Overview

A consistent full set, or CFS, algorithm ^[13] was developed for enforcing the contact condition in sheet-forming simulations. The CFS algorithm can improve the accuracy and the numerical stability while retaining the computational efficiency needed for realistic industrial application. Because the first CFS version implemented defines the contact error along the punch travel direction (or z direction), it is called Z-CFS. ^[14] Preliminary results obtained from the Z-CFS algorithm have shown a significant improvement over the DNP method. Even so, the Z-CFS method was found to have a convergence problem when the draw-in angle approaches 70 . Although some success was obtained by using case-by-case numerical tricks to obtain convergence, a better algorithm was needed.

A more advanced version of CFS algorithm has proved better in terms of convergence and computation time. Because this new CFS algorithm defines the contact error along the mesh-normal direction, it is called the N-CFS method. The N-CFS algorithm obtains a simultaneous solution of a set of nonlinear equations, including equilibrium and contact conditions. In the N-CFS algorithm, the mesh normal is consistently used in the measurement of contact error and in the calculation of contact pressure and external force, as well as in defining the external part of the stiffness equation.

The N-CFS algorithm exhibits better convergence and numerical stability in deep drawing simulation, when draw-in is significant and relative nodal displacement is large, when the draw-in angle is large (even approaching 90 ), and when the...