Ad hoc exact solutions for the stress and velocity fields in rigid,perfectly plastic materials under plane-strain conditions

Making use of convenient ad hoc assumptions we construct analytical and closed-form solutions for the problem of stress and velocity states in statically determinate rigid, perfectly plastic bodies under plane-strain conditions. The obtained solutions are expressed either implicitly including arbitrary functions, or explicitly in the form of specific functions. For the stresses they are extracted by means of the two equilibrium partial differential equations (PDEs) and the appropriate von Mises-Hencky condition; for the velocities we use the Saint Venant-von Mises theory of plasticity PDEs and the condition of incompressibility. The possibility of extending the developed solution technique for plane stress conditions is presented. Finally, several applications concerning the inverse, semi-inverse and direct problems are examined. The advantage of the proposed analytical solution methodology compared to the technique of characteristics is the general applicability delivering from the a priori construction of the slip-lines, as well as the demanded numerical solutions of the corresponding equations of characteristics.