Deformable Voronoi model for the research of the plane stress-strain state

Authors

  • Victor V. Chaiko Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus https://orcid.org/0000-0003-2490-0401
  • Oleg L. Konovalov Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

DOI:

https://doi.org/10.33581/2520-6508-2021-1-102-112

Keywords:

numerical experiment, discrete element modelling, microstructural parameters, stress-strain state, deformable Voronoi

Abstract

The paper considers an approach to modelling geomechanical processes based on the internal forces method. In particular, the problem of non-invariance of the method to rotations is investigated. An original modification of the method based on additional central forces determined by deformations of adjacent Voronoi cells is proposed. An analytical relationship between the parameters of the microstructural model and the elastic properties of the simulated material is obtained. The results of numerical experiments to verify this relationship and the accuracy of modelling the stress-strain state are presented.

Author Biographies

  • Victor V. Chaiko, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

    postgraduate student at the department of information management systems, faculty of applied mathematics and computer science

  • Oleg L. Konovalov, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

    PhD (engineering); head of the laboratory of information technologies and computer graphics and associate professor at the department of information management systems, faculty of applied mathematics and computer science

References

  1. Krasnoproshin VV, Konovalov OL, Chaiko VV. Algorithm for calculating the geometric parameters of flat hydraulically induced fractures. Vestnik of Brest State Technical University. Physics, mathematics, informatics. 2017;5:23–26. Russian.
  2. Chaiko VV, Konovalov OL, Zhuravkov MA. DEM-FVM conjugated parallel solver for hydraulic fracturing. In: 2nd International discrete fracture network engineering conference; 2018 June 20–22; Seattle, Washington, USA. Alexandria: American Rock Mechanics Association; 2018. p. 1429.
  3. Gao H, Klein P. Numerical simulation of crack growth in an isotropic solid with randomized internal cohesive bonds. Journal of the Mechanics and Physics of Solids. 1998;46(2):187–218. DOI: 10.1016/S0022-5096(97)00047-1.
  4. Zhang Z, Ge X. A new quasi-continuum constitutive model for crack growth in an isotropic solid. European Journal of Mechanics – A/Solids. 2005;24(2):243–252. DOI: 10.1016/j.euromechsol.2004.11.007.
  5. Zhao G. Development of micro-macro continuum-discontinuum coupled numerical method [dissertation]. Lausanne: École Polytechnique Fédérale de Lausanne; 2010. 224 p.
  6. Konovalov O, Ji S, Zhuravkov M. Modified virtual internal bond model based on deformable Voronoi particles. Theoretical and Applied Mechanics Letters. 2020;10(2):87–91. DOI: 10.1016/j.taml.2020.01.008.

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Published

2021-04-12

Issue

No. 1 (2021): Journal of the Belarusian State University. Mathematics and Informatics

Section

Theoretical Foundations of Computer Science

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How to Cite

Deformable Voronoi model for the research of the plane stress-strain state. (2021). Journal of the Belarusian State University. Mathematics and Informatics, 1, 102-112. https://doi.org/10.33581/2520-6508-2021-1-102-112