Biomedical Engineering Reference
In-Depth Information
Voight Model of Viscoelasticity
−
parallel spring and dashpot
Creep
F/B
1
1
s
x
−
K/B x = dx/dt
F/B
F
1/B
Sum
dx/dt
x
1
K/B
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 4.24
Creep of the Voight viscoelastic model, a parallel combination of ideal spring and dashpot
(Figure 4.19b). This model solves the differential equation
dx
=
dt
¼
1
=
B
½
F
Kx
for
x
.
K
¼
B
¼
1, and the step applied
force is 5 arbitrary units. Displacement slowly creeps toward its steady-state value.
4.5
CARTILAGE, LIGAMENT, TENDON, AND MUS
CLE
The articulating surfaces of bones are covered with articular cartilage, a biomaterial com-
posed mainly of collagen. Collagen is the main structural material of hard and soft tissues
in animals. Isolated collagen fibers have high tensile strength that is comparable to nylon
(50-100 MPa) and an elastic modulus of approximately 1 GPa. Elastin is a protein found
in vertebrates and is particularly important in blood vessels and the lungs. Elastin is the
most linearly elastic biosolid known, with an elastic modulus of approximately 0.6 MPa.
It gives skin and connective tissue their elasticity.
4.5.1 Cartilage
Cartilage serves as the bearing surfaces of joints. It is porous, and its complex mechanical
properties arise from the motion of fluid in and out of the tissue when subjected to joint
loading. Consequently, articular cartilage is strongly viscoelastic, with stress relaxation times
