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

G. Mattei,A. Ahluwalia

doi:10.1007/s11043-018-9385-0

G. Mattei, A. Ahluwalia

Open Access

https://doi.org/10.1007/s11043-018-9385-0

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Abstract

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

Highlights

To date, different testing and analysis methods are used to derive quantitative mechanical properties for describing intrinsic material behavior and predicting material responses under specific loading conditions (Mattei and Ahluwalia 2016)
The same apparent elastic moduli reported in Tirella et al (2014) for both 5% w/v Type A gelatin and PDMS (10:1 base to catalyst) tested in unconfined compression at different constant strain rates (n = 3 replicates per strain rate) were used in this work to obtain two experimental Eapp vs. εdatasets to analyze with the new Eapp(ε) fitting method
To overcome the issues of pre-stress and long experimental testing trials for viscoelastic characterization of soft materials using classical testing methods, we developed the epsilon dot method which is based on a series of rapid strain rate measurements (Mattei et al 2015b; Tirella et al 2014)

Summary

Introduction

Different testing and analysis methods are used to derive quantitative mechanical properties for describing intrinsic material behavior and predicting material responses under specific loading conditions (Mattei and Ahluwalia 2016). If a material is subjected to strain or stress inputs small enough so that its rheological functions do not depend on the input level, the material response is said to be within the linear viscoelastic range (LVR). Another popular method to characterize material viscoelastic behavior is through dynamic mechanical analysis (DMA), based on applying a small amplitude cyclic strain (or stress) input on a sample and measuring the resultant cyclic stress (or strain) response (Gabler et al 2009; Kiss et al 2004; Soong et al 2006).

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