Cortical Bone Mechanics and Composition: Effects of Age and Gender - Skeletal Aging and Osteoporosis: Biomechanics and Mechanobiology - page 59

Fig. 6 Typical stress-strain
curve of cortical bone
specimens in tension

X

E

U T

0 0.2%

Strain

The elastic modulus (E) is estimated as the slope of the initial linear part of the
stress-strain curve. The yield stress and strain (r y and e y ) are estimated using a
so-called 0.2% strain offset method. The ultimate stress (strength) of bone is
determined as the maximum stress from the stress-strain curve. The failure strain
or ductility is measured as the strain at failure of the specimen. The toughness (U T )
is estimated as the area under the stress-strain curve.

3.1.2 Cyclic Diagnostic Tests

Cyclic diagnostic tests allow for determining the changes in mechanical properties
of bone as a function of loading history [ 50 - 52 ]. Unlike the monotonic test, this
test subjects a specimen to multiple diagnostic cycles of a loading-dwell-unload-
ing-dwell-reloading sequence, in which the strain applied increases incrementally
with each cycle and dwell intervals account for bone's viscoelastic behavior
(Fig. 7 ). In each cycle, the specimen is loaded at a constant loading rate to a
designated strain level (e i ), held at that strain level for full stress relaxation (stress
relaxation dwell), unloaded with the same rate to zero stress, held for the full
recovery of creep strain (creep strain dwell), and finally reloaded to the next strain
level with a prescribed increment. This procedure is repeated until failure. During
the stress relaxation dwell, the viscoelastic response of the bone specimens can be
evaluated using the stress versus time curve (Fig. 7 ).
The mechanical properties that can be estimated at each diagnostic cycle are as
follows: (1) the instantaneous modulus (E i ) is the slope between two points, one at
the end of stress relaxation dwelling and the other at the end of creep strain
dwelling; (2) the maximum stress (r maxi ) is the peak stress in the cycle; (3) the
permanent strain (e pi ) is the residual strain value after full recovery of the creep
strain at the end of the dwelling period; (4) the total stress relaxation (Dr i )is
defined as the total change in stress from the beginning to the end of the stress
relaxation dwelling period. From the curve, the energy dissipation can also be
determined. Briefly, released elastic strain energy (U eri ) is the surface energy