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

Abstract

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.

Implementation and applications of a finite-element model for the contact between rough surfaces

“…(6) to (8). Both these steps are described in detail in [13] and [14]. With respect to the discretization of the contact conditions, the latter paper describes two possible approaches, a nodal one that enforces Eq.…”

A fictitious domain method for frictionless contact problems in elasticity using Nitsche’s method

“…We use a generalized Newton's method to solve the discrete problem (3.6) (see [27] for more details) and our finite element library GetFEM++ 1 . The tool for fictitious domain methods of GetFEM++ has been used which provides cut integration methods.…”

“…The approximated problem is then solved in a coupled way or iteratively on the multiplier using Uzawa's algorithm (see e.g. [27]). Recently in [6,7], it has been proposed an extension to the contact conditions of Nitsche's method [24,11,17] which was originally dedicated to Dirichlet's condition.…”

A Nitsche finite element method for dynamic contact: 1. Space semi-discretization and time-marching schemes

“…In this paper we propose an extension to the elastodynamics framework of the Nitsche-based method introduced previously in [13,14] in the case of unilateral contact in elastostatics. Although we restrict ourselves to the unilateral contact without friction in this study, it should be noted that Nitsche's method can be extended without much difficulty to the case of frictional unilateral contact (see [12,43]). …”