Inversion of Creep Response for Retardation Spectra and Dynamic Viscoelastic Functions

The basic problem addressed here is that of obtaining the unknown retardation time spectrum from experimental creep response curves. The spectrum may be a set of discrete times or it may be a spectrum characterized by a continuous distribution function. The present work employs a general model which assumes that the observed creep compliance is due to the summed effect of an arbitrary distribution of mechanisms. The analysis requires the solution of Fredholm integral equations of the first kind. It is well known that this problem is ill-conditioned so that any numerical scheme will have to involve some smoothing to obtain accurate solutions. The present work employs Butler’s method of constrained regularization which takes advantage of the fact that the solution is positive and uses data-dependent smoothing. This work indicates that the imposition of the positivity constraint makes the computation of the solution much better conditioned. Computations with the method of constrained regularization employing near-optimal smoothing demonstrate its superiority over the method of Schapery for obtaining accurate solutions when the data are very noisy.