The equations of the plasticity theory properties of dilating materials in the concept of plastic gas

In paper investigate the properties of equations that are used in the calculation of the plastic deformation of dilatable materials (powder steels, pure metals, non-ferrous alloys) from the concept of plastic gas. A complete system of basic equations of the theory of the flow of rigid-plastic isotropic dilatation media is given. We consider a particular case of plane deformation, for a slow steady-state plastic flow, as a result of which the initial conditions for the solution of the problem are not formulated. Taking into account that the solid medium undergoes a change in its density under loading, the law of volume compressibility is given, and the plasticity condition is reciprocally satisfied. For equations of equilibrium, continuity and the ratio of the coaxiality of de-Viators, a system of equations is constructed, and its analytical solution is given. The boundary conditions for stresses, densities, and velocities are written out for the case of planar deformation of an isotropic dilatation medium endowed with the properties of a plastic gas.