Visco-elastic stress analysis

Abstract

heated. In any case, it is clear that the most rapid convergence is obtained for small x and y and comparatively large t. Although the first term appears formidable, it turns out that in many instances the arctan and log terms are negligible. For example, if k = 103, a = 2, and xy < 4/106, the arctan and log may be neglected if an error within ±1/10 is satisfactory. Since the series is alternating, the error involved is less, in absolute value, than the first term not employed in the calculation. Thus, once k and a are fixed, one might check terms, beginning with the third, i.e., ka2xy/9&Tt3 [a2/3 + x2 + y2\, in order to obtain a range for x, y, and t so that a given error tolerance is not exceeded. From the form of each term, an inequality involving the product, xy, is simplest to handle and furnishes a good check for x and y small. As a usual occurrence the calculation of three or four terms gives sufficient accuracy for applied purposes provided a reasonable balance is maintained among the variables.

Scaling, dimensional analysis, and indentation measurements

“…In fact, theoretical studies of contacting linear viscoelastic bodies can be traced to the mid 1950s. Lee [214], Radok [215], and Lee and Radok [216] have analyzed several viscoelastic contact problems using the elastic-viscoelastic correspondence principle. Their approach was to replace the materials elastic constants in the elastic solutions of contact problems by the corresponding differential operators in the viscoelastic constitutive equation.…”

Modeling indentation in linear viscoelastic solids

“…Modeling of indentation into viscoelastic solids thus forms the basis for analyzing indentation experiments in these materials. Theoretical studies of contacting linear viscoelastic bodies became active since the mid 1950s by the work of Lee [1], Radok [2], Lee and Radok [3], Hunter [4], Gramham [5,6], Yang [7], and Ting [8,9]. In recent years, a number of authors have extended the early work to the analysis of indentation measurements [10][11][12][13][14][15].…”

On the role of scales in elastomer friction

“…This general behavior was recognized by Lee and Radok [9,10] and was verified numerically for fractal rough surfaces [11]. Further, the contact configuration at a given depth remains approximately invariant for media with thin coatings [12] and for multi-layered systems, provided the difference of elastic properties of the different layers is not too large [13].…”