Numerical solution of frictional contact problems based on a mortar algorithm with an augmented Lagrangian technique

Abstract

This work presents a frictional contact formulation to solve three-dimensional contact problems with large finite displacements. The kinematic description of the contacting bodies is defined by using a mortar approach. The regularization of the variational frictional contact problem is solved with a mixed dual penalty approach based on an augmented Lagrangian technique. In this method, the numerical results do not depend on the definition of any user-defined penalty parameter affecting the normal or tangential component of forces. The robustness and performance of the proposed algorithm are studied and validated by solving a series of numerical examples with finite displacements and large slip.

A nonsmooth frictional contact formulation for multibody system dynamics

“…Replacing Eqs. (43,45,46) into Eq. ( 42), the generalized internal forces vector of the contact element F p N can then be readily identified as conjugated to the variation of generalized coordinates of the element Φ = [q T ν N ν T T ] T as follows,…”

“…This formulation is useful for treating rigid-rigid and rigid-flexible contact with friction, which appear in many types of mechanisms. We remark that flexible-flexible contact problems are generally handled using Mortar-based formulations as in [36,42,43]. The implementation of this approach in the context of the non-smooth generalized-α integration scheme is currently under development.…”

Numerical analysis on the elastic deformation of the tools in sheet metal forming processes

“…In analogy to the internal forces of a classical finite element, the internal force vector for a single contact element derived from the augmented Lagrangian method ( Cavalieri and Cardona, 2015;Heege and Alart, 1996) is defined by:…”

An Application of Isogeometric Analysis and Boundary Integral Element Method for Solving Nonlinear Contact Problems

“…Thereby, the deformation of two bodies in contact is found. This algorithm has been widely used with FEM [14][15][16] and has recently been combined with IGA [17][18][19][20][21][22][23][24]. Nevertheless, the main disadvantage of this method is that applied contact force is not a real force.…”