Biomedical Engineering Reference
In-Depth Information
Fig. 3.8
Isochrone
stress-strain
diagram: a creep curves
as parametric function of stress
r
1
\r
2
\r
3
\......
;
b isochrones t
1
\t
2
\t
3
\......
over time and may decrease to zero depending on the material. In this process,
a sudden decrease of strain (elastic or spontaneous straining) may occur between
points B and C, and then from point C, the strain decrease may turn into backward
creep, i.e. deformation-relaxation. In the case of missing spontaneous straining,
the strain-time response follows the dashed line in Fig.
3.7
c.
In the case of small strains, for instance polymers exhibit viscoelastic material
behaviour shown by duplication of strain with duplication of stress. For finite
strains, this relation is no longer valid.
Isochrone Stress-Strain Curves. The time behavior of viscoelastic materials
may be illustrated in isochrone stress-strain curves (for short: isochrones). These
curves can be determined from creep and relaxation data by plotting the pairs r(t
1
)
and e(t
1
), r(t
2
) and e(t
2
) etc. at times t
1
;
t
2
etc. in an r-e-diagram (cf. Fig.
3.8
). The
resulting stress-strain curves are parametric functions of time. Principally, the
gradient of such curves decreases (at a fixed value of e) with increasing time
t
1
\t
2
\...
;
which is equivalent to a decrease in strength of viscoelastic material
with increasing time. In general, at small strains, the isochrones can be approxi-
mated as straight lines. In this case linear-viscoelastic material behavior exists and
the stress is proportional to strain.
3.2.3 Kinematics and Strain Tensors
3.2.3.1 One-Dimensional Case
If a body is exposed to an arbitrary external (thermo-mechanical) load, it will
deform. To quantify this deformation, it is convenient to determine the change in
length of the body to derive strain. In the case of a tensile bar which is fixed on one
end and pulled on the other (cf. Fig.
3.9
), the change in length Dl of the bar can be
derived from the difference in length l in the current configuration (CCFG) and the
length l
0
in the initial configuration (ICFG) by
