Modification of implicit algorithm for solving a problem on the elastic plasticity of bulk materials

Authors

DOI:

https://doi.org/10.15587/1729-4061.2017.109550

Keywords:

bulk material, Drucker-Prager yield criterion, return-mapping algorithm, plastic deformation

Abstract

A mathematical statement is given of the elastic-plastic behavior of isotropic bulk material using a classic model of Drucker-Prager. We have improved the return-mapping algorithm for solving numerically a problem on the mechanical state of bulk material. In order to solve a system of nonlinear equations by the Newton method, it is proposed, at each step of iterations, instead of finding the inverse matrix, to solve a system of algebraic equations, linearized by Newton, by applying the Gauss exclusion method. This makes it possible to reduce the number of arithmetic operations by about 3n2 (n is the dimensionality of SLAE) at each iteration step for each plastic finite element. We have tested the programming code developed on the high-level programming language Fortran on the example of a model material, characterized by the associative law of current, at different values of the angle of natural repose. Comparison of the obtained results of numerical experiment with the data received by applying the proprietary software revealed a deviation within 0.25–5.3 % depending on the desired magnitude

Author Biographies

Anton Karvatskii, National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" Peremohy ave., 37, Kyiv, Ukraine, 03056

Doctor of Technical Sciences, Professor

Department of Chemical, Polymer and Silicate Engineering

Yevgen Panov, National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" Peremohy ave., 37, Kyiv, Ukraine, 03056

Doctor of Technical Sciences, Professor

Department of Chemical, Polymer and Silicate Engineering

Anatolii Pedchenko, National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" Peremohy ave., 37, Kyiv, Ukraine, 03056

PhD, Junior Researcher

Scientific Research Center "Resource-Saving Technologies"

Valentin Shkil, National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" Peremohy ave., 37, Kyiv, Ukraine, 03056

Department of Chemical, Polymer and Silicate Engineering

References

  1. Fialkov, A. (2008). Processes and equipment for production of powdered carbon materials. Moscow: Aspect Press, 687.
  2. Leleka, S., Lazarev, T., Pedchenko, A., Shvachko, D. (2015). The study of uneven temperature field in billet electrodes during their graphitization in the Castner furnace. Eastern-European Journal of Enterprise Technologies, 6 (5 (78)), 28–32. doi: 10.15587/1729-4061.2015.56642
  3. Karvatskii, A., Leleka, S., Pedchenko, A., Lazariev T. (2016). Numerical analysis of the physical fields in the process of electrode blanks graphitization in the castner furnace. Eastern-European Journal of Enterprise Technologies, 6 (5 (84)), 19–25. doi: 10.15587/1729-4061.2016.83191
  4. Kutuzov, S. V., Buryak, V. V., Derkach, V. V., Panov, E. N., Karvatskii, A. Y., Vasil’chenko, G. N. et. al. (2014). Making the Heat-Insulating Charge of Acheson Graphitization Furnaces More Efficient. Refractories and Industrial Ceramics, 55 (1), 15–16. doi: 10.1007/s11148-014-9648-5
  5. De Borst, R., Crisfield, M. A., Remmers, J. J. C., Verhoosel, C. V. (2012). Non-linear finite element analysis of solids and structures. John Wiley & Sons Ltd, 516. doi: 10.1002/9781118375938
  6. Zienkiewicz, O. C., Taylor, R. L., Fox, D. D. (2014). The Finite Element Method for Solid and Structural Mechanics. Elsevier Ltd., 624. doi: 10.1016/B978-1-85617-634-7.00016-8
  7. Yu, T., Teng, J. G., Wong, Y. L., Dong, S. L. (2010). Finite element modeling of confined concrete-I: Drucker–Prager type plasticity model. Engineering Structures, 32 (3), 665–679. doi: 10.1016/j.engstruct.2009.11.014
  8. Ivorra, S., Irles, R., Estevan, L. et. al. (2010). Drucker-Prager yield criterion application to study the behavior of CFRP confined concrete under compression. World Congress on Housing. Santander (Cantabria), Spain.
  9. Öztekin, E., Pul, S., Hüsem, M. (2016). Experimental determination of Drucker-Prager yield criterion parameters for normal and high strength concretes under triaxial compression. Construction and Building Materials, 112, 725–732. doi: 10.1016/j.conbuildmat.2016.02.127
  10. Stefanov, Yu. P., Bakeev, Р. A., Akhtyamova, A. I. (2015). Simulation of the behavior of rocks beyond the elastic limit. Processes in geomedia, 4 (4), 85–91.
  11. Ustynov, K. B. (2016). About the application of plastic flow models for the description of anisotropic rocks inelastic deformation. Processes in geomedia, 3 (7), 278–287.
  12. Sinha, T., Curtis, J. S., Hancock, B. C., Wassgren, C. (2010). A study on the sensitivity of Drucker–Prager Cap model parameters during the decompression phase of powder compaction simulations. Powder Technology, 198 (3), 315–324. doi: 10.1016/j.powtec.2009.10.025
  13. Diarra, H., Mazel, V., Busignies, V., Tchoreloff, P. (2013). FEM simulation of the die compaction of pharmaceutical products: Influence of visco-elastic phenomena and comparison with experiments. International Journal of Pharmaceutics, 453 (2), 389–394. doi: 10.1016/j.ijpharm.2013.05.038
  14. Shin, H., Kim, J.-B. (2015). A numerical investigation on determining the failure strength of a powder compact in unconfined compression testing by considering the compressible character of the specimen. Powder Technology, 277, 156–162. doi: 10.1016/j.powtec.2015.02.054
  15. Fuk, D. V., Ganin, S. V., Tsemenko, V. N. (2016). Study of the consolidation of powder materials using the ABAQUS software package. St. Petersburg State Polytechnical University Journal, 1 (238), 100–110. doi: 10.5862/jest.238.10
  16. Zhou, M., Huang, S., Hu, J., Lei, Y., Xiao, Y., Li, B. et. al. (2017). A density-dependent modified Drucker-Prager Cap model for die compaction of Ag57.6-Cu22.4-Sn10-In10 mixed metal powders. Powder Technology, 305, 183–196. doi: 10.1016/j.powtec.2016.09.061
  17. Zhou, M., Huang, S., Hu, J., Lei, Y., Zou, F., Yan, S., Yang, M. (2017). Experiment and finite element analysis of compaction densification mechanism of Ag-Cu-Sn-In mixed metal powder. Powder Technology, 313, 68–81. doi: 10.1016/j.powtec.2017.03.015
  18. Karvatskii, A., Lazariev, T., Leleka, S., Pedchenko, A. (2017). CAD-systems application for solving the elastoplastic problems with isotropic hardening. Bulletin of the National Technical University «KhPI» Series: New solutions in modern technologies, 7 (1229), 55–63. doi: 10.20998/2413-4295.2017.07.08
  19. Lawrence, N. (2002). Compaq Visual Fortran. Sydney: Digital Press, 600.
  20. Gmsh. A three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. Avaialble at: http://geuz.org/gmsh/
  21. Thompson, M., Thompson, J. (2017). ANSYS Mechanical APDL for Finite Element Analysis. Oxford: Butterworth-Heinemann, 466.
  22. ParaView. An open-source, multi-platform data analysis and visualization application. Available at: http://www.paraview.org/

Downloads

Published

2017-10-24

How to Cite

Karvatskii, A., Panov, Y., Pedchenko, A., & Shkil, V. (2017). Modification of implicit algorithm for solving a problem on the elastic plasticity of bulk materials. Eastern-European Journal of Enterprise Technologies, 5(7 (89), 17–23. https://doi.org/10.15587/1729-4061.2017.109550

Issue

Vol. 5 No. 7 (89) (2017): Applied mechanics

Section

Applied mechanics

License

Copyright (c) 2017 Anton Karvatskii, Yevgen Panov, Anatolii Pedchenko, Valentin Shkil

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.

A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.