Strategy for evaluating the results

Before looking at the results that are ultimately of interest, such as stresses and deformed shapes, we need to determine whether or not the solution is quasi-static. One good approach is to compare the kinetic energy history to the internal energy history. In a metal forming analysis most of the internal energy is due to plastic deformation. In this model the blank is the primary source of kinetic energy (the motion of the holder is negligible, and the punch and die have no mass associated with them). To determine whether an acceptable quasi-static solution has been obtained, the kinetic energy of the blank should be no greater than a few percent of its internal energy. For greater accuracy, especially when springback stresses are of interest, the kinetic energy should be lower. This approach is very useful because it applies to all types of metal forming processes and does not require any intuitive understanding of the stresses in the model; many forming processes may be too complex to permit an intuitive feel for the results.

While a good primary indication of the caliber of a quasi-static analysis, the ratio of kinetic energy to internal energy alone is not adequate to confirm the quality. You should also evaluate the two energies independently to determine whether they are reasonable. This part of the evaluation takes on increased importance when accurate springback stress results are needed because an accurate springback stress solution is highly dependent on accurate plasticity results. Even if the kinetic energy is fairly small, if it contains large oscillations, the model could be experiencing significant plasticity. Generally, we expect smooth loading to produce smooth results; if the loading is smooth but the energy results are oscillatory, the results may be inadequate. Since an energy ratio is incapable of showing such behavior, you should also study the kinetic energy history itself to see whether it is smooth or noisy.

If the kinetic energy does not indicate quasi-static behavior, it can be useful to look at velocity histories at some nodes to get an understanding of the model's behavior in various regions. Such velocity histories can indicate which regions of the model are oscillating and causing the high kinetic energies.