Page 184 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

BIOMECHANICS OF THE MUSCULOSKELETAL SYSTEM 161

Toe Linear Failure

80

60
Stress (MPa) 40

20

0
0 2 4 6 8 10
Strain (%)
FIGURE 7.7 Idealized stress-strain curve for tendon or ligament. [Modified from Butler et
al. (1978).]

plastic changes undergone by the tissue, where a small number of fibrils first rupture, followed by
ultimate failure of the whole tissue.

7.2.3 Articular Cartilage

Articular cartilage is a white, dense, connective tissue, which appears as a layer anywhere from
1 to 5 mm thick on the bony articulating ends of a diarthrodial joint. Cartilage is multiphasic,
nonlinearly permeable, and viscoelastic. It consists of two phases: a solid organic matrix, composed
predominantly of collagen fibrils and proteoglycan macromolecules, and a movable interstitial fluid
phase, composed primarily of water. The ratio by wet weight of these two phases is approximately
4:1, with water accounting for roughly 80 percent of the total mass.
In mathematical models of healthy human joints, cartilage is often represented as a single-
phase, elastic material with homogeneous and isotropic properties. This approximation is valid,
provided only the short-term response of the tissue is of interest; when cartilage is loaded for
1 to 5 seconds, its response is more or less elastic (Hayes and Bodine, 1978; Hori and Mockros,
1976; Mak, 1986). In the long term, however, say more than 1 minute, the response of the tissue
is dominated by the nonlinear, viscoelastic properties of creep and stress relaxation (Hayes and
Mockros, 1971; Mow et al., 1984).
Kempson (1980) performed uniaxial compression tests on an isolated cylinder of cartilage.
Values of the elastic (Young’s) modulus for articular cartilage of the human knee ranged from
E = 8.4 to E = 15.4 MPa when measured 0.2 second after application of the force. Hori and
Mockros (1976) estimated the values of elastic modulus and Poisson’s ratio at 1 second of loading
by conducting torsion and confined compression tests on cartilage of the human tibia. The elastic
modulus of normal cartilage was reported to lie in the range E = 5.6 to E = 10.2 MPa, and that of
degenerate cartilage in the range E = 1.4 to E = 9.3 MPa. Poisson’s ratio for normal and degenerate
cartilage was also found to lie in the range υ = 0.42 to υ = 0.49.