Table 1.3.10–1 shows the section control and mass scaling options used for the analysis.

For the axisymmetric model using CAX4R elements the deformed shapes of the rod after 20 and 80 microseconds are shown in Figure 1.3.10–2 and Figure 1.3.10–3 for the COMBINED hourglass control. The results for the three-dimensional model using C3D8R elements are shown in Figure 1.3.10–5 and Figure 1.3.10–6 for the ORTHOGONAL kinematic and COMBINED hourglass section control options. The deformed shapes are also shown in Figure 1.3.10–8 and Figure 1.3.10–9 for the axisymmetric model using CAX6M elements and in Figure 1.3.10–11 and Figure 1.3.10–12 for the three-dimensional model using C3D10M elements. The results reproduce the behavior observed by Ferencz (1989).

From these figures it is clear that extremely high plastic strains develop at the crushed end of the rod, close to the axis of symmetry, resulting in severe local mesh distortion. The shortening and widening of the bar are reported in Table 1.3.10–2 for the different analysis cases. The values of the bar's spread are reported for the symmetric model, and the three-dimensional values are reported as the y-component displacement at node 91 for the model using C3D8R elements and at node 61 for the model using C3D10M elements.

The displacements and energies obtained from the analyses using different element types and section controls agree very well, except in the case of the model that uses C3D10M elements. These elements are slightly stiffer with the given mesh refinement, as demonstrated by the predicted shortening value of –12.71 in Table 1.3.10–2. This shortening value converges as the mesh is refined to the values obtained from the analyses that use other element types. Differences are less pronounced for the variations of the C3D8R element. Using the ORTHOGONAL kinematic and ENHANCED hourglass control options produces a solution similar to that for the analysis that uses the default section control parameters.

Without any mass scaling the stable time increment for the problem is observed to reduce dramatically over the course of this analysis as a result of the large changes in element aspect ratio. Local mass scaling increases the stable time increment and, thus, reduces the total time of the simulation. A comparison of the stable time increment time histories for the unscaled and scaled cases is shown in Figure 1.3.10–15. The minimum allowable stable time increment chosen resulted in a 5.9% increase in the overall mass of the rod by the end of the simulation. Although this percentage is substantial, all of the scaling is performed on the severely compressed elements near the rigid wall. Thus, the overall dynamics of the solution are unchanged, while the solution time is approximately one-third that of the unscaled case. The predicted maximum effective plastic strain for the scaled case is 5.876, which is 1.2% higher than the maximum obtained in the unscaled analysis (using the default section control options). Comparisons of kinetic energy and free end displacement time histories of the rod show excellent agreement and are presented in Figure 1.3.10–14 and Figure 1.3.10–15, respectively.