Comput Mech (2013) 51:581–601 DOI 10.1007/s00466-012-0737-3 ORIGINAL PAPER A comparative study between two smoothing strategies for the simulation of contact with large sliding Alain Batailly · Benoît Magnain · Nicolas Chevaugeon Received: 7 November 2011 / Accepted: 17 May 2012 / Published online: 13 June 2012 © Springer-Verlag 2012 Abstract The numerical simulation of contact problems is still a delicate matter especially when large transformations are involved. In that case, relative large slidings can occur between contact surfaces and the discretization error induced by usual finite elements may not be satisfactory. In particular, usual elements lead to a facetization of the contact surface, meaning an unavoidable discontinuity of the normal vector to this surface. Uncertainty over the precision of the results, irregularity of the displacement of the contact nodes and even numerical oscillations of contact reaction force may result of such discontinuity. Among the existing methods for tack- ling such issue, one may consider mortar elements (Fischer and Wriggers, Comput Methods Appl Mech Eng 195:5020– 5036, 2006; McDevitt and Laursen, Int J Numer Methods Eng 48:1525–1547, 2000; Puso and Laursen, Comput Meth- ods Appl Mech Eng 93:601–629, 2004), smoothing of the contact surfaces with additional geometrical entity (B-splines or NURBS) (Belytschko et al., Int J Numer Methods Eng 55:101–125, 2002; Kikuchi, Penalty/finite element approx- imations of a class of unilateral contact problems. Penalty method and finite element method, ASME, New York, 1982; Legrand, Modèles de prediction de l’interaction rotor/sta- tor dans un moteur d’avion Thèse de doctorat. PhD thesis, École Centrale de Nantes, Nantes, 2005; Muñoz, Comput A. Batailly (B ) Structural Dynamics and Vibration Laboratory, McGill University, Montréal, QC, Canada e-mail: alain.batailly@mcgill.ca B. Magnain Laboratoire PRISME, ENSI de Bourges, Bourges, France e-mail: benoit.magnain@ensi-bourges.fr N. Chevaugeon Gém, École Centrale Nantes, Nantes, France e-mail: nicolas.chevaugeon@ec-nantes.fr Methods Appl Mech Eng 197:979–993, 2008; Wriggers and Krstulovic-Opara, J Appl Math Mech (ZAMM) 80:77–80, 2000) and, the use of isogeometric analysis (Temizer et al., Comput Methods Appl Mech Eng 200:1100–1112, 2011; Hughes et al., Comput Methods Appl Mech Eng 194:4135– 4195, 2005; de Lorenzis et al., Int J Numer Meth Eng, in press, 2011). In the present paper, we focus on these last two methods which are combined with a finite element code using the bi-potential method for contact management (Feng et al., Comput Mech 36:375–383, 2005). A comparative study focusing on the pros and cons of each method regard- ing geometrical precision and numerical stability for contact solution is proposed. The scope of this study is limited to 2D contact problems for which we consider several types of finite elements. Test cases are given in order to illustrate this comparative study. Keywords Finite element method · Contact mechanics · Large sliding · Smooth contact surface description 1 Introduction Contact problems are inherently nonlinear since the contact area is a priori unknown and the associated hybrid force/dis- placement boundary conditions are part of the solution. The main difficulty lies in the constitutive laws of contact and friction expressed by non-smooth multivalued force–dis- placement relationships. In the finite element method frame- work, three groups of methods are usually considered for the numerical treatment of the constitutive laws of con- tact: (1) the penalty method [3, 19], (2) the Lagrange mul- tiplier method [5, 17] and (3) the augmented Lagrangian method [2, 10, 35]. While the penalty method depends on a parameter that allows controlled penetrations between the 123