On crack band model in finite element analysis of concrete fracture in engineering practice

Červenka, J; Červenka, Vladimír; Laserna, Santiago

doi:10.1016/j.engfracmech.2018.04.010

Cited by 63 publications

(38 citation statements)

References 12 publications

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“…The most popular method of reducing mesh sensitivity based on the crack band theory proposed by Bazant and Oh [ 71 ] (mesh-adjusted softening modulus) for bigger element sizes results in a very steep descending branch (or even snap-back behaviour) [ 22 ], which is close to fully brittle behaviour. Conversely, in the case of very fine meshes, models based on these assumptions become unrealistically ductile [ 49 ]. Another moot point is the experimental testing of post-cracking behaviour, since it is often difficult to distinguish whether we are measuring material response or the interaction of a sample with test equipment (due to unintended friction) [ 11 , 17 ].…”

Section: Discussionmentioning

confidence: 99%

“…The constitutive matrix is modified in the following manner:

where:

—parameter that controls softening rate. This parameter can be related to the fracture energy in compression:

where:

;

—characteristic element length (the lower bound was introduced, since models consisting of small elements predict very ductile behaviour of structures [ 49 ]),

—fracture energy for compression, b —parameter, which allows for the increased ductility of a reinforced compressive zone to be taken into account (

for an unreinforced compressive zone and

for a reinforced compressive zone), and

—initial Young modulus. Fracture energy in compression can be calculated according to (

substituted in MPa) [ 50 ]:

…”

Section: Proposed Solution Strategymentioning

confidence: 99%

“…Conversely, this phenomenon appears mostly in plain concrete and very fine meshes, which are not desirable for the NLFEA of large-scale RC structures. Based on the conclusions of Reference [ 49 ], the following limit values for element size are recommended: mesh size should be larger than approximately 1.5 the aggregate size (approximately 50 mm), mesh size should be smaller than typical crack spacing (approximately 150 mm). …”

Section: Proposed Solution Strategymentioning

confidence: 99%

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Numerically Efficient Three-Dimensional Model for Non-Linear Finite Element Analysis of Reinforced Concrete Structures

Dudziak

2021

Materials

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The paper concerns the non-linear finite element analysis (NLFEA) of Reinforced Concrete (RC) structures for engineering applications. The required level of complexity of constitutive models for such analysis was discussed and non-linear elastic models combined with the smeared cracking approach proved to be efficient. A new constitutive hypoelastic-brittle model of concrete based on these assumptions was proposed. Moreover, a method including the tension stiffening effect (TS) was developed. This phenomenon is connected with the bond properties between concrete and steel and, in some situations, has significant influence on the deflections of RC structures. It is often neglected by or included in the constitutive model of concrete. In the paper, an alternative approach was presented, in which this phenomenon is taken into account by generalising the material model of reinforcing steel. This approach is consistent with modern design standards and has solid physical foundations. The proposed models were implemented in the Abaqus code via UMAT user’s procedure coded in FORTRAN. Model verification and validation were presented in four case studies, concerning: a Willam’s test (examination on material point level), a beam with bending failure, and two beams with shear failure (with and without stirrups). The obtained results were compared with experimental outcomes and numerical results obtained by other researchers. The presented approach enables the accurate prediction not only of load capacity but of structural deformability, due to the precise description of TS. Thus, it promises to be a useful engineering tool.

show abstract

Section: Discussionmentioning

confidence: 99%

“…The constitutive matrix is modified in the following manner:

where:

—parameter that controls softening rate. This parameter can be related to the fracture energy in compression:

where:

;

—characteristic element length (the lower bound was introduced, since models consisting of small elements predict very ductile behaviour of structures [ 49 ]),

—fracture energy for compression, b —parameter, which allows for the increased ductility of a reinforced compressive zone to be taken into account (

for an unreinforced compressive zone and

for a reinforced compressive zone), and

—initial Young modulus. Fracture energy in compression can be calculated according to (

substituted in MPa) [ 50 ]:

…”

Section: Proposed Solution Strategymentioning

confidence: 99%

Section: Proposed Solution Strategymentioning

confidence: 99%

See 1 more Smart Citation

Numerically Efficient Three-Dimensional Model for Non-Linear Finite Element Analysis of Reinforced Concrete Structures

Dudziak

2021

Materials

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show abstract

“…It should be mentioned that, for this model, mesh sensitive results can occur. Therefore, if the CSC model is applied in the computations of concrete structures, then the crack band theory [30] should be employed to set a proper size of the finite element corresponding to the expected cracking zone, see also [31,32]. Wide discussion concerning smeared cracking models can be found e.g., in [27,29].…”

Section: Concrete Smeared Cracking (Csc)mentioning

confidence: 99%

Selected Concrete Models Studied Using Willam’s Test

2020

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Willam’s test is a quick numerical benchmark in tension–shear regime, which can be used to verify inelastic (quasi-brittle) material models at the point level. Its sequence consists of two separate steps: uniaxial tension accompanied with contraction—until the tensile strength is attained; and next for softening (cracking) of the material—tension in two directions together with shear. A rotation of axes of principal strains and principal stresses is provoked in the second stage. That kind of process occurs during the analysis of real concrete structures, so a correct response of the material model at the point level is needed. Some familiar concrete models are selected to perform Willam’s test in the paper: concrete damaged plasticity and concrete smeared cracking—distributed in the commercial ABAQUS software, scalar damage with coupling to plasticity and isotropic damage—both implemented in the FEAP package. After a brief review of the theory, computations for each model are discussed. Passing or failing Willam’s test by the above models is concluded based on their results, indicating restrictions of their use for finite element computations of concrete structures with predominant mixed-mode fracture.

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“…Steel-reinforced and fiber-reinforced materials have a large share in today’s engineering structures. In numerical modeling of fracture issues, it is then necessary to use a 3D computational model in conjunction with a material model of fracture-plastic (the fracture-plastic material model) [ 7 , 8 , 9 ]. The strength parameters of these materials relevant to numerical modeling include the compressive strength of concrete cubes, the tensile strength of three-point bending test, and the tensile strength of splitting perpendicular and parallel to the direction of fill.…”

Section: Introductionmentioning

confidence: 99%

Influence of the Undercut Anchor Head Angle on the Propagation of the Failure Zone of the Rock Medium

2021

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The paper presents the results of a numerical analysis (FEM) describing the effect of the undercutting head angle on the formation of the rock mass failure zone during the initial stages of failure propagation. The research was carried out in the context of developing a technology for rock extraction by controlled pull-out of undercut anchors installed in the rock mass. The focus was on the initial stage of crack propagation and its trajectory for anchors embedded at an assumed constant depth and a value of the friction coefficient of the rock against the anchor head. It is shown that smaller angles favor smaller stripping angles and an increased radial impact of the head on the rock material (in the plane perpendicular to the head axis), while the impact of heads with larger angles is found to favor larger fracture penetration angles and faster penetration towards the free rock surface.

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On crack band model in finite element analysis of concrete fracture in engineering practice

Cited by 63 publications

References 12 publications

Numerically Efficient Three-Dimensional Model for Non-Linear Finite Element Analysis of Reinforced Concrete Structures

Numerically Efficient Three-Dimensional Model for Non-Linear Finite Element Analysis of Reinforced Concrete Structures

Selected Concrete Models Studied Using Willam’s Test

Influence of the Undercut Anchor Head Angle on the Propagation of the Failure Zone of the Rock Medium

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