A Novel Approach for FRC Softening Law
DOI:
https://doi.org/10.70567/mc.v42.ocsid8529Keywords:
Fiber Reinforced Concrete, Post peak mechanical behavior, Bézier curves, Softening lawAbstract
Post peak mechanical behavior of Fiber Reinforced Concrete (FRC) under tensile stress states depends not only on the fibers material, shape, content and slenderness but also, on the mechanical and physical properties of the cement paste. Being the improvement of ductility under tension, usually, the main purpose of adding fibers to the concrete composition, an accurate consideration of the resulting post peak behavior results a key parameter for an appropriate numerical simulation of the mechanical behavior of structural FRC elements. In this work, particularly focused on steel FRC, the suitability of cubic Bézier curves is analyzed, firstly, for determining Fracture Energy in mode I of FRC and then, for replacing the traditional exponential decay function usually used for characterizing the softening parameter in concrete constitutive formulations. The results show that the use of these parametric curves allows a flexible numerical approach that can be used for characterizing concretes with very different mechanical behaviors.
References
RILEM-TC-162-TDF, test and design methods for steel fibre reinforced concrete: Sigma -Epsilon design method - final recommendation. Materials and Structures, 36(262):560–567, 2003. Model Code 2010 - Final Draft, volume 1-2. FIB Bulletin, 2012.
Banthia N. and Nandakumar N. Crack growth resistance of hybrid fiber reinforced cement composites. Cement and Concrete Composites, 25(1):3–9, 2003. http://doi.org/10.1016/S0958-
9465(01)00043-9.
Barros J., Cunha V., Ribeiro A., and Antunes J. Post-cracking behaviour of steel fibre reinforced concrete. Materials and Structures, 38(1):47–56, 2005. http://doi.org/10.1007/BF02480574.
Bažant Z.P. and Pijaudier-Cabot G. Measurement of characteristic length of nonlocal continuum. Journal of engineering mechanics, 115(4):755–767, 1989. http://doi.org/10.1061/(ASCE)0733-9399(1989)115:4(755).
Bézier P. The mathematical basis of the UNIURF CAD system. Butterworth-Heinemann, 2014. Mecánica Computacional Vol XLII, págs. 627-636 (2025) 635 Copyright © 2025 Asociación Argentina de Mecánica Computacional
Buratti N., Mazzotti C., and Savoia M. Post-cracking behaviour of steel and macrosynthetic fibre-reinforced concretes. Construction and Building Materials, 25(5):2713–2722, 2011. http://doi.org/10.1016/j.conbuildmat.2010.12.022.
Folino P. and Etse G. Performance dependent model for normal and high strength concretes. International Journal of Solids and Structures, 49(5):701–719, 2012. http://doi.org/10.1016/j.ijsolstr.2011.11.020.
Folino P., Ripani M., Xargay H., and Rocca N. Comprehensive analysis of fiber reinforced concrete beams with conventional reinforcement. Engineering Structures, 202:109862, 2020. http://doi.org/10.1016/j.engstruct.2019.109862.
Folino P. and Smilovich D. Proposal of an interpolation function between the compressive and tensile meridians of failure and yielding concrete surfaces based on Bezier curves. In PANACM 2015 - 1st Pan-American Congress on Computational Mechanics, in conjunction with the 11th Argentine Congress on Computational Mechanics, MECOM 2015, pages 261– 271. 2015.
Guinea G., Planas J., and Elices M. Measurement of the fracture energy using three-point bend tests: Part 1-influence of experimental procedures. Materials and Structures, 25(4):212–218, 1992. http://doi.org/10.1007/BF02473065.
Habib Z. and Sakaib M. G2 cubic transition between two circles with shape control. Journal of Computational and Applied Mathematics, 223:133–144, 2009. http://doi.org/10.1016/j.cam.2007.12.024.
Kato J. and Ramm E. Multiphase layout optimization for fiber reinforced composites applying a damage formulation. In 4th Colloquium on Textile Reinforced Structures (CTRS4), Anwendertagung, Dresden, Germany, pages 337–354. 2009.
Martín L., Garriga C., Cremades L., and González M. Curvas bezier en el diseño de reflectores que satisfacen las necesidades de iluminación. In X Congreso Internacional de Ingeniería de Proyectos, Valencia, España, pages 779–785. 2006.
Menezes L. and Teodosiu C. Three-dimensional numerical simulation of the deep-drawing process using solid finite elements. Journal of Materials Processing Technology, 97:100– 106, 2000. http://doi.org/10.1016/S0924-0136(99)00345-3.
Michelini E., Ferretti D., and Pizzati M. The influence of density on the fracture energy of aac: from experimental investigation to the calibration of a cohesive law. Construction and Building Materials, 400:132547, 2023. http://doi.org/10.1016/j.conbuildmat.2023.132547.
Piegl L. and Tiller W. The NURBS book. Springer-Verlag, Berlin, Germany, 1997. http://doi.org/10.1007/978-3-642-59223-2.
Sederberg T.W. Computer aided geometric design. BYU, Computer Aided Geometric Design Course Notes, 2012. Available from http://hdl.lib.byu.edu/1877/2822.
van Mier J. Fracture Processes of Concrete. CRC Press, Boca Raton, Florida, US, 1997.
Vegter H., Drent P., and Huetink J. A planar isotropic yield criterion based on mechanical testing at multi-axial stress states. In Proceedings of the NUMIFORM 1995 Conference, pages 345–350. 1995.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Argentine Association for Computational Mechanics
This work is licensed under a Creative Commons Attribution 4.0 International License.
This publication is open access diamond, with no cost to authors or readers.
Only those papers that have been accepted for publication and have been presented at the AMCA congress will be published.
