An augmented lagrangian treatment of contact problems involving friction

TLDR

The augmented Lagrangian method, successful in constrained minimization, has been applied to incompressible flow, elasticity, and frictionless contact, but frictional contact governed by Coulomb law poses a special challenge. The paper proposes a new augmented Lagrangian extension for frictional contact problems, aiming to facilitate finite element implementation. The method applies augmented Lagrangians to frictional contact, reducing ill‑conditioning and achieving near‑exact constraint satisfaction with finite penalties. Numerical examples demonstrate the method’s effectiveness for finite deformations and inelasticity.

Abstract

A framework is presented within which the method of augmented Lagrangians is readily applied to problems involving contact with friction. This method, which has enjoyed considerable success in the treatment of constrained minimization problems, has been previously applied to problems involving incompressible flow, incompressible elasticity of solids and even frictionless contact. An additional challenge to the method is provided by frictional contact problems governed by a Coulomb law, due to the special form taken by the frictional constraint. This paper describes a new extension of the augmented Lagrangian technique to frictional problems which is well-suited to finite element implementation. The proposed treatment inherits the traditional advantages of augmented Lagrangian techniques over penalty methods; namely, decreased ill-conditioning of governing equations, and essentially exact satisfaction of constraints with finite penalties. A set of numerical examples is presented in which the utility of the method is demonstrated even in the presence of finite deformations and inelasticity.