastomeric sample is incompressible and isotropic in its unstrained state and that the sample behaves as Hookean solid in simple shear. In a Mooney-Rivlin plot of a uniaxial deformation, the experimental measured stress cr, divided by a factor derived from classical models, is plotted as function of the reciprocal deformation 1/A ... 

Figure 9.18 Mooney-Rivlin plot for sulfur-vulcanized natural rubber. Solid line, equation (9.48) dotted line, equation (9.63).

The form of the stress-strain curve for rubbers subjected to unidirectional extension shows significant departures from theory. This is illustrated in Fig. 1 where curves calculated from eg. 8, shown dashed, are compared with the solid curve calculated according to the Mooney-Rivlin empirical equation which can be written... 

Finally, it is worth mentioning another approach used to describe nonlinear viscoelastic solids nonlinear differential viscoelasticity [49, 178, 179]. This theory has been successfully applied to model finite amplitude waves propagation [180-182]. It is the generalization to the three-dimensional nonlinear case of the rheological element composed by a dashpot in series with a spring. Thus in the simplest case, the stress depends upon the current values of strain and strain rate rally. In this sense, it can account for the nonlinear short-term response and the creep behavior, but it fails to reproduce the long-term material response (e.g., relaxation tests). The so-called Mooney-Rivlin viscoelastic material [183] and the incompressible version of the model proposed by Landau and Lifshitz [184] belraig to this class. 

Destrade M, Saccomandi G (2004) Finite-amplitude inhomogeneous waves in Mooney-Rivlin viscoelastic solids. Wave Motion 40 251-262... 

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