Insertion Analysis Observations

As in 1-D, we have found that blind insertion of cohesive elements in 2-D systems causes severe nodal oscillations (Figures 4.8 and 4.9), which, in turn, decrease the accuracy of the solution. Although linear damping does minimize the oscillations (Figures 4.10 and 4.11), the effect is not enough to justify its use. Instead, we have adapted the pre-stretch technique used in 1-D to the more complex 2-D problems. The results of Figures 4.12 and 4.13 show that the nodal oscillations are nearly completely minimized for each insertion time. The only drawback to the pre-stretching method is that its effectiveness is diminished at greater stress levels during insertion. Figure 4.14 shows the amplitude of the oscillations as a function of the local stress level, at the time of insertion. The nodal amplitudes are represented by the amplitude of the tractions, normalized with the maximum cohesive stress. For both the ``horizontal'' and ``mixed'' test cases (presented earlier) the oscillations are significantly minimized as a result of pre-stretching, although the ``mixed'' case retains greater oscillations after the pre-stretching then the "horizontal" case.

Figure 4.14: Effect of blind insertion vs pre-stretching on the amplitude of the traction oscillations for increasing stress insertion levels, for the ``horizontal'' and ``mixed'' cases.