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, E app (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 E app (ε) function was derived using the tangent modulus function obtained from the GM model stress-strain response to a constantε input. Material viscoelastic parameters can be rapidly derived by fitting experimental E app data obtained at different strain rates to the E app (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.

4D live imaging and computational modeling of a functional gut-on-a-chip evaluate how peristalsis facilitates enteric pathogen invasion

“…Three measurements were taken at each of the different spots: one at an initial time (0 hour); another after 2 hours, right before adding trypsin; and a third at 3 hours, an hour after trypsinization. The resulting values of τ c did not change over the first 2 hours (1.02 ± 0.03 s at 0 hour, 1.00 ± 0.04 s at 2 hours, SD) only to default to the range of PDMS values found in the literature ( 45 , 76 ) after the trypsinization process (0.68 ± 0.02 s at 2 + 1 hours, P = 1 × 10 −6 , n = 4). The value of τ c reported in ( 45 ) for PDMS varies according to polymer cross-linking, which is regulated by the concentration of linker enzymes during polymerization; the rest of constants do not seem to be indicative in this respect.…”

Development and validation of subject-specific 3D human head models based on a nonlinear visco-hyperelastic constitutive framework

“…With the LVE model parameters from the first step, a recently proposed frequency to strain rate domain conversion technique [63][64][65] is utilized to obtain the O-USS visco-hyperelastic model parameters (figure 3b). In this method, the LVE properties are first used to predict the stress versus strain responses under shear and uniaxial deformation modes, at multiple constant strain rates.…”

“…A 0.001-200 s −1 strain rate range is chosen, which is the approximate range of strain rates in real-life brain injury events [66] (note, this range extends beyond the observed strain rates in MRE measurements to permit potential extrapolation to injurious loading conditions). The stress-strain responses are then used to compute the apparent elastic moduli-strain rate spectra [63] at each brain voxel,…”

“…A 0.001–200 s −1 strain rate range is chosen, which is the approximate range of strain rates in real-life brain injury events [66] (note, this range extends beyond the observed strain rates in MRE measurements to permit potential extrapolation to injurious loading conditions). The stress–strain responses are then used to compute the apparent elastic moduli-strain rate spectra [63] at each brain voxel,4pt1emGappfalse(γ˙false)=μ∞+G0false∑i=12⁡ginormale−γLVR/false(2γ˙τifalse),1emEappfalse(ε˙false)=3Gappfalse(ε˙false),where G app and E app are strain rate-dependent apparent shear and uniaxial moduli, respectively; γ and ε denote shear strain and uniaxial strain, respectively. γ LVR is the linear viscoelastic regime (LVR) limit, which is approximately 0.01 mm mm −1 for brain tissue [28–30].…”