Methods of interconversion between linear viscoelastic material functions. Part II—an approximate analytical method

Abstract

A new, very simple approximate interconversion method is proposed and verified by examples. This technique, employing the slope of the source function on logarithmic scales, is found to substantially enhance the accuracy compared to existing approximate methods. The new method is based on the characteristic mathematical properties of the narrow-band weight functions involved in the interrelationships between broad-band material functions. With the material functions represented locally by a power law, they are interrelated in terms of adjustment factors expressed through the local, log–log slope of the given (source) function. A number of existing approximate interconversion methods are also tested and compared with the new method. In Part I ( Park and Schapery, 1998) , an efficient numerical interconversion method, based on a Prony (exponential ) series representation of both the source and target functions, was presented ; such a series representation is not needed here. The new method, when applied to the prediction of broad-band time-dependent functions from Laplace or Fourier transforms, is an approximate method of transform inversion that is applicable to functions which are not necessarily viscoelastic material functions.