Physical Concepts and Basic Fluid Mechanics
F(w)
I
A
Al(w)
I
l(o)
Ec(w)
=
53
(3.1.25)
(3.1.26)
It is clear that at
w
=
0,
or when the elastic modulus is frequency-
independent, eqn. (3.1.25) reduces to eqn. (3.1.14).
l(w)
is the length,
F(w)
is the sinusoidally applied force, and
Al(w)
is the change in length.
In Laplace notation, they showed that if a unit change in length in the
form
of
a step function is applied to the Voigt model (Fig. 3.1.3), its
force development (stress relaxation) is unbounded. When
a
unit change
in force is applied to the Maxwell model (Fig. 3.1.3), its change in length
(creep phenomenon)
is
unbounded. Thus, both models fail to represent
adequately the physical properties of blood vessels. This indicates that a
single time constant alone is not sufficient to describe either the stress-
relaxation or the creep phenomenon.
VOIGT
MAXWELL
Fig.
3.1.3:
Mechanical models of viscoelastic arteries. The spring-dashpot models are
subjected to step changes in force, and step changes in length. In a Maxwell model
(right), creep is unbounded; in a Voigt model (left), stress relaxation is unbounded.
