LAUSR

We introduce a new function, the apparent elastic modulus strain-rate spectrum, Eapp(ε˙)$E_{\mathrm{app}} ( \dot{\varepsilon} )$, 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˙$\dot{\varepsilon}$). The Eapp(ε˙)$E_{\mathrm{app}} ( \dot{\varepsilon} )$ function was derived using the tangent modulus function obtained from the GM model stress-strain response to a constant ε˙$\dot{\varepsilon}$ input. Material viscoelastic parameters can be rapidly derived by fitting experimental Eapp$E_{\mathrm{app}}$ data obtained at different strain rates to the Eapp(ε˙)$E_{\mathrm{app}} ( \dot{\varepsilon} )$ 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.