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Closed form solutions for plane-strain ideal plastic deformations. (English) Zbl 0614.73044

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
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