Special Forms of the Viscoelastic Functions

In this section, we discuss some explicit forms of the viscoelastic functions that have been found useful in practice. There are two categories (a) exponential decay models and degenerate limits of these, and (b) power law models. The bulk of the section is devoted to the first category, partly because exponential decay models are used often in later chapters. Power law models, however, are of considerable importance in that they are both simple and physically valid to a surprising degree. 

The traditional discussion of mechanical (spring and dashpot) models and the related topic of differential forms of the constitutive equations will not be included here, but are treated extensively in several older references, Gross (1953), Ferry (1970), Bland (1960) for example. See also Nowacki (1965), Flugge (1967) and Lockett (1972). A consistent development of the theory is possible without these concepts. However, they do provide insights into the nature of viscoelastic behaviour and physically motivate exponential decay models. 

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For contact problems involving transverse motion, it would seem that no simpler method than solving (2.5.1) is available, without special assumptions on the form of the viscoelastic functions. 

The shapes of the various viscoelastic functions have been abundantly illustrated graphically, specially in Chapters 2, 12, 13, and 14. However, no numerical data have been cited. Indeed, such data are very rarely given in the literature, where space restrictions usually limit the presentation to graphical form. TJius the material for derived calculations such as those in Chapter 19 is difficult to obtain. A compendium of numerical data would be of considerable value. A few examples are given here reduced to standard reference temperatures as described in Chapter 11. The units are dynes/cm for moduli, cm /dyne for compliances, sec for time (unless otherwise noted), and radians/sec for frequency. 

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