Closed form solutions for plane-strain ideal plastic deformations (Q1819993)

A Riemann plane mapping methodology to analyze plane-strain ideal plastic flow processes such as extrusion and drawing is presented. A solution function for a generalized die profile is obtained in the form of a zeroth-order Bessel function. Explicit solutions in closed form using functional approximation are obtained for the deformation forces and stresses for a wedge-shaped die without requiring numerical evaluation of any integrals. Two limiting solutions of the wedge shaped die profile, including wall friction effects, are derived and discussed. A comparison of the method and the results with the traditional slip-line field and upper-bound-lower-bound approaches is provided.