Historical Introduction to Non-linear Viscoelasticity Theory

Wineman [14] has recently reviewed the fleld of non-linear viscoelasticity, noting its 40-year history, and the limited number of engineering applications hitherto. Etrapaca, Sivaloganathan and Tend [15] have also produced a review, in which they note the large variety of different and seemingly unconnected theories. 

Non-linear viseoelastie theories can also be created by generalising the Boltzmann superposition prineiple (see Chapter 5). Leaderman [18], working on polymer fibres, was the first to do this and Findley and Lai [19] have adopted a similar approach. Non-linearity is introdueed into the Boltzmann integral by ineluding strain or stress dependence into the integrand. Leaderman s integral takes the form 

2 Multiple-Integral Theories - Green and Rivlin, Pipkin and Rogers Green and Rivlin [21] made minimal physical assumptions, to the effect that 

Stresses are objective , such that different observers will derive consistent results and 

The stress depends only on the history of the strain, or equivalently that the strain depends only on the stress history. 

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