Plane strain problems for rigid, perfectly plastic materials

This chapter focuses on the limit states and limit loads of rigid, perfectly plastic material blocks under plane strain conditions. Because of the neglect of elastic deformation, the rigid regions in the material block actually include the elastic and constrained plastic regions. First, basic concepts and governing equations of plane strain problems are formulated; then they are transformed into the equations on stress, velocity, and the radius of curvature along slip lines, together with the relevant boundary conditions. Furthermore, applications of the slip line field theory are demonstrated through four examples, that is, wedge under unilateral compression, a half plane pressed by a rigid stamper, a plane subjected to uniform pressure on its circular hole, and notched specimens under tension. Finally, the steady plastic flow problem is illustrated by the drawing of a strip through a rigid die, as a showcase of the wide applications of the slip line field theory in metal forming.