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Explicit vs. Implicit Time Integration in Metal Forming Analysis

The above animation shows the effective plastic strain in a cylindrical cup during the deep drawing process. The problem is from a Numisheet 2002 benchmark test, and was solved with ADINA 8.1, using the excellent large strain shell element MITC4 in implicit and explicit time integration.

Selection of the time integration scheme in FEM simulations depends on many factors, the most important of which is the physical nature of the problem. Highly dynamic problems (e.g., a car crash at high velocity) are usually analyzed using an explicit time integration scheme, while for other "slow" problems (such as car roll-over) implicit time integration is preferable. Another major factor affecting the choice of the time integration scheme is the computation time. Quite often, explicit time integration is chosen for "almost" static processes with only one purpose - significantly reduced computation time. To achieve this, artificial manipulation with physical parameters is usually applied.

Our featured problem is an example of such an approach. When implicit time integration was used, simulation parameters were exactly as those in a real experiment, while in explicit time integration mass scaling was applied to reduce computation time. Two different mass scaling factors were used - 10000 (model Explicit 1) and 100 (model Explicit 2). Computation times (in minutes) for implicit and explicit simulations are as follows:

Model Implicit Explicit 1 Explicit 2
Computation Time 81 10 95

The figures below compare the simulation results, for distribution of cup thickness at 45 degrees, against experimental results.

The results show that while very short computation time is achieved for explicit time integration in case of model "Explicit 1", accuracy of results is greatly sacrificed. On the other hand models "Explicit 2" and "Implicit" produce almost the same results in comparable computation time (the legend markers of these two graphs almost coincide). This simple example demonstrates that results for any explicit time integration model, where manipulation with physical properties is utilized, should be examined with caution.

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