Non-Linear Viscous Elasticity and the Eyring Shear Model

Attempts to analyze stress-strain-time relationships observed in experiments with textile fibers have been reported in a series of papers. This work has led to some general conclusions: First, the simplest three element model (spring in parallel with another spring and a dashpot in series) is adequate for the approximate explanation of a wide range of the data obtained. Second, the viscous element (dashpot) almost always appears to be non-Newtonian while the springs less frequently are non-Hookean. Third, the most striking deviations from simple behavior indicate, not a more complex model consisting of many simple elements, but that the assumed laws governing the viscous, or less frequently, elastic elements are themselves too simple. Frequently a more complex law or laws will restore the three-element model to approximate agreement with the experimental facts. Finally, any system so far investigated can be made to show the presence of a number or a distribution of relaxation times by prolonging the experiment over a period of time, or more positively, by going to a point of no instantaneous relaxation, and waiting for the inevitable long period of relaxation to appear. Procedures to deal with the general situation described here are presented. The paper begins with a condensed but essentially self-contained summary of the theoretical portions of the series of papers that preceded it. The original presentation has been clarified and recast in a form more in harmony with the present work. For experimental evidence, and supplementary information, the reader is referred to the original series. The paper continues with a discussion of the various aspects of non-linear viscous elasticity, including the topics: Six rules for analyzing stress-strain curves (presented at the meeting of the Division of High-Polymer Physics of the American Physical Society, January 31, 1947); the thixotropic viscous element, where for convenience, complex situations, in which the populations of various states enter into a time-variable viscosity, have been gathered under the name ``thixotropy''; constant force springs, where a particularly non-Hookean behavior is described.