Insertion Interval Selection

Thus far, each of our simulations used a 500 time step interval between new cohesive element insertions. This value was chosen arbitrarily and can be changed to best fit the given problem. Varying this interval effects both the simulation time and the accuracy of the solution. Table 4.7 presents the solution times for the L-angle case, using stress insertion of at intervals of

and

time steps. As the interval decreases, the total solution time increases. This time increase is a result of the increased number of selections as well as a greater number of file outputs, which currently occur after every insertion. Furthermore, the accuracy of the solution also increases with a smaller interval since the the local stresses are not able to vary significantly between the cohesive insertions. We have deduced this through observation of the distribution of failing cohesive elements; there are many more failing elements, representing greater instabilities, as the insertion interval increases ( as seen in Figures 4.38 through 4.39 ). In fact, in part b of Figure 4.39, there are many failing cohesive elements around the crack but very few cohesive elements directly ahead of the crack tip. The 10000 time step insertion interval does not allow the program to insert enough cohesive elements ahead of the crack tip so account for the speed of the crack. As a result, the crack reaches the end of the cohesive region prior to the next insertion, causing it to stop abruptly. As new elements are inserted ahead of this crack tip, it is once again able to continue propagating through the system. Unfortunately, the periodic crack arresting results in an inaccurate solution as presented in the figure. Overall, the number of cohesive elements present over time is also slightly decreased for the larger insertion intervals, as seen in Figure 4.40. This possibly effects the accuracy of the solution since fewer elements are present in the system, although the difference are only about $5\%$ .

Table 4.7: Total simulation times for insertion intervals of 100, 500, 1000, 5000 and 10000 $\Delta t$

	100	500	1000	5000	10000
[]	1609.27	1585.66	1300.31	1220.11	1148.40

**Figure 4.38:** L-angle reference case with cohesive elements inserted every (a) 100 time steps (b) 500 time steps at the 30% stress level (10x exaggeration).
**Figure 4.39:** L-angle reference case with cohesive elements inserted every (a) 1000 time steps (b) 10000 time steps at the 30% stress level (10x exaggeration) (edge key: thin = normal edge, dark = cohesive element, dashed = failing cohesive element, bold = failed cohesive element).
$\includegraphics[scale=0.33]{interval_100.eps}$ $\includegraphics[scale=0.33]{interval_500.eps}$ $\includegraphics[scale=0.33]{interval_1000.eps}$ $\includegraphics[scale=0.33]{interval_10000.eps}$

**Figure 4.40:** Number of cohesive elements present over time for insertion intervals of 100, 500, 1000, 5000 and 10000.
**Figure 4.41:** Close-up of the three intervals presented in Figure 4.40.
$\includegraphics[scale=0.6]{langle_interval_cohesive.eps}$ $\includegraphics[scale=0.6]{langle_interval_zoom_cohesive.eps}$