Elimination of redundant constraints and of progressive penetration in the LM-based PINB contact model of EUROPLEXUS

This report presents some notes on the treatment and elimination of redundant constraints and of the progressive penetration phenomenon in the hierarchic pinball-based (PINB) contact-impact model using the method of Lagrange Multipliers (LM) in EUROPLEXUS (also abbreviated as EPX). It also investigates the reasons of, and tests out some remedies for, the progressive penetration phenomenon that is observed in some applications involving smooth and prolonged contact. The code is jointly developed by the French Commissariat a l'Energie Atomique (CEA DMT Saclay) and by EC-JRC. Its application domain is the numerical simulation of fast transient phenomena such as explosions, crashes and impacts in complex three-dimensional fluid-structure systems. Recently, EPX is being used to simulate vehicle crash against obstacles such as road barriers for safety and security studies. These studies involve complex contact-impact scenarios, which in EPX are typically modelled by the method of Lagrange Multipliers (LM), although other methods (e.g. penalty-based) are also available in the code. In some test cases, the effect of friction may be important and it must be included in the numerical simulations. The present work is divided into two parts. The first part explores a new and particularly simple strategy for getting rid of redundant constraints in the hierarchic LM-based pinball method, while at the same time also improving the calculation of the contact normals. The second part focuses on another issue (besides that of constraint redundancy) which also affects in particular smooth and prolonged contact simulations with the LM method, that of progressive penetration. The reasons for this phenomenon are tentatively examined and two alternative strategies to remove or alleviate it are formulated and tested.