‘Homotopy’ of Prandtl and Nadai solutions

In the present paper we provide two families of exact solutions for the system of plane ideal plasticity using the concept of homotopy of two functions. These functions are the well-known exact solutions of Nadai (for the flow of plastic material through the wedge-shaped converging channel and for the plastic zone around a circular cavity) and solution of Prandtl.The analysis of the envelopes of corresponding characteristic curves permits to determine the boundaries for obtained solutions, which give the description of the stresses for the blocks and cavities of specific forms.