A Finite Element Formulation For Nonlinear 3d Contact Problems

Abstract

A finite element formulation to deal with friction contact between an elastic body and a
rigid obstacle is presented. Contact between flexible solids or between a flexible and a rigid solid is defined
using a non-penetration condition which is based on a representation of the interacting deforming
surfaces. A large number of contact algorithms based on the imposition of inequality constraints were
developed in the past to represent the non penetration condition. We can mention penalty methods, Lagrange
multiplier methods, augmented Lagrangian methods and many others. In this work, we developed
an augmented Lagrangian method using a slack variable, which incorporates a modified Rockafellar Lagrangian
to solve non linear contact mechanics problems. The use of this method avoids the utilization
of the well known Hertz-Signorini-Moreau conditions in contact mechanics problems (coincident with
Kuhn-Tucker complementary conditions in optimization theory). The contact detection strategy makes
use of a node-surface algorithm. Examples are provided to demonstrate the robustness and accuracy
of the proposed algorithm. The contact element we present can be used with typical linear 3-D elements.
The program was written in C++ under the OOFELIE environment. Finally, we present several
applications of validation.