Page 250 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

BONE MECHANICS 227

FIGURE 9.4 Typical stress-strain behavior for FIGURE 9.5 Creep response of cortical bone for
human cortical bone. The bone is stiffer in the longitu- three different stress levels. When a low stress is
dinal direction, indicative of its elastic anisotropy. It is applied to the bone, the strain remains constant over
also stronger in compression than in tension, indicative time, and there is no permanent deformation after
of its strength asymmetry (modulus is the same in unloading. For stresses just below yield, strains increase
tension and compression). (From Ref. 9.) with time at a constant rate, and a small permanent
deformation exists after unloading. As the magnitude
of the stress is increased, the rate of creep increases,
and a larger permanent deformation exists after
unloading. (From Ref. 109.)

can develop when large intramedullary tapered implants such as uncemented hip stems are impacted
too far into the diaphysis.
While it is often appropriate to assume average properties for cortical bone, as shown in Tables 9.1
and 9.2, it may be necessary in some cases to account for the heterogeneity that can arise from
variations in microstructural parameters such as porosity and percentage mineralization. Both mod-
ulus and ultimate stress can halve when porosity is increased from 5 to 30 percent 10,23 (Fig. 9.6a).
Small increases in percentage mineralization cause large increases in both modulus and strength (see
10
Fig. 9.6b), and while this parameter does not vary much in adult humans, it can vary substantially
across species. 24
Aging also affects the mechanical properties of cortical bone. Tensile ultimate stress decreases
at a rate of approximately 2 percent per decade 25 (Fig. 9.7a). Perhaps most important, tensile ulti-
mate strain decreases by about 10 percent of its “young” value per decade, from a high of almost

FIGURE 9.6 (a) Dependence of the ultimate tensile stress of human cortical bone on volume fraction (expressed
as a percentage). Ages of the specimens were in the range 20 to 100 years. (From Ref. 10.) (b) Modulus versus
calcium content (in mg/g of dehydrated bone tissue) for cortical bone taken from 18 different species. (From
Ref. 24.)