Non-linear Viscoelastic Behavior: Approximate Approaches, Simplified Models and the Basis for Improved Versions

The earliest approaches to non-linear viscoelasticityNon-linear viscoelasticity (simplified generalizations of Boltzmann’s superposition principleBoltzmann’s superposition principle, direct treatment of experimental creep data and semi-empirical correlationsSemi-empirical correlations) are followed by the description of the first attempts at viewing the molecular scale processes as thermally activated. A series combination of an activated “dashpot” was the model chosen to describe non-linearity and, despite its simplicity, basic agreement was obtained with experiments on specific polymer systems. It is then argued that what the field of non-linear viscoelasticity still lacks is (1) an effective account for a range of molecular structures taking part in materials’ responses and the resulting spectra of characteristic times, and (2) a general mechanistic and dynamic description of the processes at the molecular scale. With those objectives, it seemed important to illustrate how one might devise insightful physical models and formulations of the process of non-linear creepNon-linear creep. The example given is too specific, with excessive microscopic detail, thus restricting its applicability, but its application to polymer creep data suggested a strong connection of the range of retardation times to a range of “relaxor” sizes, indicating that cooperativity and clustering will hold the key for successful and desirably universal formulations of the behavior of amorphousPolymersamorphous condensed matter.