Size effect in concrete beams under bending – influence of the boundary layer and the numerical description of cracks

In the paper the size effect phenomenon in concrete is analysed. The results of numerical simulations of using FEM on geometrically similar un-notched and notched concrete beams under bending are presented. Concrete beams of four different sizes and five different notch heights under three-point bending test were simulated. In total 18 beams were analysed. Two approaches were used to describe cracks in concrete. First, eXtended Finite Element Method (XFEM) describing cracks as discrete cohesive ones with bilinear softening was chosen. Alternatively, an elasto-plastic constitutive law with Rankine criterion, associated flow rule and bilinear softening was defined. In order to ensure mesh-independent FE results, a non-local theory in an integral format as a regularisation technique was applied in the softening regime. In both approaches the influence of the decrease of the material parameters (mainly fracture energy) in the boundary layer on obtained maximum loads was studied. Additionally the influence of the averaging method in non-local plasticity was also examined. Obtained results were compared with experimental outcomes available in literature.

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On Some Problems in Determining Tensile Parameters of Concrete Model from Size Effect Tests

Polish Maritime Research ◽

10.2478/pomr-2019-0031 ◽

2019 ◽

Vol 26 (2) ◽

pp. 115-125 ◽

Cited By ~ 1

Author(s):

Ireneusz Marzec ◽

Jerzy Bobiński

Keyword(s):

Size Effect ◽

Constitutive Law ◽

Local Theory ◽

Flow Rule ◽

Extended Finite Element ◽

Three Point Bending ◽

Initial Fracture ◽

Experimental Values ◽

Rankine Criterion ◽

Force Displacement

Abstract The paper presents results of numerical simulations of size effect phenomenon in concrete specimens. The behaviour of in-plane geometrically similar notched and unnotched beams under three-point bending is investigated. In total 18 beams are analysed. Concrete beams of four different sizes and five different notch to depth ratios are simulated. Two methods are applied to describe cracks. First, an elasto-plastic constitutive law with a Rankine criterion and an associated flow rule is defined. In order to obtain mesh independent results, an integral non-local theory is used as a regularisation method in the softening regime. Alternatively, cracks are described in a discrete way within Extended Finite Element Method (XFEM). Two softening relationships in the softening regime are studied: a bilinear and an exponential curve. Obtained numerical results are compared with experimental outcomes recently reported in literature. Calculated maximum forces (nominal strengths) are quantitatively verified against experimental values, but the force – displacement curves are also examined. It is shown that both approaches give results consistent with experiments. Moreover, both softening curves with different initial fracture energies can produce similar force-displacement curves.

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A non-local rheology for dense granular flows

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2009.0171 ◽

2009 ◽

Vol 367 (1909) ◽

pp. 5091-5107 ◽

Cited By ~ 113

Author(s):

Olivier Pouliquen ◽

Yoel Forterre

Keyword(s):

Granular Flows ◽

Constitutive Law ◽

Local Theory ◽

Plane Shear ◽

Static Regime ◽

Entire Flow ◽

Non Local ◽

Inclined Planes ◽

Inertial Regime ◽

Dense Granular Flows

A non-local theory is proposed to model dense granular flows. The idea is to describe the rearrangements occurring when a granular material is sheared as a self-activated process. A rearrangement at one position is triggered by the stress fluctuations induced by rearrangements elsewhere in the material. Within this framework, the constitutive law, which gives the relation between the shear rate and the stress distribution, is written as an integral over the entire flow. Taking into account the finite time of local rearrangements, the model is applicable from the quasi-static regime up to the inertial regime. We have checked the prediction of the model in two different configurations, namely granular flows down inclined planes and plane shear under gravity, and we show that many of the experimental observations are predicted within the self-activated model.

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Non-local theory of high-rate straining followed by structure formations

Journal de Physique IV (Proceedings) ◽

10.1051/jp4:2000981 ◽

2000 ◽

Vol 10 (PR9) ◽

pp. Pr9-485-Pr9-490 ◽

Cited By ~ 2

Author(s):

T. A. Khantuleva

Keyword(s):

High Rate ◽

Local Theory ◽

Non Local

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Sensitivity of an Idealized Tropical Cyclone to the Configuration of the Global Forecast System–Eddy Diffusivity Mass Flux Planetary Boundary Layer Scheme

Atmosphere ◽

10.3390/atmos12020284 ◽

2021 ◽

Vol 12 (2) ◽

pp. 284

Author(s):

Evan A. Kalina ◽

Mrinal K. Biswas ◽

Jun A. Zhang ◽

Kathryn M. Newman

Keyword(s):

Boundary Layer ◽

Planetary Boundary Layer ◽

Weather Prediction ◽

Intensity Change ◽

Rapid Intensification ◽

Forecast System ◽

Stability Functions ◽

Non Local ◽

The Stability ◽

Heat And Moisture

The intensity and structure of simulated tropical cyclones (TCs) are known to be sensitive to the planetary boundary layer (PBL) parameterization in numerical weather prediction models. In this paper, we use an idealized version of the Hurricane Weather Research and Forecast system (HWRF) with constant sea-surface temperature (SST) to examine how the configuration of the PBL scheme used in the operational HWRF affects TC intensity change (including rapid intensification) and structure. The configuration changes explored in this study include disabling non-local vertical mixing, changing the coefficients in the stability functions for momentum and heat, and directly modifying the Prandtl number (Pr), which controls the ratio of momentum to heat and moisture exchange in the PBL. Relative to the control simulation, disabling non-local mixing produced a ~15% larger storm that intensified more gradually, while changing the coefficient values used in the stability functions had little effect. Varying Pr within the PBL had the greatest impact, with the largest Pr (~1.6 versus ~0.8) associated with more rapid intensification (~38 versus 29 m s−1 per day) but a 5–10 m s−1 weaker intensity after the initial period of strengthening. This seemingly paradoxical result is likely due to a decrease in the radius of maximum wind (~15 versus 20 km), but smaller enthalpy fluxes, in simulated storms with larger Pr. These results underscore the importance of measuring the vertical eddy diffusivities of momentum, heat, and moisture under high-wind, open-ocean conditions to reduce uncertainty in Pr in the TC PBL.

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Fracture and Size Effect of PFRC Specimens Simulated by Using a Trilinear Softening Diagram: A Predictive Approach

Materials ◽

10.3390/ma14143795 ◽

2021 ◽

Vol 14 (14) ◽

pp. 3795

Author(s):

Fernando Suárez ◽

Jaime C. Gálvez ◽

Marcos G. Alberti ◽

Alejandro Enfedaque

Keyword(s):

Reinforced Concrete ◽

Size Effect ◽

A Priori ◽

Plain Concrete ◽

Specimen Size ◽

Bending Test ◽

Orientation Factor ◽

Fibre Reinforced Concrete ◽

Softening Function ◽

Three Point Bending

The size effect on plain concrete specimens is well known and can be correctly captured when performing numerical simulations by using a well characterised softening function. Nevertheless, in the case of polyolefin-fibre-reinforced concrete (PFRC), this is not directly applicable, since using only diagram cannot capture the material behaviour on elements with different sizes due to dependence of the orientation factor of the fibres with the size of the specimen. In previous works, the use of a trilinear softening diagram proved to be very convenient for reproducing fracture of polyolefin-fibre-reinforced concrete elements, but only if it is previously adapted for each specimen size. In this work, a predictive methodology is used to reproduce fracture of polyolefin-fibre-reinforced concrete specimens of different sizes under three-point bending. Fracture is reproduced by means of a well-known embedded cohesive model, with a trilinear softening function that is defined specifically for each specimen size. The fundamental points of these softening functions are defined a priori by using empirical expressions proposed in past works, based on an extensive experimental background. Therefore, the numerical results are obtained in a predictive manner and then compared with a previous experimental campaign in which PFRC notched specimens of different sizes were tested with a three-point bending test setup, showing that this approach properly captures the size effect, although some values of the fundamental points in the trilinear diagram could be defined more accurately.

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Gradient of Soil Constitutive Model

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.168-170.1126 ◽

2010 ◽

Vol 168-170 ◽

pp. 1126-1129

Author(s):

Wen Xu Ma ◽

Ying Guang Fang

Keyword(s):

Plastic Strain ◽

Strain Gradient ◽

Soil Analysis ◽

Natural Material ◽

Flow Rule ◽

The Finite Element Method ◽

Gradient Effect ◽

Non Local ◽

Associated Flow Rule ◽

Plastic Strain Gradient

For the soil is a very complex natural material, significant strain gradient effect exist in soil analysis. Based on the "gradient" phenomenon, we add the plastic strain gradient hardening item into the traditional Cambridge yield surface. By using the consistency conditions and associated flow rule, we get the explicit expression of plastic strain gradient stiffness matrix. And the finite element method of plastic strain gradient is also shown in this article. Plastic strain gradient is actually a phenomenological non-local model containing microstructure information of the material. It may overcome the difficulties in simulating the gradient phenomenon by traditional mechanical model.

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Size Effect on Failure of Bond Splices of Steel Bars in Concrete Beams

Journal of Structural Engineering ◽

10.1061/(asce)0733-9445(1999)125:6(653) ◽

1999 ◽

Vol 125 (6) ◽

pp. 653-660 ◽

Cited By ~ 19

Author(s):

Sıddık Şener ◽

Zdenk P. Baant ◽

Emilie Becq-Giraudon

Keyword(s):

Size Effect ◽

Concrete Beams ◽

Steel Bars

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Diluted mass gap in strongly coupled non-local Yang-Mills

Journal of High Energy Physics ◽

10.1007/jhep07(2021)226 ◽

2021 ◽

Vol 2021 (7) ◽

Author(s):

Marco Frasca ◽

Anish Ghoshal

Keyword(s):

Field Theory ◽

Particle Physics ◽

Mass Scale ◽

Local Theory ◽

Quantum Field ◽

Strongly Coupled ◽

Yang Mills ◽

Mass Gap ◽

Non Local ◽

Non Locality

Abstract We investigate the non-perturbative regimes in the class of non-Abelian theories that have been proposed as an ultraviolet completion of 4-D Quantum Field Theory (QFT) generalizing the kinetic energy operators to an infinite series of higher-order derivatives inspired by string field theory. We prove that, at the non-perturbative level, the physical spectrum of the theory is actually corrected by the “infinite number of derivatives” present in the action. We derive a set of Dyson-Schwinger equations in differential form, for correlation functions till two-points, the solution for which are known in the local theory. We obtain that just like in the local theory, the non-local counterpart displays a mass gap, depending also on the mass scale of non-locality, and show that it is damped in the deep UV asymptotically. We point out some possible implications of our result in particle physics and cosmology and discuss aspects of non-local QCD-like scenarios.

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