Smeared Crack Model Research Articles

Determination of the Mortar Strength Using Double Punch Testing

The paper presents results of the Authors’ own studies on mortar strength using the DPT method. The results of experimental tests and numerical analyses are compared. Numerical analyses were performed for the 3D model, which consist of mortar, capping gypsum and steel punch. In the numerical simulation mortar was modelled using the Drucker-Prager plasticity model with strain hardening in the compression regime. For tension, a multidirectional smeared crack model was applied. The interface elements were used between mortar and gypsum and between the gypsum and steel punch in order to model the behavior of these joints. A good agreement between the results of numerical calculations and experimental research was obtained. On the basis of calibrated numerical model the effect of lining gypsum and the influence of sample thickness was analyzed.

A formulation to reduce mesh dependency in FE analyses of RC structures under imposed deformations

It is well known that in analyses of plain concrete members using smeared crack models, the constitutive behaviour of cracked concrete has to be defined as a function of the crack bandwidth so that the results are not significantly affected by the adopted mesh discretization. Crack localization can also occur in reinforced concrete (RC) elements subjected to imposed (or restrained) deformations. In that case, a different approach has to be followed to reduce the influence of the adopted mesh discretization because the mechanical response in the vicinity of each crack is governed by tension stiffening effects. This paper presents an original formulation to define a tension stiffening diagram that reduces the dependency of the results with respect to the adopted mesh refinement in structures in which crack propagation is governed by mode I (crack opening). This formulation can be applied in FE analyses based on a large-scale, smeared crack approach. Simple closed-form equations are obtained to define this type of diagram. It is demonstrated that objective results are obtained in terms of both the stiffness decrease due to cracking and the crack opening values. Concrete creep and shrinkage effects are taken into account.

A non-intrusive reduced-order model for compressible fluid and fractured solid coupling and its application to blasting

This work presents the first application of a non-intrusive reduced order method to model solid interacting with compressible fluid flows to simulate crack initiation and propagation. In the high fidelity model, the coupling process is achieved by introducing a source term into the momentum equation, which represents the effects of forces of the solid on the fluid. A combined single and smeared crack model with the Mohr–Coulomb failure criterion is used to simulate crack initiation and propagation. The non-intrusive reduced order method is then applied to compressible fluid and fractured solid coupled modelling where the computational cost involved in the full high fidelity simulation is high. The non-intrusive reduced order model (NIROM) developed here is constructed through proper orthogonal decomposition (POD) and a radial basis function (RBF) multi-dimensional interpolation method.The performance of the NIROM for solid interacting with compressible fluid flows, in the presence of fracture models, is illustrated by two complex test cases: an immersed wall in a fluid and a blasting test case. The numerical simulation results show that the NIROM is capable of capturing the details of compressible fluids and fractured solids while the CPU time is reduced by several orders of magnitude. In addition, the issue of whether or not to subtract the mean from the snapshots before applying POD is discussed in this paper. It is shown that solutions of the NIROM, without mean subtracted before constructing the POD basis, captured more details than the NIROM with mean subtracted from snapshots.

Numerical simulation of the flexural behaviour of composite glass-GFRP beams using smeared crack models

Abstract This paper presents a numerical study about the flexural behaviour of rectangular glass-GFRP composite beams, comprising annealed glass and GFRP pultruded profiles bonded with two different adhesives: (soft) polyurethane and (stiff) epoxy. The main objectives of this study were two-fold: (i) to fully characterize the non-linear behaviour of glass using the smeared crack approach; and (ii) to assess the applicability of different options to simulate adhesively bonded glass-GFRP joints. An extensive parametric study was developed to evaluate the influence of five parameters on the glass post-cracking non-linear behaviour: (i) glass fracture energy, Gf, (ii) crack band width, h, (iii) glass tensile strength, fg,t, (iv) shape of the tension-softening diagram, and (v) shear retention factor, β. The wide range of the joints' shear stiffness was simulated by either (i) assuming a perfect bond between glass and GFRP (i.e. neglecting the presence of the adhesive), or (ii) explicitly considering the adhesive, by means of using (ii.1) plane stress elements, or (ii.2) interface elements. For the beams analysed in this paper, the following material model for glass provided a good agreement with experimental results: Gf in the range of 3–300 N/m, h equal to the square root of the finite element area, fg,t = 50 MPa, linear softening diagram and β according to a quadratic power law. It was also shown that the hypothesis of perfect bond at the GFRP-glass interfaces allows for an accurate simulation of joints with high levels of interaction (epoxy), while calibrated interface elements are needed for joints with low level of interaction (polyurethane).

Strategies for numerical modeling the behavior of RC beams strengthened in shear using the ETS technique

The strategy to simulate the crack shear stress transfer in a fixed smeared crack model for concrete is crucial to correctly predict the deformational and cracking behavior of RC elements that exhibit shear failure. This work presents a shear softening law able to correctly simulate the shear stiffness degradation and stress transfer during the crack opening. In cracked concrete, the element of the matrix corresponding to the fracture mode II is represented here by a τtcr-γtcr diagram, describing the shear behavior of the ith crack. The predictive performance is evaluated simulating RC beams failing in shear strengthened using the Embedded Through-Section Technique. According to this technique holes are opened through the cross section, with the desired inclination, and steel or FRP bars are introduced into these holes and bonded to the concrete substrate with adhesive materials. The parameters influencing the shear softening law are analyzed through a parametric study, furthermore a simple rule to estimate these parameters is provided and its predictive performance is assessed. The presented approach represents a valid alternative to the shear retention function.

3D Continuum Damage Approach for Simulation of Crack Initiation and Growth in Ceramic Materials

This paper focuses on the numerical simulation of crack initiation and growth in ceramic materials. This work is devoted to nuclear fuel modelling under irradiation and more precisely to fuel pellet fragmentation assessment at macroscopic and microscopic scales. Simulation tools are developed in the framework of a cooperative program between the CEA, EDF and AREVA devoted to a unified fuel performance software environment called PLEIADES. A smeared crack model is proposed to have a continuous description of crack nucleation and growth at macroscopic scale. This unified description is based on crack extension process from the microscopic scale up to the macroscopic scale. In order to deal with unstable crack extension a specific algorithm is proposed to solve the quasi static nonlinear mechanical problem. A 3D application is presented to illustrate performances and robustness of the smeared crack approach to simulate crack extension in nuclear fuel ceramics. In this application with an internal pressure loading a new methodology is proposed in order to avoid convergence problem due to the indetermination of the quasi static formulation of a softening material equilibrium under Neumann boundary condition.

Nonlinear finite element analysis of fibre-reinforced polymer/concrete joints

The objective of this research work is to simulate the interfacial shear response of fibre-reinforced polymer/concrete joints using a micromechanics-based concrete approach. The M4 version of the microplane concrete theory is coded in FORTRAN and implemented as a parallel user-defined subroutine into the commercial finite element software package ADINA. This article first focuses on three-dimensional nonlinear micromechanics-based finite element analyses. Then, validations are carried out using experimental results of 40 fibre-reinforced polymer/concrete joints. The objective is to assess the accuracy of the microplane approach to represent the interfacial shear behaviour of the fibre-reinforced polymer/concrete joints as an alternative to implementing interface elements. At the end of this article, numerical comparisons are presented between the predictions using a phenomenological concrete constitutive law adopted in the software package (with a smeared crack model) and the micromechanics-based analysis (microplane theory) to simulate the concrete behaviour.

Application of plastic-damage multidirectional fixed smeared crack model in analysis of RC structures

This paper describes a plasticity-damage multidirectional fixed smeared cracking (PDSC) model to simulate the failure process of concrete and reinforced concrete (RC) structures subjected to different loading paths. The model proposes a unified approach combining a multidirectional fixed smeared crack model to simulate the crack initiation and propagation with a plastic-damage model to account for the inelastic compressive behaviour of concrete between cracks. The smeared crack model considers the possibility of forming several cracks in the same integration point during the cracking process. The plasticity part accounts for the development of irreversible strains and volumetric strain in compression, whereas the strain softening and stiffness degradation of the material under compression are controlled by an isotropic strain base damage model. The theoretical aspects about coupling the fracture, plasticity, and damage components of the model, as well as the model appraisal at both material and structural levels, have been detailed in a former publication. This study briefly summarizes the model formulations, and is mainly dedicated to further explore the potentialities of the proposed constitutive model for the analysis of concrete and RC structures. The model is employed to simulate experimental tests that are governed by nonlinear phenomenon due to simultaneous occurrence of cracking and inelastic deformation in compression. The numerical simulations have predicted with good accuracy the load carrying capacity, ductility, crack pattern, plastic (compressive) zone, and failure modes of all types of structures analysed. The influence of the model parameters that simulate the nonlinear behaviour of concrete under tension and compression is analysed through a parametric study.

Effect of fiber dosage and prestress level on shear behavior of hybrid GFRP-steel reinforced concrete I-shape beams without stirrups

Abstract Corrosion of steel reinforcements embedded in concrete elements is generally known as one of the most common reasons that shorten the service life of the structures. The present study aims to contribute in overcoming this problem by replacing steel stirrups as shear reinforcement of concrete beams using a steel fiber reinforced self-compacting concrete (SFRSCC). In the present research the potential of SFRSCC for improving the shear resistance of the beams without stirrups is explored. In order to further reduce the risk of corrosion in this type of beams, a hybrid system of flexural reinforcement composed of a steel strand and GFRP rebars is applied and properly arranged in order to assure a relatively thick concrete cover for the steel reinforcement. The GFRP bars are placed with the minimum cover thickness for providing the maximum internal arm and, consequently, mobilizing efficiently their relatively high tensile strength. The effectiveness of applying different dosages of steel fibers and varying the prestress force to improve the shear behavior of the designed beam are evaluated. By considering the obtained experimental results, the predictive performance of a constitutive model (plastic-damage multidirectional fixed smeared crack model) implemented in a FEM-based computer program, as well as the one from three analytical formulations for estimating shear resistance of the developed beams were assessed. The FEM-based simulations have provided a good prediction of the deformational response and cracking behavior of the tested beams. All the analytical formulations demonstrated acceptable accuracy for design purposes, but the one proposed by CEB-FIP Modal Code 2010 predicts more conservative shear resistance.

Modelling complex cracks with finite elements: a kinematically enriched constitutive model

A continuum constitutive framework with embedded cohesive interface model is presented to describe the failure of quasi-brittle materials. Both cohesive behaviour for cracking inside the fracture process zone and elastic bulk behaviour are treated at integration points making implementation straightforward. In this sense, the proposed approach is simpler than existing ones that focus on element enrichments, such as the extended finite element method, while share similarities with smeared crack models, and offers the capability to correctly model quasi-brittle failure in post-peak regime at constitutive level. In this work, the formulation is introduced, numerical algorithms described and static and dynamic fracture simulations with complex crack patterns are conducted to demonstrate the capability and advantage of the proposed approach.

A two-phase material approach to model steel fibre reinforced self-compacting concrete in panels

This work presents an experimental and numerical approach to ascertain the mechanical behaviour of steel fibre reinforced self-compacting concrete in laminar structures. Four-point flexural tests were performed on prismatic specimens extracted from a SFRSCC panel; the specimens’ behaviour was then modelled under the FEM framework. SFRSCC is assumed as a two-phase material, i.e. plain concrete and discrete steel fibres. The nonlinear material behaviour of the plain matrix was simulated using 3D smeared crack model, while the fibre reinforcement mechanisms were modelled using micro-mechanical behaviour laws determined from experimental fibre pull-out tests. The good performance of the developed numerical strategy was demonstrated.

Cohesive/adhesive failure interaction in ductile adhesive joints Part I: A smeared-crack model for cohesive failure

This paper proposes a new methodology for the finite element (FE) modelling of failure in adhesively bonded joint. Unlike current methods, cohesive and adhesive failures are treated separately. Initial results show the method׳s ability to give accurate prediction of failure of adhesive joints subjected to thickness-induced constraint and complex multi-axial loading using a single set of material parameters. The present paper (part I), focuses on the development of a smeared-crack model for cohesive failure. Model verification and validation are performed comparing the model predictions with experimental data from 3 point bending End Notched Flexure (3ENF) and Double Cantilever Beam (DCB) fracture tests conducted on adhesively bonded composite panels of different adhesive thicknesses.

Cohesive/adhesive failure interaction in ductile adhesive joints Part II: Quasi-static and fatigue analysis of double lap-joint specimens subjected to through-thickness compressive loading

This paper proposes a new methodology for the finite element (FE) modelling of failure in adhesively bonded joints. Cohesive and adhesive failure are treated separately which allows accurate failure predictions for adhesive joints of different thicknesses using a single set of material parameters. In a companion paper (part I), a new smeared-crack model for adhesive joint cohesive failure was proposed and validated. The present contribution gives an in depth investigation into the interaction among plasticity, cohesive failure and adhesive failure, with application to structural joints. Quasi-static FE analyses of double lap-joint specimens with different thicknesses and under different levels of hydrostatic pressure were performed and compared to experimental results. In all the cases studied, the numerical analysis correctly predicts the driving mechanisms and the specimens’ final failure. Accurate fatigue life predictions are made with the addition of a Paris based damage law to the interface elements used to model the adhesive failure.

Triaxial Constitutive Model for Concrete under Cyclic Loading

AbstractThis paper presents a material model for the analysis of concrete under multiaxial, cyclic loading conditions. An elastoplastic formulation, having a nonassociative flow rule to capture compression-dominated behavior, is combined with a rotating smeared-crack model to capture the tension-dominated behavior. The proposed formulation resolves the issues that exist in many available concrete material models related to properly capturing the crack opening and closing behavior and accounting for the effect of confinement on the strength and ductility under compression-dominated stress states. The accuracy of the model is validated through analyses for reinforced concrete components. A parametric study demonstrates the importance of accounting for the increase in ductility due to the confinement effect. Additional analyses elucidate the impact of using different yield surfaces for the elastoplastic model on the simulation results.

FEM-based parametric analysis of a typical gravity dam considering input excitation mechanism

This paper studies computer-aided parametric analysis on the finite element model of a typical concrete gravity dam. The coupled dam–foundation–reservoir system is modeled based on Lagrangian–Eulerian approach. The nonlinearity in the dam is originated from a developed rotating smeared crack model. Different types of input ground motions are used for excitation of the structural system, i.e. near-fault vs. far-field, real vs. artificial, and uniform vs. non-uniform. The spatial varying ground motions and endurance time acceleration functions are generated based on a non-stationary random process. Finally, results are presented in terms of displacement and crack propagation. Relative importance of different parameters is compared and an optimum numerical model is suggested for potential applications.

Modelling the nonlinear behaviour and fracture process of AS4/PEKK thermoplastic composite under shear loading

The accurate determination of non-linear shear behaviour and fracture toughness of continuous carbon-fibre/polymer composites remains a considerable challenge. These measurements are often necessary to generate material parameters for advanced computational damage models. In particular, there is a dearth of detailed shear fracture toughness characterisation for thermoplastic composites which are increasingly generating renewed interest within the aerospace and automotive sectors. In this work, carbon fibre (AS4)/thermoplastic Polyetherketoneketone (PEKK) composite V-notched cross-ply specimens were manufactured to investigate their non-linear response under pure shear loading. Both monotonic and cyclic loading were applied to study the shear modulus degradation and progressive failure. For the first time in the reported literature, we use the essential work of fracture approach to measure the shear fracture toughness of continuous fibre reinforced composite laminates. Excellent geometric similarity in the load-displacement curves was observed for ligament-scaled specimens. The laminate fracture toughness was determined by linear regression, of the specific work of fracture values, to zero ligament thickness, and verified with computational models. The matrix intralaminar fracture toughness (ply level fracture toughness), associated with shear loading was determined by the area method. This paper also details the numerical implementation of a new three-dimensional phenomenological model for carbon fibre thermoplastic composites using the measured values, which is able to accurately represent the full non-linear mechanical response and fracture process. The constitutive model includes a new non-linear shear profile, shear modulus degradation and load reversal. It is combined with a smeared crack model for representing ply-level damage initiation and propagation. The model is shown to accurately predict the constitutive response in terms of permanent plastic strain, degraded modulus as well as load reversal. Predictions are also shown to compare favourably with the evolution of damage leading to final fracture.

A Hybrid Model to Predict Localised Cracks of Reinforced Concrete Slabs in Fire

This paper presents a robust hybrid finite element procedure for predicting the large individual cracks within reinforced concrete floor slabs at elevated temperatures. For modelling the cracks formations and propagations within the floor slabs, the smeared crack model is used for modelling early stages of crack evolution, and then the ‘delayed extended finite element method (D-XFEM) is proposed for capturing individual big cracks within the floor slabs. The new model has been validated against previous fire test results. A series of parametric studies has been conducted on a composite floor to understand the influences of different protection conditions of the support steel beams on both global responses and cracking patterns of the composite floor under fire conditions.

Probabilistic Nonlinear Analysis of Bubble Tower Structure due to Extreme Pressure and Temperature

This paper presents an application of the probabilistic analysis of structural resistance of the bubble tower structure of a VVER 440/213. The evaluation is based on an extension of the smeared crack model developed on base of Kupfer's bidimensional failure criterion, rotated crack, CEB-FIP model of failure energy and implemented into the ANSYS system. The non-linear analysis was considered for the median values of the input data and the probabilistic analysis models the uncertainties of loads, material resistance and other modeling issues.

Numerical simulation on structural behavior of UHPFRC beams with steel and GFRP bars

This study simulates the flexural behavior of ultra-high-performance fiber-reinforced concrete (UHPFRC) beams reinforced with steel and glass fiber-reinforced polymer (GFRP) rebars. For this, micromechanics-based modeling was first carried out on the basis of single fiber pullout models considering inclination angle. Two different tension-softening curves (TSCs) with the assumptions of 2-dimensional (2-D) and 3-dimensional (3-D) random fiber orientations were obtained from the micromechanics-based modeling, and linear elastic compressive and tensile models before the occurrence of cracks were obtained from the mechanical tests and rule of mixture. Finite element analysis incorporating smeared crack model was used due to the multiple cracking behaviors of structural UHPFRC beams, and the characteristic length of two times the element width (or two times the average crack spacing at the peak load) was suggested as a result of parametric study. Analytical results showed that the assumption of 2-D random fiber orientation is appropriate to a non-reinforced UHPFRC beam, whereas the assumption of 3-D random fiber orientation is suitable for UHPFRC beams reinforced with steel and GFRP rebars due to disorder of fiber alignment from the internal reinforcements. The micromechanics-based finite element analysis also well predicted the serviceability deflections of UHPFRC beams with GFRP rebars and hybrid reinforcements.

Crack width analysis of reinforced concrete members under flexure by finite element method and crack queuing algorithm

In reinforced concrete design, it is necessary to evaluate the crack widths so as to ensure compliance with the design codes. However, crack width analysis is not easy and so far only empirical formulas, which do not agree with each other, are available for rough estimation. Particularly, the smeared crack models, which do not allow for bond–slip of reinforcing bars, would not give any crack widths. On the other hand, the discrete crack models are difficult to apply because of the need to adaptively generate discrete crack elements to follow the crack formation. Herein, a new finite element method for discrete crack analysis, which does not require the use of discrete crack elements, is developed. The reinforcing bars are modeled by discrete bar elements and their bond–slip is allowed for using interface elements. Moreover, a crack queuing algorithm is employed to simulate the stress redistribution during cracking and a cracking criterion based on both tensile strength and fracture toughness is adopted to cater for stress concentration at crack tips for correct prediction of crack number, spacing and widths.