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Article information
2019 , Volume 24, № 6, p.90-98
Potapov I.I., Reshetnikova O.V.
The use of a stationary hypoplastic model for modelling the motion of granular medium
Purpose. The aim of this study is а development of mathematical models that describe the complex motion of a granular medium in the process of its disintegration that allows evaluating the possibility of using a simplified stationary hypoplastic model to describe this process. Methodology. To describe the motion of a granular medium, the classical equations of motion and mass conservation were used. The calculation of the deviator of the stress tensor is performed within the framework of a simplified hypoplastic model. The work uses the hypothesis of a linear relationship between the pressure function and the density of the granular medium. This hypothesis is typical for smoothed particle methods, one of the variants of which is proposed for the numerical implementation of the problem. Results. A new mathematical model of the problem of the motion of a granular medium in the process of its disintegration is formulated. An algorithm for solving the problem based on the method of smoothed particles is proposed. The problem of disintegration of a sand pillar is solved numerically. A comparative analysis of the obtained solutions with experimental data is accomplished. Findings. Using the assumption that the propagation velocity of elastic waves that determine the stress-strain state in sand particles is much higher than the velocities of particles arising from sand shedding, an approximate model for calculating the stress state of a moving granular medium based on a stationary hypoplastic model is presented. To solve the problem, the method of smoothed particles with a small smoothing parameter was implemented with the help of a new combined interpolation core in the calculations. To verify the mathematical model and the selected method, the implementation of the smoothed particle method was performed and the problem of disintegration of the sand column was solved. The obtained solution of the problem shows satisfactory agreement with the experimental data.
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Keywords: granular medium motion, smoothed particle method, hypoplastic model of stress-strain state, yield criterion
doi: 10.25743/ICT.2019.24.6.011.
Author(s):
Potapov Igor Ivanovich
Dr.
Position: General Scientist
Office: Computer center of Far East Branch of the Russian Academy of Sciences
Address: 680000, Russia, Khabarovsk, 65, Kim U Chena street
Phone Office: (4212) 22-72-67
E-mail: potapov2i@gmail.com
Reshetnikova Olga Vladimirovna
PhD.
Position: Research Scientist
Office: Computer center of Far East Branch of the Russian Academy of Sciences
Address: 680000, Russia, Khabarovsk, 65, Kim U Chena street
Phone Office: (4212) 22-72-67
E-mail: ov13@yandex.ru
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Bibliography link:
Potapov I.I., Reshetnikova O.V. The use of a stationary hypoplastic model for modelling the motion of granular medium // Computational technologies. 2019. V. 24. № 6. P. 90-98
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