Coulomb–Mohr media, Prandtl perfectly plastic media, compessibility, flow, principal stress, asymptotic directions, conjugate directors, hyperbolicity, characteristics

The paper deals with flows of compressible media with the zero intermediate principal increment of the strain tensor. Such flows can be observed for loosely bonded Coulomb–Mohr media and the generalized Prandtl perfectly plastic solids in plane strain states. The Prandtl solids have the constitutive equation related the maximum tangent stress to the mean (exactly median) stress. In the case of Coulomb–Mohr media, the specified dependence is linear. The intermediate principal stress has no effect on yielding or transition to a limit state. Under these conditions, it is then possible to prove the hyperbolicity of the system of differential equations of kinematics and to obtain differential relations along the characteristic lines, which consist of linear elements which are not instantaneously elongate.

Radayev Yuri Nickolaevich e-mail: radayev@ipmnet.ru, y.radayev@gmail.com, Dr. Sci. Phys. & Math., Professor, Leading Researcher, Institute for Problems in Mechanics of RAS, Moscow, Russia.