Advertisement

Numerical Calculation of Deformations of Composite Material with Fiber Inclusions

  • Petr V. SivtsevEmail author
  • Djulustan Ya. Nikiforov
Conference paper
  • 85 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11958)

Abstract

In the numerical simulation of the stress-strain state of a composite material, a problem may arise associated with a large computational complexity due to the grid resolution of a large number of inclusions. It is especially difficult to resolve elongated bodies having linear dimensions that differ by several orders of magnitude, such as fibers. In this paper, we attempt to model fibers in the form of one-dimensional lines, which can significantly reduce the computational complexity of the problem. Comparison of the results for the three-point bending of a concrete block is presented. For the numerical solution, the finite element method was applied using the FEniCS computing platform.

References

  1. 1.
    Smarzewski, P.: Influence of basalt-polypropylene fibres on fracture properties of high performance concrete. Compos. Struct. 209, 23–33 (2019)CrossRefGoogle Scholar
  2. 2.
    Sivtseva, A.V., Sivtsev, P.V.: Numerical simulation of deformations of basalt roving. In: Dimov, I., Faragó, I., Vulkov, L. (eds.) FDM 2018. LNCS, vol. 11386, pp. 501–508. Springer, Cham (2019).  https://doi.org/10.1007/978-3-030-11539-5_58CrossRefGoogle Scholar
  3. 3.
    Zakharov, P.E., Sivtsev, P.V.: Numerical calculation of the effective coefficient in the problem of linear elasticity of a composite material. Math. Notes NEFU 24(2), 75–84 (2017)zbMATHGoogle Scholar
  4. 4.
    Stepanov, S.P., Vasilyeva, M.V., Vasil’ev, V.I.: Generalized multiscale discontinuous Galerkin method for solving the heat problem with phase change. J. Comput. Appl. Math. 340, 645–652 (2018)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Vasil’ev, V.I., et al.: Numerical solution of a fluid filtration problem in a fractured medium by using the domain decomposition method. J. Appl. Ind. Math. 12(4), 785–796 (2018)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Akkutlu, I.Y., Efendiev, Y., Vasilyeva, M., Wang, Y.: Multiscale model reduction for shale gas transport in a coupled discrete fracture and dual-continuum porous media. J. Nat. Gas Sci. Eng. 48, 65–76 (2017)CrossRefGoogle Scholar
  7. 7.
    Kolesov, A.E., Sivtsev, P.V., Smarzewski, P., Vabishchevich, P.N.: Numerical analysis of reinforced concrete deep beams. In: Dimov, I., Faragó, I., Vulkov, L. (eds.) NAA 2016. LNCS, vol. 10187, pp. 414–421. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-57099-0_46CrossRefzbMATHGoogle Scholar
  8. 8.
    Logg, A., Mardal, K.A., Wells, G.N.: Automated Solution of Differential Equations by the Finite Element Method. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-23099-8CrossRefzbMATHGoogle Scholar
  9. 9.
    Antonov, M.Y., Grigorev, A.V., Kolesov, A.E.: Numerical modeling of fluid flow in liver lobule using double porosity model. In: Dimov, I., Faragó, I., Vulkov, L. (eds.) NAA 2016. LNCS, vol. 10187, pp. 187–194. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-57099-0_18CrossRefzbMATHGoogle Scholar
  10. 10.
    Avvakumov, A.V., Vabishchevich, P.N., Vasilev, A.O., Strizhov, V.F.: Solution of the 3D neutron diffusion benchmark by FEM. In: Lirkov, I., Margenov, S. (eds.) LSSC 2017. LNCS, vol. 10665, pp. 435–442. Springer, Cham (2018).  https://doi.org/10.1007/978-3-319-73441-5_47CrossRefGoogle Scholar
  11. 11.
    Valentino, P., Furgiuele, F., Romano, M., Ehrlich, I., Gebbeken, N.: Mechanical characterization of basalt fibre reinforced plastic with different fabric reinforcements-Tensile tests and FE-calculations with representative volume elements (RVEs). In: Convegno IGF XXII (2013)Google Scholar
  12. 12.
    Smarzewski, P.: Processes of cracking and crushing in hybrid fibre reinforced high-performance concrete slabs. Processes 7(1), 49 (2019)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Ammosov North-Eastern Federal UniversityYakutskRussia

Personalised recommendations