Adaptive Quasi-Linear Viscoelastic Modeling - Computational Modeling in Tissue Engineering - page 67

Fig. 5 Experimentally recorded stress histories for four incremental ramp-and-hold tests
performed on a single reconstituted collagen specimen [ 55 ]. The nominal strain increment is
0.0667 in all tests. The ramp portion is expanded in time scale for clarity. a Initial strain of 0;
b Initial strain of 0.0667; x c Initial strain of 0.1333; d Initial strain of 0.2000

0.2667, respectively. As the stress was zero initially, r o (e = 0) = 0. Calibration
k 1 , k 2 and k 3 required calculation of the model prediction of the hold stresses. For
the g i functions given by Eq. ( 51 ), the G i functions are:

; G 2 ð t Þ¼ s 2 ; G 3 ð t Þ¼ s 3 :

1 e t = s 1 1 e t = s 2 1 e t = s 3

G 1 ð t Þ¼ s 1 ð 54 Þ

Substituting these into Eq. ( 45 ), the hold stress is:

e t = s i :

X

3

Þ þ 0 : 0667
20

e 20 = s i 1

r Hn ð t Þ¼ r o 0 : 0667n ð k i 0 : 0667n ð Þ s i ð 55 Þ

i ¼ 1

The hold-relaxation stress prediction is, in this case, an exponential function
with the same exponents as the reduced relaxation functions:

Þ þ X

3

Þ e t = s i ; r Hn ð t Þ¼ r o 0 : 0667n ð c i 0 : 0667n ð ð 56 Þ

i ¼ 1