Blind Cohesive Node Insertion Results

In order to analyze the effect of blind insertion, we dynamically insert the selected nodes ($\char93 12$ through $\char93 20$) at time step 0 ($0.0$ $s$), $2500$ ($6.25$ $s$), $5000$ ($12.5$ $s$) or $10000$ ($25.0$ $s$). Node $15$ is monitored in Figures 3.11 through 3.14 to determine the effect of varying the time of insertion. From these figures we can see that blind insertion appears to have an oscillatory effect on the nodal velocities. The amplitude of the oscillations increases if the insertion is performed after the dilatational wave has passed, or some stress has built up near the proposed nodes. For the current case, having a wave speed of $1.0$ $m/s$ and time step of $0.0025$ $s$, it takes the wave approximately $4000$ time steps (or $10$ $s$) to reach the first cohesive node - node $\char93 12$. Prior to this time, the local stress is zero and so the blind insertion is stable as seen by Figures 3.11 and 3.12.

Figure 3.11: Velocity profile of node $\char93 15$ resulting from blind insertion at the $0th$ time step ($0.0$ $s$).
Figure 3.12: Velocity profile of node $\char93 15$ resulting from blind insertion at the $2500th$ time step ($6.25$ $s$).

Figure 3.13: Velocity profile of node $\char93 15$ resulting from blind insertion at the $5000th$ time step ($12.5$ $s$).
Figure 3.14: Velocity profile of node $\char93 15$ resulting from blind insertion at the $10000th$ time step ($25.0$ $s$).

These severe velocity oscillations are likely the result of the sudden application of volumetric stresses on the cohesive elements during the dynamic insertion. Although the oscillatory effect in 1-D appears to be limited to the local node. The neighbor nodes experience only minimal effects which are nearly indistinguishable. This localization of the disturbances is very important because we are able to insert cohesive nodes without fear of affecting the rest of the system too adversely. In the next sections we will attempt to completely remove these oscillations through either the use of damping or pre-deformation of cohesive elements.