A finite element formulation for nonlinear 3D contact problems

FEDERICO CAVALIERI; ALBERTO CARDONA; VICTOR D. FACHINOTTI; JOSÉ RISSO

Córdoba

Congreso; XVI Congreso sobre Métodos Numéricos y sus Aplicaciones (ENIEF 2007); 2007

Asociación Argentina de Mecánica Computacional

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.