Analysis of Plane-Strain Metal Forming Problem with Linear Programming Method

A method to determine the states of strain and stress in plastically deforming billet under plane-strain condition is proposed by applying the upper and lower bound theorems to finite element method. With the linear programming method, the upper bound value of forming load is minimized and the lower bound value is maximized to obtain optimum fields of velocity and stress, respectively. As an example, plane-strain extrusion is treated. The upper and lower bound values of extrusion pressure are in comparatively good agreement with those of slip line field method. It is confirmed that the calculated velocity and stress fields present good approximations of the exact fields.