Stable fitting of noisy stress relaxation data

Abstract

The mechanical behavior of a viscoelastic material can often be described by a spectrum of Maxwell-Wiechert elements. The inverse problem associated with estimating the parameters of this spectrum from the results of viscoelastic relaxation (ramp-and-hold) test is in general ill-posed and unstable, with estimates highly sensitive to initial conditions and noise. Here, we demonstrate stable estimation of a continuous viscoelastic spectrum from stress relaxation experiments using Tikhonov regularization. We assess the effects of noise and sampling frequency on these estimates, and describe regularization parameter selection. We demonstate the algorithm by estimating the viscoelastic relaxation spectra of soft vinyl samples.