Problem of a piston in a plastic medium with cultivation

The article discusses the self-similar problem of the motion of a spherical piston in a medium with dry friction and the differential connection between the first invariant of the stress tensor and the second invariant of the tensor of the deformation rates. For the case of flow with a shock wave, the method of a stationary wave is used to obtain the required relationships at a strong discontinuity. It is disclosed that the velocity of the piston, as well as the relationship between the cultivation coefficients and the dry friction, are determined by the smoothness of the friction.Translated from Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, 86–93, September–October, 1974.