Jenkins, Artis C.; Desai, Prateen V. Closed form solutions for plane-strain ideal plastic deformations. (English) Zbl 0614.73044 Int. J. Mech. Sci. 29, 491-505 (1987). 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. MSC: 74C15 Large-strain, rate-independent theories of plasticity (including nonlinear plasticity) 74C20 Large-strain, rate-dependent theories of plasticity 74R20 Anelastic fracture and damage 74C99 Plastic materials, materials of stress-rate and internal-variable type Keywords:Riemann plane mapping methodology; plane-strain ideal plastic flow processes; extrusion; drawing; generalized die profile; zeroth-order Bessel function; Explicit solutions in closed form; functional approximation; deformation forces; stresses; wedge-shaped die; limiting solutions; wall friction effects PDFBibTeX XMLCite \textit{A. C. Jenkins} and \textit{P. V. Desai}, Int. J. Mech. Sci. 29, 491--505 (1987; Zbl 0614.73044) Full Text: DOI