Smeared Crack Model Research Articles

Blind competition on the numerical simulation of slabs reinforced with conventional flexural reinforcement and fibers subjected to punching loading configuration

AbstractThis paper describes the 3rd Blind Simulation Competition (BSC) organized by the fib WP 2.4.1 which aims to assess the predictive performance of models based on the finite element method (FEM) for analysis and design of fiber reinforced concrete (FRC) structures submitted to loading and support conditions that promote punching failure mode. Fiber reinforcement is used in an attempt to eliminate conventional punching reinforcement and provide technical and economic advantages. The two tested real‐size prototypes represent a column‐slab interior region of an elevated steel‐fiber reinforced concrete (E‐SFRC) slab where anti‐progressive collapse reinforcement is disposed in the alignment of columns/piles. Despite a punching failure surface being formed in both experimentally tested prototypes at the rupture stage, fiber reinforcement was able to mobilize the yield capacity of the conventional flexural reinforcement, providing high deformation capacity, and ductility to the prototypes. The average post‐peak load‐carrying capacity of the tested prototypes at a deflection seven times higher than the deflection at yield initiation of the conventional reinforcement was still 90% of the average peak load. Regarding the BSC, a total of 26 proposals were received and involved 94 participants from 29 institutions and 17 countries, with 53.9% using smeared crack models (SCMs), 30.8% a concrete damage plasticity (CDP) model, 3.8% discrete crack models (DCMs) and 11.5% considered as “other models.” From these simulations it was verified, in average terms, that SCM assured the best predictive performance apart from the average strain in the SFRC and the maximum crack width which were better predicted by DCM. More accurate predictions were obtained by using in‐house software than by adopting commercial software.

Mesoscale Model for Composite Laminates: Verification and Validation on Scaled Un-Notched Laminates.

This paper presents a mesoscale damage model for composite materials and its validation at the coupon level by predicting scaling effects in un-notched carbon-fiber reinforced polymer (CFRP) laminates. The proposed material model presents a revised longitudinal damage law that accounts for the effect of complex 3D stress states in the prediction of onset and broadening of longitudinal compressive failure mechanisms. To predict transverse failure mechanisms of unidirectional CFRPs, this model was then combined with a 3D frictional smeared crack model. The complete mesoscale damage model was implemented in ABAQUS®/Explicit. Intralaminar damage onset and propagation were predicted using solid elements, and in-situ properties were included using different material cards according to the position and effective thickness of the plies. Delamination was captured using cohesive elements. To validate the implemented damage model, the analysis of size effects in quasi-isotropic un-notched coupons under tensile and compressive loading was compared with the test data available in the literature. Two types of scaling were addressed: sublaminate-level scaling, obtained by the repetition of the sublaminate stacking sequence, and ply-level scaling, realized by changing the effective thickness of each ply block. Validation was successfully completed as the obtained results were in agreement with the experimental findings, having an acceptable deviation from the mean experimental values.

Ultimate strength of light-rail hybrid cable-stayed bridge including concrete tension softening effect

This paper presents an analysis of the ultimate strength of a light-rail hybrid cable-stayed bridge (CSB) and discusses the influences of the concrete tension softening effect (CTSE), which is defined as the tensile strength of concrete being much less than its compressive strength. Both geometrical and material non-linearities are considered. A finite-element model of the bridge was established using Ansys software, with material non-linearity considered through the fibre beam element Beam189. An algorithm was written using Fortran language for the uniaxial concrete constitutive model to consider the CTSE (i.e. the concrete smeared crack model). The results showed that the CTSE significantly influenced the ultimate strength of the investigated bridge when the side-span concrete girder dominates the failure of the bridge as estimated by calculations. It is essential to consider the CTSE for the evaluation of the ultimate strength of a light-rail hybrid CSB.

Effective Prediction of Concrete Constitutive Models for Reinforced Concrete Shear Walls under Cyclic Loading.

One of the most challenging elements of modeling the behaviour of reinforced concrete (RC) walls is combining realistic material models that can capture the observable behaviour of the physical system. Experiments with realistic loading rates and pressures reveal that steel and concrete display complicated nonlinear behaviour that is challenging to represent in a single constitutive model. To investigate the response of a reinforced concrete structure subjected to dynamic loads, this paper's study is based on many different material models to assess the advantages and disadvantages of the models on 2D and 3D RC walls using the LS-DYNA program. The models consisted of the KCC model and the CDP model, which represented plasticity and distinct tensile/compressive damage models, and the Winfrith model, which represented plasticity and the smeared crack model. Subsequently, the models' performances were assessed by comparing them to experimental data from reinforced concrete structures, in order to validate the accuracy of the overall behaviour prediction. The Winfrith model demonstrated satisfactory results in predicting the behaviour of 2D and 3D walls, including maximum strength, stiffness deterioration, and energy dissipation. The method accurately predicted the maximum strength of the Winfrith concrete model for the 2D wall with an error of 9.24% and for the 3D wall with errors of 3.28% in the X direction and 5.02% in the Y direction. The Winfrith model demonstrated higher precision in predicting dissipation energy for the 3D wall in both the X and Y directions, with errors of 6.84% and 6.62%, correspondingly. Additional parametric analyses were carried out to investigate structural behaviour, taking into account variables such as concrete strength, strain rate, mesh size, and the influence of the element type.

An SPIM-FEM adapting coupling approach for the analysis of quasi-brittle media

This paper presents an adaptive coupling approach between meshless Smoothed Point Interpolation Methods (SPIMs) and the Finite Element Method (FEM) for the physically nonlinear analysis of quasi-brittle media. The nonlinear behaviour is represented by scalar damage and smeared-crack models. In the proposed adaptive coupling approach, the domain is initially discretised with a relatively coarse FEM mesh. During the solution process, FEM patches are replaced by meshless discretisations according to certain selection criteria. Refinement is also considered.

Numerical simulation of concrete structures—From research to engineering application

AbstractThe paper describes the authors' contribution to the evolution of numerical simulation of concrete structures based on the nonlinear finite element method. The formulation of constitutive relations for concrete material is a keystone of this approach, whereas cracking is the dominant feature. Two distinct methods of crack modeling were developed, namely, the discrete and the smeared crack models. Blind prediction benchmarks of the experimental tests are used for model verification. Application of the numerical simulation in the design of concrete structures is supported by the global safety format, where the uncertainty sources, due to the material and the resistance model, are considered. A structural assessment of a prestressed reinforced concrete viaduct is shown as an example of application.

Implementation of a smeared crack model in the finite element method and its application to two-dimensional nonlinear analysis of concrete beams

This paper describes the implementation of a two-dimensional rotating smeared crack model within the framework of a nonlinear finite element analysis code, and its application to the mechanical behavior of the plain concrete. In this work, the formulation of three concrete softening law subjected to fracture Mode-I is adapted, considering infinitesimal strains, static loads and two-dimensional conditions. The rotating smeared crack model and the three softening laws are all implemented in Fortran language, into the open source software for nonlinear finite element analysis HYPLAS. The pre- and post-process for a graphical representation of the mesh and the results are done with GMSH or GiD. Finally, three experimental tests of concrete beams of other authors are simulated. The concentration of the displacement contour lines obtained in the simulation represents the crack patterns in the solid. The relationship between the applied load and the representative displacement in each analysis step describes the mechanical response of the beam. Other computed parameters were the crack opening and the principal stresses in the solid. The numerical results were satisfactory in comparison with the experimental tests.

UNI-axial dynamic tests on a stone masonry subassembly before and after interventions

The present study deals with the seismic response of three-leaf stone masonry subassemblies before and after the application of intervention techniques. In detail, shaking table tests are performed on a scaled substructure in the Laboratory for Earthquake Engineering, at the National Technical University of Athens (NTUA). The substructure consists of two parallel walls. One wall is of rectangular section, whereas the other is provided with a portion of transverse wall at its mid-length. A flexible timber floor rests on the top of the walls. Sine-sweep and dynamic tests are performed perpendicular to the two walls, before and after interventions. The aim of this work is to experimentally study the response of three leaf masonry walls against in-plane and out-of-plane seismic actions, to investigate the effect of the transverse wall to the out-of-plane behavior of walls (and vice versa) and to assess the effect of a selected set of interventions on the behavior of the substructure. The results of this study confirm the vulnerability of three leaf masonry structures, evidenced by the premature detachment of masonry leaves. They prove the significant role of the transverse wall, in reducing the width of the separation cracks observed in the walls subjected to out-of-plane actions followed by an increase of its in-plane damage, as well as the positive effect (in terms of load and deformation capacity) of grouting the walls and enhancing the diaphragm action of the floor. Additionally, the experimental results of this study can serve as a validation tool for the calibration of numerical models and as input for further analytical research. In this paper, the calibration of a smeared crack model that is based on macro-modeling approach is presented, along with a comparison between experimental and numerical results for the specimen before interventions, based on the performed calibration.

Flexural-shear strengthening of reinforced concrete T-beams subjected to asymmetric loading using CFRP system combined by NSM strips and U-wraps

This paper presents a developed three-dimensional (3D) finite element model (FEM) of flexural and shearstrengthening of reinforced concrete (RC) T-beams using a CFRP (Carbon Fiber-Reinforced Polymer) system combined by near-surface mounted (NSM) strips and U-wraps subjected by asymmetric loading. The 3D FEM was verified by experimental results. Concrete was simulated by a total-strain-based rotating smeared crack model. NSM CFRP strips and CFRP U-wrap sheets were modeled as shell elements. Steel reinforcement and NSM CFRP strips were embedded in concrete, corresponding to a perfect bond. U-wrap sheets were modeled as a shell element and bonded to the concrete surface using an interface element, considering appropriate bond properties. Four RC T-beams from an experimental work were analyzed, and predictions of the applied load-displacement curve and failure mode were presented to demonstrate the accuracy of the developed finiteelement analysis. It is shown that the finite element results of T-beams agree well with the experimental behavior in terms of applied load versus displacement and failure mode. Moreover, a parametric study was conducted to examine the influence of some design-oriented parameters such as concrete compressive strength, amount of longitudinal tension reinforcement, amount of stirrups, multiple layers of externally bonded (EXB) CFRP sheets, and flange width.

Modeling 3D transverse elasto-plastic damage of unidirectional fiber-reinforced polymer composites using a smeared crack approach

This work presents a novel formulation of a 3D smeared crack model for unidirectional fiber-reinforced polymer composites based on a stress invariant approach for transverse yielding and failure initiation, and on a continuum damage approach. This formulation is developed to facilitate the implementation in an implicit solver, increasing solution robustness and computational efficiency in quasi-static and long duration analyses. The performance of the model is evaluated using monotonic and non-monotonic damage evolution, verified with single element tests to demonstrate the consistency of the proposed formulation. Additional benchmark examples regarding off-axis tension and compression tests are simulated and compared with the experimental results, showing good agreement for the plastic response, failure load and failure strain.

Characterization of the tension softening behavior of UHPC

Fracture simulation of concrete structures, which entails generating rational and accurate crack growth through the material, requires the tension softening curve as a constitutive property. Unlike regular concrete, the tension softening behavior of ultra-high performance concrete (UHPC) is highly pronounced and extends to large deformation levels. However, data about this property and, especially, how it is affected by key variables (i.e., fiber dosage and type of fiber used) is lacking. In this paper, a set of direct tension tests (DTT) are conducted to formulate an empirical relationship for UHPC in the tension softening range. The experimental variables are fiber type (two kinds of straight fiber and hooked), fiber length (lf = 13, 19 or 30 mm), and fiber volume fraction (Vf = 1.0 %, 1.5 %, and 2.0 %). The energy absorption capacity of UHPC is found to be different for different type of fibers, due to a difference in strain hardening as well as the pronounced softening phase. A dimensionless tension-softening curve for UHPC that is a function of fiber type, length and volume fraction is proposed as a generalized softening expression (expressed using two parameter a and b) and then implemented into a hybrid rotating/fixed crack smeared crack model. Four-point bending test (4PBT) specimens that correspond to the DTT specimens are made and tested to provide validation data. These validations confirm the model's adeptness at accurately emulating all facets of the 4PBT specimen's response. Following the validation, a response surface for parameters 'a' and 'b' is developed, enabling the generation of the softening curve across the entire spectrum of lf, Vf, and fiber type, without having to monitor the entire range of the softening response.

Modelling intralaminar damage mechanisms in fibre reinforced polymers at finite strains

An approach to predict intralaminar failure mechanisms in laminate fibre-reinforced composites, at finite strains, is proposed. Transverse matrix cracking is described by a smeared crack model, activated by an invariant-based failure criterion, where an embedded cohesive crack is considered in the continuum description. A deformation gradient decomposition based on homogenisation considerations is developed for a more objective finite strain kinematic description of transverse cracks. The local equilibrium problem is established in the reference configuration to naturally include re-orientation of the fracture plane, and the employed cohesive law is able to deal with non-monotonic loading. Moreover, a continuum damage model formulated in terms of the Green–Lagrange strain tensor is used for longitudinal failure. The simulation of an open-hole multi-directional specimen subjected to tension illustrates the ability of the proposed constitutive equations to capture experimental observations.

Two-dimensional integrated mixed-mode smeared crack model for simulating FRC structures

This paper describes the implementation and assessment of the predictive performance of a two dimensional mixed-mode fracture smeared crack model (MMFSCM) in a finite element method (FEM) based software. The referred constitutive model is based on the integration of the aggregate interlock and fibre pullout resisting mechanisms to simulate the behaviour of Fibre Reinforced Concrete (FRC) in both fracture mode I and II. The models used to simulate the contribution of each resisting mechanism predict the normal and shear stresses at the crack level based on the crack opening and sliding displacements. For this purpose, two aggregate interlock models and three fibre pullout models are used. The appraisal of this approach is conducted by simulating two numerical case studies consisting of a three-point notched beam bending test (3PNBBT) for assessing the structural behaviour in mode I, and shear panel tests to appraise the predictive performance of the model in mode II. In addition, modifications to the original formulation of the fibre pullout models are proposed, and a multi-linear branch model is also developed and implemented in order to facilitate the use of inverse analysis tools for defining the mode I behaviour. The numerical simulations have predicted with good accuracy the experimental responses, both in mode I and mode II, capturing not only the peak loads but also the evolution trend of the post-peak responses of the analysed scenarios. The modifications proposed to the fibre pullout models enhanced the overall predictive performance of the MMFSCM. The multi-linear branch model exhibited excellent performance, capturing the experimental response with very good accuracy in all 3PNBBT simulations.

A smeared crack formulation for simulating fracture of fibre-reinforced concrete by means of a trilinear softening diagram

This study presents a smeared crack model for reproducing the fracture behaviour of FRC that is based on an embedded crack formulation used lately with this material. In both cases, a trilinear softening diagram allows reproducing the post-peak behaviour correctly. The model proposed here differs from the one on which it is inspired, since it is a smeared crack model based on the crack band concept where the material damage is isotropic and controlled by a damage factor ranging from 0 to 1, while the original model is an embedded crack model that allows fracture in three directions per element. This new formulation overcomes some limitations of the embedded crack model, that could only be used with triangular elements with an only integration point, since it can be used with triangular and quadrilateral elements with any number of integration points. Unlike previous models, developed for commercial codes, this model is developed in OOFEM, a free finite element code developed at the Czech Technical University in Prague (Czech Republic) and Chalmers University of Technology (Sweden), thus providing the general public with an advanced tool that allows reproducing fracture in structural elements made with fibre-reinforced concrete elements. This work shows that the proposed formulation provides similar results to those obtained with the model on which it is inspired under different situations: mode I fracture, size effect analysis and, finally, modes I and II mixed fracture.

Bending behavior of strain hardening cementitious composites based on the combined fiber-interface constitutive model

Strain-hardening cementitious composites (SHCC) are a class of fiber-reinforced cementitious composites characterized by strain hardening behavior accompanied by multiple cracking, which is designed by tailoring matrix, fiber, and fiber/matrix interface based on the micromechanics theory. At present, there are several numerical simulation methods to study the multiple cracking behavior, such as discrete crack model, unity finite element method, 3D smeared crack model, multiscale constitutive models, and lattice model. However, it is difficult to provide a good balance between accuracy and computational efficiency due to the vast number of fiber and the complex relationship between fibers, matrix, and interface. This paper developed a combined fiber-interface constitutive model based on the single fiber pull-out theory, and established a combined unit. A three-dimensional two-phase finite element model was established, which had been proved to be effective on simulating the cracking behavior of SHCC. Furthermore, the effects of fiber volume fraction and matrix cracking strength on the four-point bending properties of SHCC were investigated. Further study showed that there was a critical matrix cracking strength for a specified fiber and matrix. This value can optimize the design of SHCC to achieve high strength and high toughness performance.

Explicitly quantifying the effect of bond stress on the failure of reinforced concrete membranes

AbstractThe bond stress disturbs the compressive stress in the concrete of reinforced concrete (RC) membrane elements. However, the contribution of bond stress to the compression in the cracked concrete struts was usually neglected. In this study, the contribution of bond stress to the maximum compression in the cracked RC was quantified by explicitly considering the bond stress in the truss model. It is found that the bond stress has a significant contribution to the maximum compressive stress in the cracked RC. For pure shear, the contribution of bond stress to the compressive stress in the concrete is at least two times of the average (apparent) compression. In addition, the proposed model can determine the failure of RC membrane elements through simple uniaxial constitutive relations of materials, instead of the modified ones in the smeared crack models. The failure of RC membrane elements can be predicted in a simple manner with good accuracy.

Standardized RC beam tests for modeling the fiber bridging effect in SFRC

Fiber reinforcement is a promising solution to cracking problems and improving the concrete’s structural performance. The residual strength of the cracked concrete can characterize the reinforcement efficiency. However, quantifying the residual performance of steel fiber-reinforced concrete (SFRC) is challenging. The existing methodologies provide empirical formulas for estimating the residual strength using test results of SFRC elements in which a predominant crack governs the mechanical resistance. For instance, the 0.5 mm crack width determines the minimum value considered in the RILEM standard formulas. Thus, the SFRC strength evolution at earlier cracking stages remains unknown. At the same time, such a crack approximation is irrelevant to structural cases when reinforcement bars stimulate the formation of multiple cracks, and the 0.1–0.2 mm crack typically corresponds to the yielding of the steel bars. This study describes an alternative approach for quantifying the average residual stresses in SFRC elements with multiple cracks. It hypothesizes the possibility of separating the mechanical resistance components, corresponding to tension stiffening and fiber bridging effects characteristic of SFRC elements with bar reinforcement, using standardized small-scale specimens to estimate the fiber contribution. The laboratory tests of the plain concrete and SFRC beams with bar reinforcement illustrate the proposed technique. The Rilem standard three-point bending tests and the numerical simulation of full-scale beams verify the analysis’s adequacy. The developed model is suitable for finite element simulations (employing the smeared crack model); the capability of separating the tension stiffening and fiber bridging effects ensures its versatility.

Vector-based damage-driven computational homogenization with localized gradient enhanced boundary conditions for multi-scale modelling of quasi-brittle materials

Although a lot of progress has been made in computational homogenization, it is still a difficult challenge to emerge and evolve localization bands robustly and to tackle the size dependency issue for brittle and quasi-brittle materials. In this paper, a vector-based damage-driven computational homogenization with localized gradient enhanced boundary conditions is proposed. In the homogenization, the crack band theory is used to up-scale the damage at the micro level to the macro level based on the unit cell size and element size. The vector-based homogenization introduces damage in the principal direction based on the smeared crack model. The updated localized displacement gradients are introduced in the boundary conditions of unit cells to localize crack propagation between adjacent unit cells. The localized displacement gradients are updated iteratively to consider crack open and closure as well as the influences of surrounding elements. Incremental sequentially linear analysis is used to guarantee computational robustness. Size objectivity and localization have been demonstrated for different unit cell sizes and element sizes compared with the direct simulation method (DSM). In addition, an array of voids is considered in the notched beam test for further validation.

Modelagem computacional de vigas de concreto simples e reforçados com fibras de aço sem armadura transversal

Abstract Finite element analysis with nonlinear material behavior modeling can be used to design concrete structures. This study aimed to develop a computational model to represent the shear behavior of concrete beams without transverse reinforcement described in the literature, with or without steel fibers. Two different approaches of finite element analysis were investigated, namely smeared and discrete crack models. The results of the smeared crack model were compared with the results of double-notched push-through tests, and an empirical equation for the shear retention factor of plain concrete was suggested. The computational model using a discrete crack approach with representation of the aggregate interlocking mechanism was compared with the results of push-of test, and an accurate correlation was observed up to the maximum shear stress. It was concluded that the discrete crack approach provided the most accurate representation of the shear behavior of a non-reinforced beam with a shear span-to-depth ratio of 2.17. However, for a non-reinforced beam with a shear span-to-depth ratio of 2.66, the smeared crack approach accurately represents the shear strength and stiffness of the beam. The shear retention factor had little influence on the overall behavior of a steel fiber-reinforced concrete beam. Finally, it was concluded that a variable shear retention factor should be used in the smeared crack approach with fixed crack, as a constant shear retention factor tends to overestimate the shear strength of beams.

On Flexure-Shear Interaction in Fibre Model for the Analysis of RC Section

This paper investigates the effects of flexure-shear interaction on the force-deformation response of RC section. The analysis is performed using an improved version of fibre section model to consider the interaction of shear force. The model uses a supplementary shear strain field, in addition to the ‘plane-section’ hypothesis, for section kinematics. The concrete is modelled using a bi-axial stress-strain model based on a rotating, smeared-crack model with equivalent uniaxial stress-strain relation in principal directions. The confining effect of stirrups is considered by using Mander model. The reinforcing bars are modelled using a uniaxial stress-strain relation. The use of bi-axial model allow the flexure-shear interaction to reflect at the material point. The fibre section model is used to analyse an RC section to study the moment-curvature and shear force-shear strain response for increasing levels of shear forces and bending moments. The results shows that the moment-curvature and shear force-shear strain diagrams are significantly influenced by the presence of large shear force and bending moment respectively.