A revision of the SOLI model of rigid bodies in EUROPLEXUS

This report presents a revision and re-formulation of the so-called "old" model for the simulation of rigid bodies (SOLI model) in the EUROPLEXUS code. This model is based on the substitution ("decomposition") of the discretized rigid body by a mechanically equivalent set of four points in 3D space (two points in 2D space, but the 2D version of the model has not been implemented yet). The rigidity of the equivalent mechanical system is enforced by a suitable set of constant-distance constraints on the equivalent points via the Lagrange multipliers method. Although EUROPLEXUS is primarily dedicated to the simulation of deformable mechanical systems (both fluids and structures), it is not infrequent that at least some (solid) parts of the numerical model behave at least approximately as rigid, non-deformable bodies. A class of problems where a rigid model might be useful is that of crashes. For example, when treating the impact and crash of vehicles in the framework of protection of public spaces against terrorist attacks, e.g. by means of road barriers, some parts (typically the vehicle body and some components) are highly deformable while others (e.g. the engine) are comparatively much stiffer and could be treated as rigid. Modelling such nearly-rigid parts as a very stiff solid severely penalizes the transient explicit solution because of the drop it causes on the stability step of the time integration procedure. What is needed is the possibility of treating a rigid body in a more rigorous, but also in a more general manner than by simple blockages. The present report presents a possible approach to this task (the SOLI model) that was historically implemented in EUROPLEXUS and has been recently completely revised and enhanced by several new features (NODE, ELE2, HYBR, FEXT directives) in order to make it more functional to vehicle crash simulations for the protection of public spaces.