Biomedical Engineering Reference
In-Depth Information
Fig. 6.1
The stress-strain curves for a spring (
left
)andforadamper(
right
)
Fig. 6.2
The stress-strain curve of a viscoelastic material
which denotes an element characterizing the combined effect of elastic and viscous
behavior in a material. Notice that for
n
=
0 we have a pure elastic element (spring),
whereas for
n
1 we have a pure viscous element (dashpot).
When the material undergoes a dynamical excitation, the stress will lead the
strain in phase with an angle
ϕ
between 0 en
π/
2 radians. The amplitude of the
stress is
E
d
·
=
ε
, from
sin
ωt
ϕ(ω)
σ(t)
=
E
d
(ω)
·
ε
·
+
(6.5)
The plot of the stress and strain below shows that part of the energy is stored and
part is dissipated, resulting in hysteresis.
The most simple combination of the basic elements presented above is a series
spring-dashpot, referred to as the
Maxwell element
and depicted in Fig.
6.3
.
For a constant strain variation (i.e. step inputs) we have
t
τ
)
e
(
−
σ(t)
=
E
·
ε
·
(6.6)
η
with
τ
0 the spring will be fully
taut, whereas the damper will remain unchanged. Within some time, the damper will
=
E
, the relaxation time, as from (
6.4
). At time
t
=
