Adaptive Quasi-Linear Viscoelastic Modeling - Computational Modeling in Tissue Engineering - page 59

ðÞ¼ Z

t

V ð e Þ
ni

g i t s ð Þ Ded ðÞ ds ¼ Deg i ðÞ; ð 31 Þ

1

and the stress is:

Þþ De X

M

r n ðÞ¼ r o nDe ð k i nDe ð Þ g i ðÞ: ð 32 Þ

i ¼ 1

With R n (t) again denoting the experimentally recorded time course for the
relaxation of stress in the nth relaxation test, the function r o (e) can be calibrated
as:

r o nDe ð Þ¼ R n t !1 ð Þ: ð 33 Þ

Then, the values of k i (nDe) may be calibrated so that the integrals I n in Eqs. ( 27 )
are minimized for known shape functions, or the integral I in Eq. ( 28 ) is minimized
for parametric shape functions. As before, the functions k i at intermediate strain
levels may be estimated by interpolation.

3.2.2 Generalized Fung QLV Model

In the Generalized Fung QLV model, the predicted stress for the input strain
function of Eq. ( 30 ) is:

Þþ X
i

r n ðÞ¼ r o nDe ð A i nDe ð Þ g i ðÞ: ð 34 Þ

r o (e) can be calibrated using Eq. ( 33 ), and the functions A i can be calibrated at nDe
so that the integrals I n in Eqs. ( 27 ) are minimized for known shape functions, or the
integral I in Eq. ( 28 ) is minimized for parametric shape functions. As before,
interpolation may be used for intermediate strains.

3.3 Single, Large Amplitude Ramp-and-Hold Test

The ideal stepwise stretch is the preferred protocol for testing a viscoelastic
material. However, in many practical applications performing an ideal stepwise
stretch is not possible because of challenges associated with stretching the tissue
sufficiently fast, preventing tissue damage, avoiding significant wave motion, and
logging data with sufficient speed. The ramp-and-hold test is an alternative test
protocol that usually generates more accurate data compared with the stepwise
relaxation tests.