Rubber phenomenology strain dependence

The behaviour predicted for a rubber with U given by an equation of the form (6.48) has been discussed and compared with experimental data in sections 6.3.2 and 6.3.4. The prediction is either good or at least describes the data to a first approximation at low strain, depending on the type of strain. The statistical theory is, however, an improvement on the phenomenological theories discussed there in three ways ... 

The Payne effect [9] has been extensively investigated because it directly impacts the fuel consumption. From a phenomenological point of view, beyond a strain higher than a few 0.1 %, the storage modulus of filled rubber departs firom a plateau value Gq and collapse to a minimum value. The decrease in the storage modulus is accompanied by a maximum of the loss modulus, G". The amplitude of the Payne effect, AG) Gq — G increases with the filler content, the specific surface of the filler [12] and strongly depends on the surface properties of the fillers and its dispersion [13] within the matrix. On the contrary it decreases with temperature... 

It will be convenient to discuss these various aspects separately as follows (1) behaviour at large strains in Chapters 3 and 4 (finite elasticity and rubber-like behaviour, respectively) (2) time-dependent behaviour in Chapters 5-7 and 10 (viscoelastic behaviour) (3) the behaviour of oriented polymers in Chapters 8 and 9 (mechanical anisotropy) (4) non-linearity in Chapter 11 (non-linear viscoelastic behaviour) (5) the non-recoverable behaviour in Chapter 12 (plasticity and yield) and (6) fracture in Chapter 13 (breaking phenomena). However, it should be recognised that we cannot hold to an exact separation and that there are many places where these aspects overlap and can be brought together by the physical mechanisms, which underlie the phenomenological description. 

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