Vehicle Crashworthiness and Occupant Protection - Chapter 3

Finite Element Analytical Techniques
and Applications to Structural Design
on the interactive pre-processing software of the models. The main goal was to
quickly incorporate structural changes in an existing numerical model.
The main programming effort has been to increase the efficiency of the solvers
themselves. Explicit finite element codes have been optimized to the point that
they run in a 99 percent vectorized mode. Although it must be said that the
element-by-element nature of the codes lends itself particularly well for vectorized
processing, this was certainly a remarkable achievement considering the nodal
force assembly, and the search algorithms in the contact-impact routines. A similar,
even more important effort is continuously displayed in the parallelization of the
codes achieving ever better scaling performance on both shared memory and
distributed memory machines. A major advance was the replacement of nodebased
contact search algorithms by so-called segment-based search algorithms.
The old algorithms based on the search of a nearest master node for every slave
node are always computer-time consuming even if bucket sorting improves this
situation. With the new segment-based search methods, an algorithm was
introduced that is not only computationally much more efficient, but also improves
on many of the shortcomings of older algorithms.
Finally, a number of techniques were developed in order to allow explicit simulations
to run with a constant timestep value. This at first seems a non-trivial matter since
the stable time step of the analysis is linearly dependent upon the shortest mesh
dimension in the model. As deformation changes (reduces) this dimension, a
drop of the timestep seems mathematically unavoidable. Indeed it is not possible
to keep a constant timestep during a crash simulation with highly deforming shell
elements without changing the physics of the problem. Several methods were
developed to achieve this. They vary from the so-called small strain formulations
where the influence of the change in geometry upon the element stiffness is
ignored from a certain point on (or during the entire analysis), to a controlled
reduction of the material’s elastic modulus as it plastically deforms. The most
widely used method is mass scaling. As an element dimension decreases, the
corresponding material density or nodal masses are increased in such a way that
the resulting time step remains constant.
These options render crashworthiness simulations feasible and useful in about
75 percent of all cases. Although the physics of the problem are locally modified,
this is not a major objection if one considers that the local stress distributions
must have been wrong before mass scaling (or any of the other constant timestep
options) was applied. Since a vehicle crash is by nature a small strain event, no
large membrane strains should really occur in the shell elements that represent
the car body. Consequently, the mesh dimensions should not change and the
timestep should ideally be constant.
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