Geodesic
Modelling and simulation of deformation and failure of reinforced concrete beams under four-point bending
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 6, pp. 679-689.

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A new mathematical model for the four-point bending of reinforced concrete beams is developed and investigated. The model takes into account multi-modulus concrete behavior, nonlinear stress-strain relationships, and damage evolution. An algorithm for a numerical implementation of the model is proposed. The corresponding boundary value problem is solved by the hp-version of the least-squares collocation method in combination with an acceleration of an iterative process based on Krylov subspaces and parallelizing. Special attention is given to the influence of mathematical model parameters on the results of numerical simulation. The results are compared with experimental data and three-dimensional simulation. A satisfactory agreement is shown.
Keywords: reinforced concrete, nonlinear stress-strain relationships, four-point bending, multi-modulus behavior, damage evolution, crack, modelling and simulation. 
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Vasily A. Belyaev; Artem I. Boltaev; Luka S. Bryndin; Sergey K. Golushko; Arsenii G. Gorynin; Vasily P. Shapeev. Modelling and simulation of deformation and failure of reinforced concrete beams under four-point bending. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 6, pp. 679-689. http://geodesic.mathdoc.fr/item/JSFU_2021_14_6_a1/

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