Properties of natural materials - Orthopaedic Biomaterials in Research and Practice - page 118

found in vertebral bodies, owing to a transition of cancellous bone from
an open or network sponge to a closed cell sponge structure.

effects of
anatomic location

The mechanical properties of bone are highly localized, in terms of
their dependence on the anatomic location. This reflects the evolutionary
changes to support the magnitudes and directionality of forces that are
experienced at the respective locations. The classic understanding of the
modulus of cortical bone is based on femoral diaphyseal bone. However,
the mineral content of cortical bone can vary by anatomic location and
from the effects of aging or disease. The relevant mechanical properties
can also vary on the basis of the type of loading that is typically observed
at the site of interest. For example, in a region where flexural bending is
commonly experienced, flexural modulus would be the relevant property.
The flexural modulus of the human cortical tibia bone is approximately
5.4-6.8 GPa and decreases to approximately 4.9 GPa in the human iliac
crest and 2.5 GPa in the human vertebra. While the longitudinal modu-
lus of femoral and tibia diaphyseal cortical bone is approximately 17 to
20 GPa, it decreases to approximately 5 to 15 GPa for the vertebra end-
plates and to approximately 0.1 to 0.4 GPa in the subchondral bone of
the glenoid. Similarly, the mechanical properties of cancellous bone vary
between anatomic locations, as well as within different regions of the same
anatomic site. The tissue modulus of cancellous bone has been reported to
range from 0.76 to 10 GPa in tension and from 3.2 to 5.4 GPa in bending.

PROBLEM 5.2
What is the resulting local strain in the bone at the insertion of the ten-
don in Problem 5.1?

ANSWER:
186 με. From Figure 5.7, estimate the modulus of cortical bone in vivo
to be 100/0.07 = 14 GPa. Thus, a stress of 2.6 MPa produces a strain of
1.86 × 10 −4 or 186 με. Activities of everyday life produce strains in corti-
cal bone between 100 and 1000 με.

Fracture of bone Since bone is viscoelastic, its work of failure may be expected to increase

with strain rate. This is the case for both cancellous and cortical bone
with the increase being approximately 10% per decade (10-fold) increase
in strain rate. At physiologic strain rates, failure is of a “delamination”
type, with the fracture line following previous defects, such as cement
lines, lacunae, Haversian canals, and so on. However, at very high strain
rates, such as encountered in high-velocity-missile impacts, the work of
fracture is greatly reduced, and the fracture surfaces propagate at ran-
dom, producing considerable comminution.
Cortical bone, when tested in compression parallel to the fiber axis
of the long bone from which it is taken, frequently shows a buckling or
delamination failure, reminiscent of the buckle fracture seen in imma-
ture bones in children (Figure 5.13). When tested in tension, the frac-
ture is transverse and brittle, with some minor pullout of lamellae and