Biomedical Engineering Reference
In-Depth Information
Fig. 23.10
Delamination in
case of prestress in both
directions after 950 time
increments (i.e.
9
.
5
·
10
−
2
mm displacement
of top boundary). Distribution
of (
a
) chemical potential
(N
/
mm
2
), (
b
) flow in the
x
-direction (mm
/
s), (
c
)flow
in the
y
-direction (mm
/
s)
In mode II a very similar phenomenon occurs. A sharp pressure (or chemical
potential) gradient develops as the shear band proceeds, causing a fluid flow across
the band. This fluid flow transfers the stress concentration at the crack tip from
the fluid to the effective stress, resulting in a (delayed) shear band propagation,
recreating thereby the steep pressure gradient across the newly created shear band.
The crack chemical potential tracing in Fig.
23.11
are indicative of a model that
cannot resolve the variations imposed by the stepwise progression of the crack. On
the contrary, the flow tracings in Fig.
23.8
are obtained though discontinuous en-
richment of the chemical potential field. This approach exempts from resolving the
steep chemical potential gradients and reconstructs the steep gradients from the an-
alytical solution of Terzaghi. From the poromechanical theory, we can infer that the
continuous approach as taken in Fig.
23.11
, can only capture the flow and pressure
(or chemical potential) variations correctly if the time step is larger than
x
2
/cK
,
in which
x
is the characteristic mesh size. From this criterion we infer that for
