TABLE OF CONTENTS The contact problem in sheet-metal forming processes is complex. Contact between the tool and sheet is highly nonlinear because of its asymmetry, where at a position in space a node is either free or is rigidly constrained depending on an infinitesimal change of position normal to the tool surface. The boundary conditions dramatically change as a result of change in the contact region, which evolves continually and unpredictably. Three basic constraints for contact arise.
Impenetrability: A sheet node may not lie inside a tool.
Unilateral contact: A sheet node in contact may not have an external force directed toward the tool surface (no adhesion), whereas a noncontacting node has no external contact force.
Friction conditions: A node in contact may have an external force whose direction depends on the incremental displacement and sheet normal, and whose magnitude may depend on the normal force and on friction law. If sticking is allowed, the external force and direction may depend entirely on the internal force imbalance.
In sheet forming, these conditions lead to more severe nonlinearity in a given time step than either the material law or the geometry of the problem. Furthermore, because the conditions change abruptly in space, the usual derivatives are not available for use in a Newton-Raphson type of procedure. For these reasons, the contact and friction algorithms are the most critical part of FEM programs for sheet-forming analyses.
A sliding node is...
