The theory of Mooney and Rivlin

Mooney (1940, 1948) and Rivlin (1948) derived eq. (3.54) on the basis that the rubber was incompressible 

It is interesting to compare eq. (3.54) with the expressions obtained from the statistical theories (Fig. 3.20). According to both the affine network model and the phantom network model of James and Guth, the reduced stress remains constant and independent of strain, which is not the case for the Mooney-Rivlin equation. 

According to Flory, the coefficient C2 is related to the looseness with which the crosslinks are embedded within the structure. This is supported by the fact that C2 has been found to decrease with increasing solvent content in swelled rubbers. At a polymer content of i 2 = 0.2, C2 approaches zero. 

The elasticity of rubbers is predominantly entropy-driven which leads to a number of spectacular phenomena. The stiffness increases with increasing temperature. Heat is reversibly generated as a consequence of an applied elastic force and stretching. 

The affine network model assumes that the network consists of phantom Gaussian chains, that all network changes are entropical, that deformation is affine and that the volume remains constant during deformation, and yields the following expression for the free energy change accompanying the deformation Ui, A2, 

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The theory of Mooney and Rivlin, which is based on continuum mechanics, yields the following expression for a uniaxially stressed rubber ... 

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