A new analytical method for estimating lumped parameter constants of linear viscoelastic models from strain rate tests

Abstract

We introduce a new function, the apparent elastic modulus strain-rate spectrum, Eapp(ε˙) , for the derivation of lumped parameter constants for Generalized Maxwell (GM) linear viscoelastic models from stress-strain data obtained at various compressive strain rates (ε˙). The Eapp(ε˙) function was derived using the tangent modulus function obtained from the GM model stress-strain response to a constant ε˙ input. Material viscoelastic parameters can be rapidly derived by fitting experimental Eapp data obtained at different strain rates to the Eapp(ε˙) function. This single-curve fitting returns similar viscoelastic constants as the original epsilon dot method based on a multi-curve global fitting procedure with shared parameters. Its low computational cost permits quick and robust identification of viscoelastic constants even when a large number of strain rates or replicates per strain rate are considered. This method is particularly suited for the analysis of bulk compression and nano-indentation data of soft (bio)materials.