Some numerical slipline field solutions for drawing through circular dies

A method is presented for the generation of slipline fields and their hodographs for the problem of plane strain drawing a rigid, perfectly plastic (rpp) material through frictionless circular dies. An optimization scheme is given, using a readily available multivariable optimization routine, which will reliably adjust the shape of an assumed slipline to ensure hodograph convergence. A number of programme runs using different geometries show some interesting oscillatory variations in the computed stress distributions along the die surface and across the exit slipline.