Geodesic
Numerical calculation of the effective coefficient in the problem of linear elasticity of a composite material
Matematičeskie zametki SVFU, Tome 24 (2017) no. 2, pp. 75-84 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the numerical calculation of the effective coefficient of the linear elasticity problem on a representative volume element having a similar volume fraction of fibers. The obtained effective coefficient is used to solve the complete problem on a coarse grid. As an example, the problem of calculating the deformation of a concrete block with the inclusion of steel fibers under the action of a three-point bending is considered. The computational implementation of the problem is carried out by the finite element method using the FEniCS computing platform.
Keywords: numerical homogenization, linear elasticity, composite material, mathematical modeling
Mots-clés : effective coefficient. 
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P. E. Zakharov; P. V. Sivtsev. Numerical calculation of the effective coefficient in the problem of linear elasticity of a composite material. Matematičeskie zametki SVFU, Tome 24 (2017) no. 2, pp. 75-84. http://geodesic.mathdoc.fr/item/SVFU_2017_24_2_a5/

[1] Christensen R. M., Lo K. H., “Solutions for effective shear properties in three phase sphere and cylinder models”, J. Mechanics and Physics of Solids, 27:4 (1979), 315–330 | DOI

[2] Li L. X., Wang T. J., “A unified approach to predict overall properties of composite materials”, Materials Characterization, 54:1 (2005), 49–62 | DOI

[3] Gusev A. A., “Representative volume element size for elastic composites: a numerical study”, J. Mechanics and Physics of Solids, 45:9 (1997), 1449–1459 | DOI

[4] Kari S., Berger H., Gabbert U., “Numerical evaluation of effective material properties of randomly distributed short cylindrical fibre composites”, Comput. Materials Sci., 39:1 (2007), 198–204 | DOI

[5] Theocaris P. S., Stavroulakis G. E., Panagiotopoulos P. D., “Calculation of effective transverse elastic moduli of fiber-reinforced composites by numerical homogenization”, Composites Sci. Technol., 57:5 (1997), 573–586 | DOI

[6] Kolesov A. E. et al., “Numerical analysis of reinforced concrete deep beams”, Numerical Analysis and Its Applications: 6th International Conference, NAA 2016 (Lozenetz, Bulgaria, June 15-22, 2016), Springer-Verl., 2016, 414–421 | MR

[7] Smarzewski P., Por ba J., Rentflejsz A., “Experimental testing of high performance fibre reinforced concrete deep beams”, Civil Engineering and Architecture, 10:1 (2012), 15–26

[8] Sivtsev P. V., “Numerical simulation of the elasticity problem of reinforced concrete slabs”, Vestn. Severo-Vost. Feder. Univ., 2015, no. 4, 98–109

[9] Automated solution of differential equations by the finite element method: The FEniCS book, Lecture Notes in Computational Science and Engineering, 84, eds. Logg A., Mardal K. A., Wells G., Springer-Verl., 2012 | MR