Adaptive Quasi-Linear Viscoelastic Modeling - Computational Modeling in Tissue Engineering - page 71

applicable to exponential shape functions) to obtain the same time constants as
those found for the Adaptive QLV model, which results in slightly different m ni
coefficients. Note that the functions A i of the Generalized Fung QLV model differ
fundamentally from the k i functions of the Adaptive QLV model: although they are
on the same order of magnitude, one is placed inside the convolution integral,
while the other is placed outside.

4.3 Assessment of Predictions

The predictive ability of a model may be examined against experimental data that
was not used for calibration. As described above, the incremental ramp-and-hold
protocol always provides such data for model evaluation. The subsequent single
large amplitude ramp-and-hold test, which occurred at a different strain rate,
provides additional data for model evaluation. In this section we provide examples
of model calibration using both sets of data.

4.3.1 Incremental Ramp Stresses

The ramp loading stresses predicted by the Adaptive QLV model are:

0 : 0667 ð n 1 Þþ 0 : 0667
20

r Pn ð t Þ¼ r o t

c i ð t Þ;

X

þ 0 : 0667
20

0 : 0667 ð n 1 Þþ 0 : 0667
20

k i t ð 62 Þ

i

where G i functions are given in Eq. ( 54 ), and those predicted by the Generalized
Fung QLV model are:

0 : 0667 ð n 1 Þþ 0 : 0667
20

r Pn ð t Þ¼ r o t

Z e t ð = s i ds :

t

X

3

þ 0 : 0667
20

0 : 0667 ð n 1 Þþ 0 : 0667
20

A i t ð 63 Þ

i ¼ 1

0

Using the model parameters calibrated to the hold-relaxation data, the model pre-
diction for the ramp stress histories were calculated for each incremental test and
compared to experimental data (Fig. 10 )[ 55 ]. Both the Adaptive QLV and General-
ized Fung QLV models could reasonably predict the ramp stresses during incremental
testing. The predictions of these two calibrated QLV models were slightly different for
the ramp loading stress, although both models reproduced the hold-relaxation data
almost identically. The Adaptive QLV model exhibited a slightly larger upward cur-
vature for the ramp stresses compared with the Generalized Fung QLV model.