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

Loosely bonded granular media are common in construction industry and in view of it are interesting for mathematics and continuum mechanics. The most important quality of granular media is their porosity and irreversible compressibility (loosening) in the course of a flow process. The paper deals with flow kinematic of the irreversibly compressible Coulomb–Mohr granular media and the generalized perfectly plastic Prandtl media, characterized by a relationship between the maximum tangential stress and the average (the exactly median) stress. For the Coulomb– Mohr model this relationship is linear. The intermediate principal normal stress does not have any effect on yielding. The study is restricted to those states of yielding that can be described by the yield condition which does not include the intermediate principal stress. In this case, which is realized, in particular, under conditions of plane flows, it is possible to establish the hyperbolicity of the system of kinematic differential equations. This system is formulated in the curvilinear coordinate net determined by the principal directions of the strain tensor increment. The method of asymptotic directors known from a number of previous discussions is employed for the given analysis. Kinematic equations in the general three-dimensional case are also considered.

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.