Multibody System Dynamics

, Volume 41, Issue 3, pp 275–295 | Cite as

Energy-consistent simulation of frictional contact in rigid multibody systems using implicit surfaces and penalty method

  • Roberto Ortega
  • Juan Carlos García Orden
  • Marcela Cruchaga
  • Claudio García


We present a conservative formulation for the frictional contact forces developed in the framework of an energy-consistent method. Bilateral constrains, that is, joints and rigid links, are imposed using the augmented Lagrange technique, provided that the constraints are exactly satisfied. We propose a formulation based on a penalty method to deal with the contact problem including damping and friction. The numerical scheme guarantees that the energy is consistently preserved or unconditionally dissipated. The treatment of the contact constraint also constitutes a novel aspect of this investigation. It is based on the description of implicit surfaces given an efficient strategy for detecting and evaluating the contact. The numerical tests exhibit a good energy preservation performance. Moreover, we use the proposed formulation to analyze a mechanism including a revolute joint with frictional clearance.


Multibody system Constraint equations Contact Impact Energy consistent method Penalty 



The authors thank the support given by Chilean Council for Scientific and Technological Research (PAI79130042) and the Scientific Research Projects Management Department of the Vice Presidency of Research, Development and Innovation (DICYT-VRID) at Universidad de Santiago de Chile (project “Aporte Basal 061516CSSA”).


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© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Departamento de Ingeniería MecánicaUniversidad de Santiago de ChileSantiagoChile
  2. 2.ETSI de Caminos, Canales y PuertosUniversidad Politécnica de MadridMadridSpain

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