Efficient numerical methods to approach solutions of quasi-static contact problems

Abstract

In this paper, a new boundary element method and generalized Newton method for the resolution of quasi-static contact problems with friction in 2D is presented. The time discretization of the model and the mixed duality-fixed point formulation combined with augmented lagrangian approach are considered. This leads at each time step, to a system of static contact problem with Coulomb friction, where the study is carried out by the dual–primal active set method. After proving the well-posedness of the regularized dual problem and convergence to the solutions of the static problem, the generalized Newton method based on active set strategy method and fixed point method are constructed. An error estimate for the Galerkin discretization is established and some numerical examples are presented.

Keywords

• Quasi-static contact problem
• Boundary element method
• Dual–primal active set Method
• Augmented lagrangian