Treating side-on shell contact with penalty-based pinballs in EUROPLEXUS

This report presents some improvements in the EUROPLEXUS code concerning the treatment of shell contact by hierarchic pinballs with the penalty method, when side-on impact occurs between shells. The scope is to avoid the severe spurious penetrations that had been observed in some recent applications involving this type of contact. The origin of this problem is investigated and two alternative strategies are formulated and tested in order to correct the problem. The first strategy is based on a specific treatment of contact between shells, different from and more sophisticated than that involving continuum elements. The different contact sub-cases such as face-on, aligned side-on, perpendicular side-on, oblique side-on, etc., have to be identified and suitably treated. While successful in several situations, this approach is rather complex to be implemented in practice and may possibly lead to a degradation of the performance of the penalty-based contact algorithm. The second strategy relies upon the a priori elimination of the potentially redundant constraints which typically arise with the hierarchic pinball method. Such elimination was recently tested within the Lagrange Multipliers version of the pinball contact method, where it can be used in order to avoid the singularity of the constraints system of equations. While unnecessary in principle with the penalty method, such elimination is highly beneficial also in the penalty case because it may allow to use the parent pinball characteristics (diameter, cross-section) in order to evaluate the penalty force, independently from the hierarchy level used. This approach, at least in principle, avoids the necessity of detecting all the different contact sub-cases so that penalty-based shell contacts can be treated like continuum-based ones, with obvious advantages as concerns the simplicity of implementation and the efficiency.