On Applications of Adaptive Strategies for General Shell Structures in Crashworthiness Analysis Using LS-DYNA

Adaptive strategies are nowadays applied in a rather standard fashion in linear static analyses where reliable global and local estimators are available for many problems [22],[23],[5]. Con- siderable progress has been achieved for nonlinear problems [14], [4][8][9][13][17], also in- volving contact [21], because fairly reliable estimators exist, resulting in efficient procedures. However, for transient loading only limited success has been achieved so far [19],[20],[15],[11][12]. This is due to the fact that inertia effects and time integration schemes introduce additional complexity and approximations. As a result, no reliable error estimation is yet possible for large deformation dynamic problems such as metalforming and crashwor- thiness analyses. Adding to the difficulties is the complexity of the structures to be analyzed. Crashworthiness models violate, at least in parts, the continuum mechanics approximations such as multiple shell connections, spotwelds or shell-beam connections. Although proposals for the adaptive static analysis of composite shell connections exist [15], these cannot easily be applied to dynamic problems. In particular, the a-priori definition/detection of such non- continuous parts is a difficult task and contact regions need high resolution to achieve reason- able error estimation. Furthermore, there is no reliable error estimation possible for the very efficient and simplified shell elements with reduced integration and hourglass control - the "work-horse" in crashworthiness analysis. Nevertheless, some standard error indicators have been implemented and tested for some large deformation problems in LS-DYNA with some success [9]. As a consequence, for very general, large scale crash models in industrial practice currently only adaptive procedures remain which use error indicators based on simple ideas such as geometrical relative deformations [3]. These methods have to be combined with adaptive meshing schemes which allow only a certain level of refinement due to efficiency reasons. Additionally, the refinement has to be restricted to various points in time. In particular for deep drawing applications, it often appears to be very beneficial to step back in time and re- start the analysis with an adapted mesh at a previous point in time. LS-DYNA [7] has been recently enhanced by the capability to allow adaptive schemes for certain type of shell connections. In addition, it was observed that it is very effective to refine the mesh in metalforming applications prior to contact with small radii. The introductions of these so-called look-ahead algorithms limit the number of back-steps in time to almost zero. This contribution highlights these new features in LS-DYNA. The numerical examples range from metalforming analysis, simple buckling analysis of a structural member to a complex crashworthiness model. The merits and the limits of the currently available methods in LS- DYNA are illustrated. This may lead to further insight on how future efficient error estimators could be developed on a sound mathematical basis, even for large deformation problems with high complexity. Some hints are given to use the implemented indicator and the adaptive meshing efficiently improving the quality of the analyses.