Properties of natural materials - Orthopaedic Biomaterials in Research and Practice - page 111

At a fundamental, structure-free level, all bone has the same prop-
erties, with these being dependent on the relative proportions of three
phases: organic, mineral, and void. In vivo , the void phase is filled with
cells, cell processes, and fluid. These have not been shown to contribute
to either the static or dynamic properties of fully wet bone. Dry bone, of
course, has considerably different properties, but these are not relevant
to either tissue mechanics or to the selection of materials to augment
or replace bone. A further simplification is the observation that healthy
cortical bone possesses a fixed amount of organic tissue per unit volume,
approximately 0.6 g/cm 3 , and that its density then varies directly as its
mineral content up to a peak near 2 g/cm 3 . Osteoporotic bone is appar-
ently “normal” at this level of structure; its inferior mechanical proper-
ties derive from an absence of bone material per unit volume. Other
diseases, such as the osteomalacias, may result in deficiencies of organic
material, whereas osteopetrotic bone is essentially hypermineralized
“normal” bone.
Cortical bone is a modestly viscoelastic tissue with E R / E U = 0.95-
0.98. Over a wide range of strain rates over several orders of magni-
tudes, the modulus only increases by a factor of approximately 2. It
is highly anisotropic, displaying a fiber pattern or grain that is nearly
parallel to the long axes of long bones, with the ratios of tensile mod-
uli in the radial:transverse:longitudinal direction being approximately
1:1:2. Long bones are thus better able to resist stresses along the long
axis than across the long axis. In tension, it displays apparently elastic-
plastic behavior, with a “yield” strain of 0.5%-0.6% and an ultimate
strain near 3% (Figure 5.7). There is some doubt about this latter value
since in vivo studies and observations are consistent with considerable
ductility, perhaps as high as 5%-6%, whereas in vitro studies, even of
tissues that are fully wet, frequently show much more brittle behav-
ior, with ε u , as low as 0.9%-1%. Although these values are higher than
those for dry bone, which is quite brittle and fails at ultimate strains
of 0.4%-0.5%, the uncertainty reflects a previously discussed problem
common to tissue mechanics: the failure to consider postmortem prop-
erty changes.

Dry

?

100

Wet

σ
(MPa)

50

0.01 0.02 0.03 0.04

ε

FIGUre 5.7 stress-strain curves for wet and dry cortical bone.