On the inference of viscoelastic constants from stress relaxation experiments

Abstract

Several constitutive theories have been proposed in the literature to model the viscoelastic response of materials, including widely used rheological constitutive models. These models are characterized by certain parameters (“time constants”) that define the time scales over which the material relaxes. These parameters are primarily obtained from stress relaxation experiments using curve-fitting techniques. However, the question of how best to estimate these time constants remains open. As a step towards answering this question, we propose an optimal experimental design approach based on ideas from information geometry, namely Fisher information and Kullback–Leibler divergence. The material is modeled as a spring element in parallel with multiple Maxwell elements and described using a one- or two-term Prony series. Treating the time constants as unknowns, we develop expressions for the Fisher information and Kullback–Leibler divergence that allow us to maximize information gain from experimental data. Based on the results of this study, we propose that the largest time constant estimated from a stress relaxation experiment for a linear viscoelastic material should be at most one-fifth of the total time of the experiment in order to maximize information gain. Our results also provide confirmation that the equilibrium modulus of the material cannot be reliably determined from curve-fitting to data from a stress relaxation experiment.