ON THE CONNECTION BETWEEN AND THE PRACTICAL REALIZATION OF THE CLASSICAL PRANDTL AND HILL SOLUTIONS OF PLASTICITY THEORY

We examine the connection between the classical solutions of the problem of the indentation of a flat punch into a homogeneous plastic half-plane. It is shown that the Prandtl solution is stable for the entire range of variation of the contact friction forces, while the Hill solution is unstable. We show that the Prandtl solution corresponds to the minimal values of the power of the deformation energy dissipation and the contact loads for the equalized contact stresses. The Prandtl and Hill solutions are not mutually exclusive, as has been considered previously but correspond to two sequential stages of the process. The alternation of the solutions leads to change of the kinematic characteristics of the process with constancy of the contact load.