Adaptive Quasi-Linear Viscoelastic Modeling - Computational Modeling in Tissue Engineering - page 72

Fig. 8 Elastic part of the stress (a) and three nonlinear functions: A 1 (b), A 2 (c) and A 3 (d) for
Generalized Fung QLV model. Gray circles are calibrated values based on experimental data and
black curves are incrementally linear interpolations
4.3.2 Single, Large Amplitude Ramp-and-Hold Test
The final test of the model fits came from the single, large amplitude ramp-and-
hold test, performed at a loading rate different from that used for model calibra-
tion. The ramp loading and hold relaxation stresses of the tissue specimen in the
large amplitude ramp-and-hold test (Fig. 11 a and b, respectively) show that, for
the first 3 s of the ramp loading, the tissue stress remains almost zero, while the
nominal strain increased (linearly) to about 0.08. In these reconstituted collagen
specimens, this is an indicator of plastic deformation that increased the initial zero
stress length of the specimens over the course of the series of incremental ramp-
and-hold tests that preceded the single, large amplitude ramp-and-hold experiment
presented in Fig. 11 . The models were adapted for this inelastic deformation by
increasing the zero stress length of the tissue for both elastic and viscous com-
ponents of the stress by plastic strain increments De i . These additional parameters
were calibrated using the hold relaxation stress in the large amplitude ramp-and-
hold test without altering the already calibrated shape functions or nonlinear
functions. We were able to calibrate these plastic strains for an excellent fit of the
hold relaxation data in both the Adaptive QLV and Generalized Fung QLV models
(Fig. 11 d and f, respectively).