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Constitutive modeling, non-linear behavior, and the stress-optic law

Constitutive modelling of the stress-strain response of rubbery polymers is described, with an emphasis on the limits to linearity for both neat and filled rubber (the latter due to the Payne effect). Deviations from the Boltzmann superposition principle (time-strain invariance) under reversing strain histories are reviewed, including a discussion of the Mullins effect. The chapter also reviews the application of the stress optic law and the conditions causing its breakdown: internal stress, the glass transition, orientational coupling, and creep recovery. Different empirical rules for nonlinear flow are considered, including the Cox-Merz rule and the relations of Laun and Gleissle.