mechanics, tension, deformations, plasticity, elasticity.

The general approach in mathematical modeling of contact problems with the possible presence of the volumes of intermediate ‘lubricants’ has been discussed in the paper. The characterized peculiarities for considered processes are analyzed; the physical explanations for each case are given. The ways of their inclusion into mathematical model are indicated. In the second part it is considered the individual class of contact problems in which the plastic flows take place in a comparatively thin plastic layer between two converging surfaces of external bodies. The known Ilyushin’s theory of plastic flow in a thin layer is developed in the following cases of: a) taking account of anisotropic properties of contact surfaces; b) preservation of the physical volumes of ‘lubricants’ along the contact in the process of stamping. The both peculiarities are demonstrated by the author on the solutions of the specific practical problems, the qualitative conclusions of the solutions are also given.

Kadymov Vagid Ahmedovich

e-mail: vkadymov@yandex.ru, Dr. Sci. Phys. & Math., Professor, Moscow State Humanitarian and Economic University, Moscow, Russia.