An exact elastoplastic solution for the plane wedge problem of an elastic linear-hardening material

A closed-form elastoplastic solution is presented for a plane wedge of elastic linear-hardening material subjected to an arbitrary concentrated force at its vertex. Hencky's deformation theory and von Mises's yield criterion are used to describe the constitutive relations. Solutions are derived for both plane stress (thin) and (incompressible) plane strain (thick) wedges, and they are given for both the elastic and plastic zones. The solution is general in the sense that it contains three adjustable parameters. Solutions of two typical half-plane problems are obtained by applying the general solution directly.