Insertion with Pre-Stretch

Thus far, we have seen that blind insertion causes severe nodal oscillations which are directly related to the local stress at the insertion time. Although damping was able to slightly minimize these oscillations, it is not the optimal method. Instead we apply a pre-stretch to cohesive elements during their insertion so that the equilibrium and stability of the local system is maintained and better minimization can be achieved.

Using the reference problem we test the pre-stretch insertion method at the $0th$ ($0.0$ $s$), $2500th$ ($1.0$ $s$) and $5000th$ ($2.0$ $s$) time step. Figures 4.12 and 4.13 show the separation profiles for tracking node of the "horizontal" and "mixed" insertion cases. As we can see from these figures, the separations for each insertion are very close to the reference solution. We can therefore conclude that the cohesive element insertion with pre-stretching method is able to capture the solution accurately and at any insertion time (or local stress level).

Although greatly minimized, the oscillations are more pronounced for the "mixed" insertion case which has an angled cohesive elements. This is most likely due to the shear separations that this angled cohesive element experiences. Under the current insertion method, the separations for each cohesive node are equally distributed to the neighboring cohesive nodes. Then each cohesive node uses an average of all of the separations contributed to by the various cohesive elements. Although, this has found to be the best method thus far, it is unable to completely minimize all of the nodal oscillations since an averaged separation is used. Future research in this area may provide a more optimal method for applying the separations.

Figure 4.12: Normalized separation of the tracking node for ``horizontal'' insertion with with pre-stretching at the $0th$ ($0.0$ $s$), $2500th$ ($1.0$ $s$) and $5000th$ ($2.0$ $s$) time step.
Figure 4.13: Normalized separation of the tracking node for ``mixed'' insertion with with pre-stretching at the $0th$ ($0.0$ $s$), $2500th$ ($1.0$ $s$) and $5000th$ ($2.0$ $s$) time step.