The multi-time step nodal subcycling algorithm, presented in the beginning of this chapter, has shown to generate significant computational time savings, while maintaining a fairly accurate solution. The solution does begin to degrade though for excessive time step differences in the subcycled and non-subcycled regions, as well as for small region ratios. In this section we present the results of combining both the subcycling and dynamic insertion algorithms.
As a test case we present the mode I crack specimen shown in
Figure 4.42 whose bulk material has
properties of PMMA. The critical time step for this problem is
, which is a
reduction
of the problem's Courant condition. In order to initiate the
subcycling portion of the simulation, we pre-insert cohesive
elements in a small region near the crack tip. This region
is therefore given a time step of
while
the larger outer region has a time step
.
The simulation was run for time steps for a reference
solution having cohesive elements present everywhere and
no subcycling, for a second reference solution using a
stress insertion and for three solutions using both
dynamic insertion and subcycling with
parameters of
and
. The final crack
profiles for each of the above simulations are presented in
Figures 4.44 through 4.46.
From these figures we can see that the combined solutions closely
match both reference solutions. Only the
combined solution
appears to have a different final solution. Careful observation
of this solution shows that there are large instabilities near
the crack tip - as seen by the large number of failing cohesive elements.
These instabilities as well as the effect of a large time
step in the non-subcycled region have most likely compounded the
errors present in the solution. In addition, at the end of the simulation,
the region ratio is much lower than its initial value - as seen
in Figure 4.43. This increase in
subcycled nodes increases the instabilities as discussed in the
subcycling section earlier in this chapter.
Although the solution loses some accuracy for the larger subcycling
parameters, significant savings can still be achieved for the lower
values - as presented by Table 4.8.
The % savings is presented for both the savings with respect to
the reference solution using cohesive elements everywhere at the
beginning as well as the reference solution of only dynamic
insertion at the stress level - the latter savings is presented
in parentheses in the table. We can see that the major savings
for the combined solutions is a direct results of the dynamic
insertion and only small overall percentage is obtained through
subcycling.
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