Biomedical Engineering Reference
In-Depth Information
Elastic Model
−
simple spring
1
K
Stress Relaxation
x
F
6
5
4
3
2
1
0
−
1
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Time t [s]
FIGURE 4.21
Simulink model (top) and stress relaxation test of the purely elastic model, which solves
F
¼
Kx
.
Applied step displacement
x
¼
5 and spring constant
K
¼
1. Force linearly follows displacement.
Maxwell Model of Viscoelasticity
−
series spring and dashpot
Creep
x1 + F/K = x
x1
F
/B = dx1/d
t
1
Integrator
1
1/B
F
Sum
x
F/K
x = F/K + integral(F/B)
1
1/K
30
25
20
15
10
5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Time t [s]
FIGURE 4.22
Creep of the Maxwell viscoelastic model, a series combination of ideal spring and dashpot
(Figure 4.19a). The spring constant
K
¼
1, and dashpot damping coefficient
B
¼
1 (arbitrary units). This system is sub-
x
¼
F
=
K
þ
R
F
=
B
jected to a step change in force, and displacement
. The spring instantly
responds, followed by creep of the ideal dashpot, which may extend as long as force is applied.
x
arises by solving
