Plane deformation characteristics of compressible materials

Conclusions The plane deformation of metal powders and porous solids analyzed with resort to the approximation of an ideal plastic solid is described by a system of differential equations and partial derivatives which can be of the hyperbolic, parabolic, or elliptic type. The characteristics of the equations (when they are present) are lines along which the material experiences no elongation. Regions containing these lines exist during shaping under conditions of a well-developed free surface (the equations are of the hyperbolic type); in omnidirectional compression and compression in shells, in the absence of a free surface, there are no such zones (the equations are of the elliptic type).Translated from Poroshkovaya Metallurgiya, No. 3(231), pp. 14–21, March, 1982.The author wishes to thank Professor B. A. Druyanov for helpful discussion.