Mullins effect rubber elasticity

It will be appreciated that in the relations considered above the rubber has been treated as a perfectly elastic material, whereas in practice there several factors that cause departure from pure elastic behaviour. Hysteresis and the Payne effect are considered in Chapter 9, set, stress relaxation and creep in Chapter 10 and the Mullins effect was covered in Chapter 5. 

So far the micro-mechanical origin of the Mullins effect is not totally understood [26, 36, 61]. Beside the action of the entropy elastic polymer network that is quite well understood on a molecular-statistical basis [24, 62], the impact of filler particles on stress-strain properties is of high importance. On the one hand the addition of hard filler particles leads to a stiffening of the rubber matrix that can be described by a hydrodynamic strain amplification factor [22, 63-65]. On the other, the constraints introduced into the system by filler-polymer bonds result in a decreased network entropy. Accordingly, the free energy that equals the negative entropy times the temperature increases linear with the effective number of network junctions [64-67]. A further effect is obtained from the formation of filler clusters or a... 

Ogden RW, Roxburgh DG (1999) A pseudo-elastic model for the Mullins effect in filled rubber. Proc R Soc A 455 2861-2877... 

The Mullins effect, which can be considered as a hysteretic mechanism related to energy dissipated by the material during deformation, corresponds to a decrease in the number of elastically effective network chains. It results from chains that reach their limit of extensibility by strain amplification effects caused by the inclusion of undeformable filler particles [24,25]. Stress-softening in filled rubbers has been associated with the rupture properties and a quantitative relationship between total hysteresis (area between the first extension and the first release curves in the first extension cycle) and the enei-gy required for rupture has been derived [26,27]. 

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