An augmented Lagrangian frictional contact formulation for nonsmooth multibody systems

GALVEZ JAVIER; CARDONA ALBERTO; CAVALIERI FEDERICO J.; BRÜLS OLIVIER

Budapest

Congreso; 9th European Nonlinear Dynamics Conference; 2017

Budapest University of Technology and Economics

Various numerical strategies are available to deal with the dynamics of multibody systems with contacts. Regularizationtechniques and nonsmooth techniques are the two main approaches to deal with contact problems. In the present workwe focus on nonsmooth and implicit techniques, initially introduced by Moreau and Jean. The interaction laws arewritten as multi mappings relating contact unknowns (impulses and relative velocities). A fundamental property of theMoreau-Jean scheme is that the unilateral constraints are imposed at velocity level. As recognized by many authors, thischoice leads to interesting consistency and stability properties of a simulation algorithm for dynamic contact analysis.As the unilateral constraints are not imposed at position level, some penetration can be observed in the simulated results.Another property of the Moreau-Jean algorithm is that the complete system is integrated in time using a method whichis only first-order accurate. To improve the quality of the numerical results the Moreau-Jean scheme is proposed inwhich enforces the constraint at velocity level, but also at position level. As a result, penetration is avoided. Also in thisscheme the terms of the motion equation are split in to two parts, on the one hand the smooth contribution and on theother the nonsmooth contribution. This splitting makes it possible to integrate in the time domain the smooth part using ahigher-order scheme, in that case the generalized−α method was used.The present work extends this technique to include friction following the idea proposed by Alart and Curnier. Thismethod leads to an implicit formulation of the contact problem which can be solved at every time step using a Newtonsemi-smooth algorithm. This means that the contact status, which can be defined as gap (no contact between bodies),slip (contact between bodies with relative velocity at the contact point) and stick (contact between bodies without relativevelocity at the contact point), is updated at every iteration of the Newton process according to an active set method.