Contact modeling in forging simulation

The problem of contact in forging simulation is overviewed and revised in this paper. The integral form of equilibrium equations must be solved subject to the incompressibility and impenetrability or contact conditions. Minimization techniques such as the Lagrange multipliers method, the penalty function method or the augmented Lagrangian method have been used to convert the problem to the unconstrained form. These approaches are based on solving the equilibrium equations while preventing any constraints to be violated. An alternative is to solve the equilibrium equations regardless of the constraints. Then, if any of the constraints is found to be violated, a simple projection is used to force the node back to the contact zone. The major drawback of this simpler approach is the loss of volume/mass in the time steps. A quick remedy is to choose very small loading steps. In this paper, a simple velocity-based projection technique will be proposed to overcome the above mentioned deficiency. In this method the projection procedure is performed iteratively using a modified velocity field in such a way that the final position of the node will be exactly on the contact surface. This is very similar to the so-called “Return Mapping” algorithm in computational plasticity.