Metadata (abstracts and keywords) for the articles in the journal
Y. N. Radayev On the theory of the Coulomb–Mohr media and generalized Prandtl plastic solids // Vestnik I. Yakovlev Chuvach State Pedagogical University. Series: Mechanics of a limit state . 2018. № 4(38). p. 3-24
Author(s):
Y. N. Radayev
Index of UDK:
539.374
DOI:
Title:
On the theory of the Coulomb–Mohr media and generalized Prandtl plastic solids
Three-dimensional flows of perfectly plastic medium are considered within the framework of the Coulomb–Mohr continuum model. The model is to be used in applied problems related to limit states and flows of sands, rocks and any other kind of granular media. A generalization of the Coulomb–Mohr continuum model due to L. Pandtl is discussed. The present study is based on a notion of asymptotic directions of the stress tensor and the strain tensor increment and as well on instantaneously not elongated directors which are orthogonal to the asymptotic directions and lie in the plane normal to the intermediate principal stress axis. By making use of mechanical sense of asymptotic directions the canonical dyadic representations of the stress tensor and the strain tensor increment are obtained. The associated flow rule are discussed and applied to study of three-dimensional irreversible kinematics of the Coulomb–Mohr media. It is shown that the dilatation rate is always positive excepting the case of zero internal friction. Orientations of the instantaneously not elongated linear material elements are found. The strain tensor increment represented in three dimensions by means of the instantaneously not elongated directors is obtained. A kinematical constraint to three-dimensional flows of the Coulomb–Mohr media imposed by the associated flow rule is discussed. The constraint is to be treated as an equation to determine the intermediate principal stress not involved in the formulation of the Coulomb–Mohr limit state condition. The intermediate principal stress is proved to be the exactly median principal stress for the media with zero internal friction.
The contact details of authors:
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.