Generalized Newton's methods for the approximation and resolution of frictional contact problems in elasticity

Yves Renard (1, 2, 3)

1 LaMCoS - Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne]
2 ICJ - Institut Camille Jordan
3 MMCS - Modélisation mathématique, calcul scientifique

In this paper, some new generalized Newton's methods for the resolution of elastostatic frictional contact problem approximated by finite elements are presented and compared to existing ones. A numerical experimentation is performed to compare the different methods, especially with respect to the sensitivity to the method parameter. Two different strategies to approximate the contact and friction condition are considered: a nodal and an integral one. Existence and uniqueness results of the solution to the discretized problem are also discussed.

Keywords: Contact; friction; augmented Lagrangian; generalized Newton's method; Nitsche's method

Domains: Numerical Analysis [math.NA]

Yves Renard. Generalized Newton's methods for the approximation and resolution of frictional contact problems in elasticity. Computer Methods in Applied Mechanics and Engineering, 2013, 256, pp.38-55. ⟨10.1016/j.cma.2012.12.008⟩. ⟨hal-00722114v3⟩