# Structure identification of metal fibre reinforced cementitious composites

## Main Article Content

## Abstract

Mechanical properties of metal fibre reinforced cementitious composites, because of the danger of micro- and macro-cracking due to the mechanism of quasi-brittle fracture, depend strongly on the macrostructural homogeneity and directional distribution of fibres. Thus some low-invasive or quite non-destructive measurement techniques, together with non-expensive, quick, robust and reliable algorithms for evaluation of corresponding material parameters, are needed. This paper demonstrates some promising classes of such approaches, based on image processing and indirect magnetic and electromagnetic measurements, with the aim of the development of general methodology for technical evaluation of such materials.

## Article Details

How to Cite

VALA, Jiří.
Structure identification of metal fibre reinforced cementitious composites.

**Proceedings of the Conference Algoritmy**, [S.l.], p. 244-253, feb. 2016. Available at: <http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/413>. Date accessed: 22 sep. 2017.
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Articles

## References

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[12] S. Karkkainen and E. B. Vedel Jensen, Estimation of fibre orientation from digital images. Image Analysis and Stereology, 20 (2001), pp. 199–202.

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[15] J. F. Lataste, M. Behloul and D. Breysse, Characterisation of fibres distribution in a steel fibre reinforced concrete with electrical resistivity measurements. NDT & E International (Independent Nondestructive Testing and Evaluation), 41 (2008), pp. 638–647.

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[21] O. Ouchetto, S. Zouhdi, A. Bossavit, G. Griso and B. Miara, Modeling of 3D periodic mutiphase composites by homogenization. IEEE Transactions on Microwave Theory and Techniques, 54 (2006), pp. 2615–2619.

[22] N. Ozyurt, L. Y. Woo, T. O. Mason and S. P. Shah, Monitoring fiber dispersion in fiber reinforced cementitious materials: comparison of AC-impedance spectroscopy and image analysis. ACI Materials Journal, 103 (2006), pp. 340–347.

[23] T. Pospíšil, On statistical description of random structures. Engineering Mechanics, 17 (2010), pp. 383–392.

[24] M. Pieper and P. Klein, Application of simple, periodic homogenization techniques to nonlinear heat conduction problems in non-periodic, porous media. Heat and Mass Transfer, 48 (2012), pp. 291–300.

[25] L. Rizzuti and F. Bernardino, Effects of fibre volume fraction on the compressive and flexural experimental behaviour of SFRC. Contemporary Engineering Sciences, 7 (2014), pp. 379– 390.

[26] T. Roubíček. Nonlinear Partial Differential Equations with Applications. Birkh ̈ auser, Basel, 2006.

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[28] A. H. Sihvola and I. V. Lindell, Effective permeability of mixtures. Progress in Electromagnetics Research, 6 (1992), pp. 153-180.

[29] D. V. Soulioti, N. M. Barkoula, A. Papietis and T. E. Matikas, Effects of fibre geometry and volume fraction on the flexural behaviour of steel-fibre reinforced concrete. International Journal for Experimental Mechanics, 47 (2011), pp. 535–541.

[30] M. O. Steinhauser, Computational Mulsiscale Modeling of Fluids and Solids, Springer, 2008.

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[33] M. Tunák and A. Linka, Analysis of planar anisotropy of fibre systems by using 2D Fourier transform. Fibres & Textiles in Eastern Europe, 15 (2007), pp. 86–90.

[34] R. Urban, P. Fiala, M. Hanzelka and J. Mikulka, Stochastic models of electrodynamics and numerical models. 33rd PIERS (Progress In Electromagnetics Research Symposium) in Taipei (China), 2013, pp. 33–37.

[35] S. Van Damme, A. Franchois, D. De Zutter ND L. Taerwe, Nondestructive determination of the steel fiber content in concrete slabs with an open-ended coaxial probe. IEEE Transactions of Geoscience and Remote Sensing, 42 (2004), pp. 2511–2521.

[36] J. Vala and M. Hora ́k, Nondestructive identification of engineering properties of metal fibre composites. 10-th ICNAAM (International Conference of Numerical Analysis and Applied Mathematics) in Kos (Greece), AIP Conference Proceedings, 1479 (2012), pp. 2208–2211.

[37] J. Vala and T. Grohová, A magnetic approach to the identification of effective characteristics of metal fibre composites used in civil engineering. Recent advances in integrity, reliability and failure – 4-th International Conference in Funchal (Madeira), 2013, pp. 731-750.

[38] G. Weidemann, R. Stadie, J. Goebbels and B. Hillemeier, Computer tomography study of fibre reinforced autoclaved aerated concrete. Materials Testing, 50 (2008), pp. 278–285.

[39] H.-J. Wichmann, H. Budelmann and A. Holst, Determination of steel fiber dosage and steel fiber orientation in concrete. In: Nondestructive Testing of Materials and Structures, Springer 2013, pp. 239–245.

[40] K. W. Whites and F. Wu, Effects of particle shape on the effective permittivity of composite materials with measurements for lattices of cubes. IEEE Transansactions on Microwave Theory and Techniques, 50 (2002), pp. 1723–1729.

[2] A. Cerrone, P. Wawrzynek, A. Nonn, G. H. Paulino and A. Ingraffea, Implementation and verification of the Park-Paulino-Roesler cohesive zone model in 3D. Engineering Fracture Mechanics, 120 (2014), pp. 6–42.

[3] D. Cioranescu and P. Donato, An Introduction to Homogenization. Oxford University, 1999.

[4] V. M. C. F. Cunha, J. A. O. Barros and J. M. Sena-Cruz, An integrated approach for modelling the tensile behaviour of steel fibre reinforced self-compacting concrete. Cement and Concrete Research, 41 (2011), pp. 64–76.

[5] Y. Efendiev and T. Y. Hou, Multiscale Finite Element Methods. Springer, 2009.

[6] M. Faifer, L. Ferrara, R. Ottoboni and S. Toscani, Low frequency electrical and magnetic methods for non-destructive analysis of fiber dispersion in fiber reinforced cementitious composites: an overview. Sensors, 13 (2013), pp. 1300–1318.

[7] M. Faifer, R. Ottoboni, S. Toscani and L. Ferrara, Nondestructive testing of steel-fiberreinforced concrete using a magnetic approach. IEEE Transactions on Instrumentation and Measurement, 60 (2011), pp. 1709–1711.

[8] S. Giordano, Effective medium theory for dielectric ellipsoids. Journal of Electrostatics, 58 (2003), pp. 59–76.

[9] L. Hobst, O. Anton, J. Vodička and J. Ščučka, Homogeneity detection of fibre-concrete structures by using radiographic technique. In: Nondestructive Testing of Materials and Structures, Springer 2013, pp. 323–328.

[10] L. Hobst and P. Bılek, Various control methods developed for fibre concrete structures. Recent advances in integrity, reliability and failure – 4-th International Conference in Funchal (Madeira), 2013, pp. 721-730.

[11] V. Isakov, Inverse Problems for Partial Differential Equations. Springer, 2006.

[12] S. Karkkainen and E. B. Vedel Jensen, Estimation of fibre orientation from digital images. Image Analysis and Stereology, 20 (2001), pp. 199–202.

[13] A. Krasnikovs, V. Zaharevskis, O. Kononova, V. Lusi, A. Galushchak and E. Zaleskis, Fiber concrete properties control by fibers motion – investigation in fresh concrete during casting. Industrial Engineering – 8th International DAAAM Baltic Conference in Tallin, 2012, Part V: Materials Engineering, #10, 6 pp.

[14] G. Kristensson, Homogenization of spherical inclusions. Progress in Electromagnetic Research, 42 (2003), pp. 1–25.

[15] J. F. Lataste, M. Behloul and D. Breysse, Characterisation of fibres distribution in a steel fibre reinforced concrete with electrical resistivity measurements. NDT & E International (Independent Nondestructive Testing and Evaluation), 41 (2008), pp. 638–647.

[16] P. Mallet, C. A. Guérin and A. Sentenac, Maxwell-Garnett mixing rule in the presence of multiple scattering: derivation and accuracy. Physical Review, B 72 (2005), 14205/1–9.

[17] V. A. Marchenko and E. Ya. Khruslov, Homogenization of Partial Differential Equations. Birkh ̈ auser, 2006.

[18] P. J. M. Monteiro, C. Y. Pichot and K. Belkebir, Computer tomography of reinforced concrete. In: Materials Science of Concrete, Chapter 12, American Ceramics Society, 1998.

[19] G. Nguetseng and N. Svanstedt, σ-convergence. Banach Journal of Mathematical Analysis, 5 (2011), pp. 101–135.

[20] S. J. Orfanidis, Electromagnetic Waves and Antennas. Rutgers University, Piscataway (NJ, USA), 2014.

[21] O. Ouchetto, S. Zouhdi, A. Bossavit, G. Griso and B. Miara, Modeling of 3D periodic mutiphase composites by homogenization. IEEE Transactions on Microwave Theory and Techniques, 54 (2006), pp. 2615–2619.

[22] N. Ozyurt, L. Y. Woo, T. O. Mason and S. P. Shah, Monitoring fiber dispersion in fiber reinforced cementitious materials: comparison of AC-impedance spectroscopy and image analysis. ACI Materials Journal, 103 (2006), pp. 340–347.

[23] T. Pospíšil, On statistical description of random structures. Engineering Mechanics, 17 (2010), pp. 383–392.

[24] M. Pieper and P. Klein, Application of simple, periodic homogenization techniques to nonlinear heat conduction problems in non-periodic, porous media. Heat and Mass Transfer, 48 (2012), pp. 291–300.

[25] L. Rizzuti and F. Bernardino, Effects of fibre volume fraction on the compressive and flexural experimental behaviour of SFRC. Contemporary Engineering Sciences, 7 (2014), pp. 379– 390.

[26] T. Roubíček. Nonlinear Partial Differential Equations with Applications. Birkh ̈ auser, Basel, 2006.

[27] V. A. Rukavishnikov and A. O. Mosolapov, New numerical method for solving timeharmonic Maxwell equations with strong singularity. Journal of Computational Physics, 231 (2012), pp. 2438-2448.

[28] A. H. Sihvola and I. V. Lindell, Effective permeability of mixtures. Progress in Electromagnetics Research, 6 (1992), pp. 153-180.

[29] D. V. Soulioti, N. M. Barkoula, A. Papietis and T. E. Matikas, Effects of fibre geometry and volume fraction on the flexural behaviour of steel-fibre reinforced concrete. International Journal for Experimental Mechanics, 47 (2011), pp. 535–541.

[30] M. O. Steinhauser, Computational Mulsiscale Modeling of Fluids and Solids, Springer, 2008.

[31] N. Svanstedt, Multiscale stochastic homogenization of convection-diffusion equations. Applications of Mathematics, 53 (2008), pp. 143–155.

[32] L. Tartar, Quelques remarques sur l’homognsaition. In: Functional Analysis and Numerical Analysis – Proceedings of the Japan-France Seminar, Japanese Society for Promotion of Science (1978), pp. 136–212.

[33] M. Tunák and A. Linka, Analysis of planar anisotropy of fibre systems by using 2D Fourier transform. Fibres & Textiles in Eastern Europe, 15 (2007), pp. 86–90.

[34] R. Urban, P. Fiala, M. Hanzelka and J. Mikulka, Stochastic models of electrodynamics and numerical models. 33rd PIERS (Progress In Electromagnetics Research Symposium) in Taipei (China), 2013, pp. 33–37.

[35] S. Van Damme, A. Franchois, D. De Zutter ND L. Taerwe, Nondestructive determination of the steel fiber content in concrete slabs with an open-ended coaxial probe. IEEE Transactions of Geoscience and Remote Sensing, 42 (2004), pp. 2511–2521.

[36] J. Vala and M. Hora ́k, Nondestructive identification of engineering properties of metal fibre composites. 10-th ICNAAM (International Conference of Numerical Analysis and Applied Mathematics) in Kos (Greece), AIP Conference Proceedings, 1479 (2012), pp. 2208–2211.

[37] J. Vala and T. Grohová, A magnetic approach to the identification of effective characteristics of metal fibre composites used in civil engineering. Recent advances in integrity, reliability and failure – 4-th International Conference in Funchal (Madeira), 2013, pp. 731-750.

[38] G. Weidemann, R. Stadie, J. Goebbels and B. Hillemeier, Computer tomography study of fibre reinforced autoclaved aerated concrete. Materials Testing, 50 (2008), pp. 278–285.

[39] H.-J. Wichmann, H. Budelmann and A. Holst, Determination of steel fiber dosage and steel fiber orientation in concrete. In: Nondestructive Testing of Materials and Structures, Springer 2013, pp. 239–245.

[40] K. W. Whites and F. Wu, Effects of particle shape on the effective permittivity of composite materials with measurements for lattices of cubes. IEEE Transansactions on Microwave Theory and Techniques, 50 (2002), pp. 1723–1729.