Abstract:
A closed mathematical model is formulated, which takes into account elastoplastic deformations and the medium capability of accumulating the energy of internal self-balanced stresses. Satisfaction of the diffeomorphism postulate (assumption of displacement field smoothness) is not required; as a result, the strains depend on the stresses and second derivatives of the stresses with respect to the coordinates. The model involves a linear structural parameter. Relations that take into account local bending of the elementary volumes of the medium are derived.
Citation:
A. F. Revuzhenko, O. A. Mikenina, “Elastoplastic model of rocks with a linear structural parameter”, Prikl. Mekh. Tekh. Fiz., 59:2 (2018), 167–176; J. Appl. Mech. Tech. Phys., 59:2 (2018), 332–340
\Bibitem{RevMik18}
\by A.~F.~Revuzhenko, O.~A.~Mikenina
\paper Elastoplastic model of rocks with a linear structural parameter
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2018
\vol 59
\issue 2
\pages 167--176
\mathnet{http://mi.mathnet.ru/pmtf606}
\crossref{https://doi.org/10.15372/PMTF20180117}
\elib{https://elibrary.ru/item.asp?id=32773505}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2018
\vol 59
\issue 2
\pages 332--340
\crossref{https://doi.org/10.1134/S0021894418020177}
Linking options:
https://www.mathnet.ru/eng/pmtf606
https://www.mathnet.ru/eng/pmtf/v59/i2/p167
This publication is cited in the following 14 articles:
D. S. Zhurkina, S. V. Lavrikov, “Calculation of Stress Concentration in Influence Zone of Mining Face within Gradient-Type Elastoplastic Modeling”, J Min Sci, 60:3 (2024), 375
S. V. Lavrikov, “Development of Mathematical Modeling Methods and Solution of Present-Day Problems in Geomechanics at the Institute of Mining SB RAS”, J Min Sci, 60:4 (2024), 533
A. F. Revuzhenko, “Two Concepts of Continuum Deformation Kinematics: Displacement Field of Points and Displacement Fields of Material Planes”, J Min Sci, 60:4 (2024), 567
S. V. Lavrikov, O. A. Mikenina, PHYSICAL MESOMECHANICS OF CONDENSED MATTER: Physical Principles of Multiscale Structure Formation and the Mechanisms of Nonlinear Behavior: MESO2022, 2899, PHYSICAL MESOMECHANICS OF CONDENSED MATTER: Physical Principles of Multiscale Structure Formation and the Mechanisms of Nonlinear Behavior: MESO2022, 2023, 020088
Tatyana A. Mladova, Lecture Notes in Networks and Systems, 200, Current Problems and Ways of Industry Development: Equipment and Technologies, 2021, 529
Alexandr Revuzhenko, Sergey Lavrikov, L.D. Pavlova, V.I. Klishin, “Mathematical models of rock mass affected by high pressure gradients”, E3S Web Conf., 330 (2021), 01004
VI Altukhov, SV Lavrikov, AF Revuzhenko, “Stress concentration analysis in rock pillars in the framework of non-local elastic model with structural parameter”, IOP Conf. Ser.: Earth Environ. Sci., 773:1 (2021), 012007
A. F. Revuzhenko, S. V. Lavrikov, O. A. Mikenina, NUMERICAL METHODS FOR SOLVING PROBLEMS IN THE THEORY OF ELASTICITY AND PLASTICITY (EPPS 2021), 2448, NUMERICAL METHODS FOR SOLVING PROBLEMS IN THE THEORY OF ELASTICITY AND PLASTICITY (EPPS 2021), 2021, 020018
Sergey Lavrikov, L.D. Pavlova, V.I. Klishin, “Mathematical model and numerical calculations of disastrous pressure phenomena in rock mass with weakening cavity”, E3S Web Conf., 330 (2021), 01005
S. V. Klishin, “Discrete-Element Modeling of Strain Localization in Granular Medium at Passive Pressure Application to a Retaining Wall”, J Min Sci, 57:5 (2021), 740
A. F. Revuzhenko, O. A. Mikenina, “Elastoplastic Model of Rocks with Internal Self-Balancing Stresses. Continuum Approximation”, J Min Sci, 56:2 (2020), 159
S. V. Lavrikov, A. F. Revuzhenko, “MATHEMATICAL MODELING OF UNSTABLE DEFORMATION IN ROCK MASS WITH REGARD TO SELF-BALANCING STRESSES”, J Min Sci, 56:6 (2020), 887
A. F. Revuzhenko, O. A. Mikenina, “Elastoplastic Model of Rock with Internal Self-Balancing Stresses”, J Min Sci, 54:3 (2018), 368
S. V. Lavrikov, A. F. Revuzhenko, AIP Conference Proceedings, 2051, 2018, 020167
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