Crush and Crash Simulations Using Implicit Integration
In today’s engineering practice, crush and crash simulations are almost always performed using explicit integration. There are various reasons for this 'exclusive approach'.
Crash events are quite rapid events, occurring over relatively small time periods, entailing very large deformations and complex contact conditions that may almost require small time step solutions. Hence a small time step explicit time integration simulation of the problem is naturally pursued.
The advantage of the explicit time integration solution is that no equilibrium iterations are performed, the solution is simply marched-forward, and that 'fast' elements and solution schemes are used — although with tuning of parameters and care is needed in setting these. Actually, these 'fast' elements may be unstable in static solutions and implicit dynamic solutions of slow events.
Crush events are, on the other hand, slow dynamic events, occurring over relatively large time periods. They are almost static events. Again, very large deformations and complex contact conditions are encountered. These simulations when performed with explicit time integration require mass scaling and also careful setting of tuning parameters in order to obtain a valid solution.
Then, of course, there are events that would be considered as in-between true crash and crush situations.
There are clearly many advantages in performing, both, crash and crush analyses using implicit time integration — that is, if that is possible with the program used.
One of our continuous aims in the ADINA developments has been to establish an analysis tool that can be used reliably and effectively for, both, crash and crush simulations — to use implicit integration or explicit integration, whichever technique is most appropriate, based on the physics of the problem. In each of these analyses, implicit or explicit solutions, we always aimed to use stable methods not based on tuning of parameters.
In our developments we have focused on implicit time integration techniques because we see that such techniques, if stable, reliable and efficient, will be very attractive. The implicit solution techniques offered in ADINA, version 8.7, are
- an improved contact solution procedure that can handle double-sided contact of shell surfaces, including the modeling of folds, sliding, and losing contact;
- a new 3D-shell element for very large deformation, large elastic-plastic strain, solutions;
- an effective implicit time integration scheme for large deformations that does not require the setting of parameters, see Ref.
In the implicit time integration solution, iterations are performed in each time step to ensure nodal point and element equilibrium. This feature is a key ingredient of the dynamic simulation. Of course, to simulate fast crash events, the implicit time integration may still require a relatively large number of steps to be able to follow the complex contact and strain conditions; however, even then, the method may be computationally competitive when compared to explicit integration.
In the explicit central difference method time integration, we use full numerical integration for the elements, and hence our solutions are usually considerably more expensive than obtained using other codes, but reliable.
We show below the results obtained in the simulation of the crashing and crushing of a tube. The problem geometry is shown in Figure 1.
Figure 1 Schematic of problem
Two cases are considered: the piston motion at 1 mph, and the piston motion at 30 mph. The 1 mph case is solved using implicit time integration, and the 30 mph case is solved twice, in a first run using implicit integration and in a second run using explicit integration. The same mesh, elements, material model, etc. are used in all analyses, and full integration is always employed.
The resulting force-deflection curves are shown in Figure 2. Note that the peak forces calculated in the explicit and implicit solutions of the 30 mph case are practically the same and considerably higher than in the 1 mph case. The responses after the peak forces have been reached are, overall, quite similar, although in all cases no initial imperfection was imposed onto the models, and, of course, different time step sizes have been used in the explicit and implicit solutions. Hence some differences in buckling and folding behaviors must be expected, and these account for the differences in the force vs. displacement results for the 30 mph solutions after 5 mm.
(a) Displacement scale from 0 to 160 mm
(b) Detail showing displacement scale from 0 to 20 mm
Figure 2 Force-deflection curves
The animation at the top of this page shows the solution obtained for the 1 mph case. The animations below show for this case the large plastic strains and details of the contact conditions, where the folding in double-sided contact is clearly seen.
These solutions illustrate — although only to a limited extent since much more could be shown — how ADINA can be used reliably for simulations of crash and crush problems. We believe that, in particular, the implicit integration approach can be very effective.
- K.J. Bathe, "Conserving Energy and Momentum in Nonlinear Dynamics", Computers & Structures, Vol. 85, pp. 437-445, 2007.
Crash, crush, implicit, explicit, time integration, contact, folding, large deformation