A mixed formulation for frictional contact problems prone to Newton like solution methods
Computer Methods in Applied Mechanics and Engineering
Accurate modeling of contact using cubic splines
Finite Elements in Analysis and Design - multi-field finite elements
Curve-fitting with piecewise parametric cubics
SIGGRAPH '83 Proceedings of the 10th annual conference on Computer graphics and interactive techniques
Mathematical and Computer Modelling: An International Journal
Direct numerical simulation of the dynamics of sliding rough surfaces
Computational Mechanics
| Hi-index | 0.00 |
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 tackling 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 Methods 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 approximations 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/stator dans un moteur d'avion Thèse de doctorat. PhD thesis, École Centrale de Nantes, Nantes, 2005; Muñoz, Comput 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 regarding 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.