Two‐scale finite element modelling of reinforced concrete structures: Effective response and subscale fracture development

Sciegaj, Adam; Larsson, Fredrik; Lundgren, Karin; Nilenius, Filip; Runesson, Kenneth

doi:10.1002/nme.5776

Cited by 13 publications

(29 citation statements)

References 25 publications

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“…al. [32]. A symbolic representation of a twodimensional reinforced concrete structure is given in Fig.…”

Section: Fully-resolved Problemmentioning

confidence: 99%

“…Note that, although the above formulation maintains generality, the boundary conditions on the local fields need to be specified in order to produce a solvable system. Even though a couple of choices are possible, the focus of this paper is put on Dirichlet boundary conditions, as they have numerous advantages, such as reliability and ease of implementation [32]. For brevity, we define the macroscopic strain,ε, and macroscopic slip gradient,ḡ, as the gradients of the macroscopic displacementū and slips, respectively:…”

Section: General Formulationmentioning

confidence: 99%

“…The effective response of an RVE of reinforced concrete subjected to macroscopic strain was studied by the authors in [32]. The new formulation in the current work requires that, in addition to the macroscopic strain, also the macroscopic slip and slip gradient are imposed upon the RVE.…”

Section: Subscale Responsementioning

confidence: 99%

“…As a result, the failure mode and general behaviour of the reinforced concrete structure were well captured. In a recent work by the authors [32], a two-scale model of reinforced concrete was developed and used within FE 2 setting. Large RVEs were required to give acceptable results in terms of the crack widths, which was attributed to the model assumption of the reinforcement slip varying only locally, i.e., at the subscale.…”

Section: Introductionmentioning

confidence: 99%

“…This approach is applied in this paper, where the existing two-scale model of reinforced concrete [32] is extended to allow for reinforcement slip transfer between the macroscale elements. The multiscale formulation is devised using the variationally consistent homogenisation, proposed by Larsson et al [21].…”

Section: Introductionmentioning

confidence: 99%

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A multiscale model for reinforced concrete with macroscopic variation of reinforcement slip

et al. 2018

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A single-scale model for reinforced concrete, comprising the plain concrete continuum, reinforcement bars and the bond between them, is used as a basis for deriving a two-scale model. The large-scale problem, representing the "effective" reinforced concrete solid, is enriched by an effective reinforcement slip variable. The subscale problem on a Representative Volume Element (RVE) is defined by Dirichlet boundary conditions. The response of the RVEs of different sizes was investigated by means of pull-out tests. The resulting two-scale formulation was used in an FE 2 analysis of a deep beam. Load-deflection relations, crack widths, and strain fields were compared to those obtained from a single-scale analysis. Incorporating the independent macroscopic reinforcement slip variable resulted in a more pronounced localisation of the effective strain field. This produced a more accurate estimation of the crack widths than the two-scale formulation neglecting the effective reinforcement slip variable.

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“…al. [32]. A symbolic representation of a twodimensional reinforced concrete structure is given in Fig.…”

Section: Fully-resolved Problemmentioning

confidence: 99%

Section: General Formulationmentioning

confidence: 99%

Section: Subscale Responsementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A multiscale model for reinforced concrete with macroscopic variation of reinforcement slip

et al. 2018

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Multi‐scale composite finite element modeling of three‐dimensional prestressed reinforced concrete structural members: Part I—A comprehensive framework

Díaz¹

2022

Civil Engineering Design

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The goal of this work is to develop a complete theoretical framework for the numerical modeling of three‐dimensional prestressed reinforced concrete structural members, soil mixture, and their interactions. This numerical formulation is based on the construction of a new composite finite element, in order to tackle the multi‐scale problem. For this purpose, the mechanical behavior of each microstructure component material will be modeled as follows: (a) for the plain concrete (PC) and the soil mixture, an anisotropic‐damage‐elastoplastic model equipped with the strong discontinuity approach will be taken into account; (b) a polycrystal plasticity model, for the steel rebars and prestrssed tendons will be captured through a new strategy solution of discontinuous bifurcation problem, with the main objective to represent the multi‐cracking phenomenon; (c) regarding the mechanical behavior of the aggregates and rocks (skeleton—hydro mechanic problem) in the PC and soil mixture, respectively, an anisotropic‐damage‐double‐poro‐polycrystal plasticity model equipped with softening material will be considered. An advanced failure algorithm based on the marching tetrahedron and the pseudo‐termic problem will be developed. Finally, the zone that characterizes the interaction between the structural member and the soil mixture will be encrusted inside the composite finite element.

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On a volume averaged measure of macroscopic reinforcement slip in two‐scale modeling of reinforced concrete

Sciegaj

Larsson

Lundgren

et al. 2019

Numerical Meth Engineering

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SUMMARY A two‐scale model for reinforced concrete, in which the large‐scale problem formulation is enriched by an effective reinforcement slip variable, is derived from the single‐scale model describing the response of plain concrete, reinforcement steel, and the bond between them. The subscale problem on the representative volume element (RVE) is correspondingly defined as finding the response of the RVE subjected to effective variables (strain, slip, and slip gradient) imposed from the large scale. A novel volumetric definition of effective reinforcement slip and its gradient is devised, and the corresponding subscale problem is formulated. The newly defined effective variables are imposed on the RVE in a weak sense using Lagrange multipliers. The response of the RVEs of different sizes was investigated by means of pull‐through tests, and the novel boundary condition type was used in FE2 analyses of a deep beam. Locally, prescribing the macroscopic reinforcement slip and its gradient in the proposed manner resulted in reduced RVE‐size dependency of effective work conjugates, which allows for more objective description of reinforcement slip in two‐scale modeling of reinforced concrete. Globally, this formulation produced more consistent amplitudes of effective slip fluctuations and more consistent maximum crack width predictions.

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Two‐scale finite element modelling of reinforced concrete structures: Effective response and subscale fracture development

Cited by 13 publications

References 25 publications

A multiscale model for reinforced concrete with macroscopic variation of reinforcement slip

A multiscale model for reinforced concrete with macroscopic variation of reinforcement slip

Multi‐scale composite finite element modeling of three‐dimensional prestressed reinforced concrete structural members: Part I—A comprehensive framework

On a volume averaged measure of macroscopic reinforcement slip in two‐scale modeling of reinforced concrete

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