Biomedical Engineering Reference
In-Depth Information
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cycles
maxi
Stress
relaxation
dwell
maxi
Reload
Load
U
hi
0i
E
i
U
mi
U
e0
U
eri
pi
Unload
ε
i
Creep strain
dwell
Time
Strain
Fig. 7 A novel progressive loading protocol designed to determine the evolution of bone
properties as a function of increasing strain
dissipation of newly formed microdamage, which can be estimated as the area
under the unloading curve minus the elastic recovery energy (U
e0i
). Plastic strain
energy (U
pi
) is the energy dissipation by permanent deformation of bone, which
can be approximated as the summation of cumulative areas between loading
and reloading curves of the successive cycles (U
mi
) minus U
eri
. Finally, hysteresis
energy (U
hi
) is the energy dissipation by the viscoelastic response of bone,
which can be calculated as the area between the loading and unloading curves
(i.e., the hysteresis loop).
3.2 Elastic Properties of Cortical Bone
3.2.1 Elastic Modulus
The elastic properties of human cortical bone at the macroscopic (also called
apparent or continuum) level are usually considered transversely isotropic, with
the first principal direction along the longitudinal axis of the bone [
53
]. This is
largely because osteons are oriented along the long axis and located in a random
distribution in the transverse plane of bone. The experimental data (Table
1
) show
that the elastic modulus of human cortical bone is much lower in the transverse
direction than the longitudinal direction, whereas the elastic moduli of bone in
transverse directions (transverse to the long axis) are similar [
54
,
55
]. Thus, a
complete characterization of the elastic behavior of cortical bone requires five
elastic constants: longitudinal elastic modulus (E
L
) and Poisson's ratio (m
L
),
transverse elastic modulus (E
T
) and Poisson's ratio (m
T
), and transverse shear
modulus (G
T
).
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