7. Conclusion

This document presents the use of dynamic transient methods for the simulation of slow and highly nonlinear evolutions [bib1]. The dynamic operators thus used for the resolution can be seen as particular solvers making it possible, in some cases, to obtain solutions for which the quasistatic algorithm available in Code_Aster (around the operator STAT_NON_LINE) shows great convergence difficulties (in the sense of balance verification).

These dynamic methods should be used as a last resort because mastering them is more difficult than the quasistatic framework. This is even more striking with explicit methods since the quality of the solution is not guaranteed by an accurate check of the balance at every moment.

The first step is to adapt the model to dynamic methods. The main aim is to ensure the correct consistency of the conditions imposed and the correct definition of density and overall damping (Rayleigh). Control methods, non-local approaches and linear research cannot be used dynamically. In addition, it is necessary to introduce a global damping model (Rayleigh or modal) whose level is stronger than in classical dynamics (currently 20% equivalent modal damping).

Then, it is recommended to start by using an implicit transient method (DYNA_NON_LINE with a time pattern like NEWMARK, or HHT). From the point of view of optimizing the calculation time, it is recommended to conduct all the weakly non-linear phases in a semi-static manner and to switch to transient (implicit to begin with) only when significant non-linearities appear (this may result in a marked increase in the number of iterations at convergence, or even a subdivision of the time step).

In case of failure, including with a complete HHT diagram and relatively strong structural damping (up to 30% equivalent modal damping), the user can switch to explicit. Other adaptations must then be made, such as increasing the density in order to obtain a sufficiently large critical time step and to modify the damping.

In all dynamic cases, it is essential to analyze the evolution of acceleration over time, in order to ensure the validity of the slow evolution hypothesis. The effects of inertia should remain low.