Microplane Model M5f for Multiaxial Behavior and Fracture of Fiber-Reinforced Concrete

Despite impressive advances, the existing constitutive and fracture models for fiber-reinforced concrete (FRC) are essentially limited to uniaxial loading. The microplane modeling approach, which has already been successful for concrete, rock, clay, sand, and foam, is shown capable of describing the nonlinear hardening–softening behavior and fracturing of FRC under not only uniaxial but also general multiaxial loading. The present work generalizes model M5 for concrete without fibers, the distinguishing feature of which is a series coupling of kinematically and statically constrained microplane systems. This feature allows simulating the evolution of dense narrow cracks of many orientations into wide cracks of one distinct orientation. The crack opening on a statically constrained microplane is used to determine the resistance of fibers normal to the microplane. An effective iterative algorithm suitable for each loading step of finite element analysis is developed, and a simple sequential procedure for identifying the model parameters from test data is formulated. The model allows a close match of published test data on uniaxial and multiaxial stress–strain curves, and on multiaxial failure envelopes.     

Modified Microplane Model for Reinforced Concrete under Static and Dynamic Loadings

A smeared dynamic constitutive model is proposed for reinforced concrete based on microplane Model M4, in which the modified Menegotto-Pinto model for steel was adopted and the strain rate effect was taken into account by introducing parallel moving of envelope line. The model was established based on the hypothesis that the strains of concrete and steel bars have parallel coupling. Then the contribution of steel to total stress tensor was derived by projecting the section area of steel bars to three orthogonal directions. This model was calibrated by fitting with the test data, and its validity was verified by simulating a bridge-ship collision application using LS-DYNA embedded with a user-defined material subroutine.     

Probabilistic Nonlocal Theory for Quasibrittle Fracture Initiation and Size Effect.?I: Theory

The nonlocal generalization of Weibull theory previously developed for structures that are either notched or fail only after the formation of a large crack is extended to predict the probability of failure of unnotched structures that reach the maximum load before a large crack forms, as is typical of the test of modulus of rupture (flexural strength). The probability of material failure at a material point is assumed to be a power function (characterized by the Weibull modulus and scaling parameter) of the average stress in the neighborhood of that point, the size of which is the material characteristic length. This indirectly imposes a spatial correlation. The model describes the deterministic size effect, which is caused by stress redistribution due to strain softening in the boundary layer of cracking with the associated energy release. As a basic check of soundness, it is proposed that for quasibrittle structures much larger than the fracture process zone or the characteristic length of material, the probabilistic model of failure must asymptotically reduce to Weibull theory with the weakest link model. The present theory satisfies this condition, but the classical stochastic finite-element models do not, which renders the use of these models for calculating loads of very small failure probabilities dubious. Numerical applications and comparisons to test results are left for Part II.     

Theoretical Model for Fiber-Reinforced Polymer-Confined Concrete

Fiber-reinforced polymer (FRP) composites have found increasingly wide applications in civil engineering due to their high strength-to-weight ratio and high corrosion resistance. One important application of FRP composites is as a confining material for concrete, particularly in the strengthening or seismic retrofit of existing reinforced concrete columns by the provision of a FRP jacket. FRP confinement can enhance both the compressive strength and the ultimate strain of concrete significantly. This paper presents a new stress–strain model for FRP-confined concrete in which the responses of the concrete core and the FRP jacket as well as their interaction are explicitly considered. Such a model is often referred to as an analysis-oriented model. The key novel feature of the proposed analysis-oriented model, compared to existing models of the same kind, is a more accurate and more widely applicable lateral strain equation based on a careful interpretation of the lateral deformation characteristics of unconfined, actively confined, and FRP-confined concrete. Through comparisons with independent test data, the proposed model is shown to be accurate not only for FRP-confined concrete but also for concrete confined with a steel tube, demonstrating the wide applicability of the model to concrete confined with different confining materials. The accuracy of the proposed model is also shown to be superior to existing analysis-oriented stress-strain models through comparisons with test data.     

Vertex Effect in Strain-Softening Concrete at Rotating Principal Axes

The inelastic behavior of concrete for highly nonproportional loading paths with rotating principal stress axes is studied. Test cylinders are first loaded in compression under uniaxial stress and then torsion is applied at constant axial displacement. Proportional compressive-torsional loading tests are also carried out for comparison. The tests demonstrate that the response of concrete for load increments parallel in the stress space to the current yield surface is highly inelastic (i.e., much softer than elastic) in the peak load range and especially in the postpeak range. The classical tensorial models of plasticity type incorrectly predict for such load increments the elastic stiffness. The experiments are simulated by three-dimensional finite element analysis using the microplane model M4, in which the stress-strain relations are characterized not by tensors but by vectors of stress and strain on planes of various orientations in the material. It is shown that the observed vertex effect is correctly predicted by this model, with no adjustment of its material parameters previously calibrated by other test results. The experiments are also simulated by a state-of-the-art fracture-plastic model of tensorial type and it is found that the vertex effect cannot be reproduced at all, although an adjustment of one material parameter suffices to obtain a realistic postpeak slope and achieve a realistic overall response. What makes the microplane model capable of capturing the vertex effect is the existence of more than 60 simultaneous yield surfaces. Capturing the vertex effect is important for highly nonproportional loading with rotating principal stress axes, which is typical of impact and penetration of missiles, shock, blasts, and earthquake.     

Fracturing Rate Effect and Creep in Microplane Model for Dynamics

The formulation of microplane model M4 in Parts I and II is extended to rate dependence. Two types of rate effect in the nonlinear triaxial behavior of concrete are distinguished: (1) Rate dependence of fracturing (microcrack growth) associated with the activation energy of bond ruptures, and (2) creep (or viscoelasticity). Short-time linear creep (viscoelasticity) is approximated by a nonaging Maxwell spring-dashpot model calibrated so that its response at constant stress would be tangent to the compliance function of model B3 for a time delay characteristic of the problem at hand. An effective explicit algorithm for step-by-step finite-element analysis is formulated. The main reason that the rate dependence of fracturing must be taken into account is to simulate the sudden reversal of postpeak strain softening into hardening revealed by recent tests. The main reason that short-time creep (viscoelasticity) must be taken into account is to simulate the rate dependence of the initial and unloading stiffness. Good approximations of the rate effects observed in material testing are achieved. The model is suitable for finite-element analysis of impact, blast, earthquake, and short-time loads up to several hours duration.     

Confinement-Shear Lattice Model for Concrete Damage in Tension and Compression: II. Computation and Validation

The concrete material model developed in the preceding Part I of this study is formulated numerically. The new model is then verified by comparisons with experimental data for compressive and tensile uniaxial tests, biaxial tests, and triaxial tests, as well as notched tests of mode I fracture and size effect.     

Closed-Form Solutions for Flexural Response of Fiber-Reinforced Concrete Beams

A constitutive law for fiber-reinforced concrete materials consisting of an elastic perfectly plastic model for compression and an elastic-constant postpeak response for tension is presented. The material parameters are described by using Young’s modulus and first cracking strain in addition to four nondimensional parameters to define postpeak tensile strength, compressive strength, and ultimate strain levels in tension and compression. The closed-form solutions for moment-curvature response are derived and normalized with respect to their values at the cracking moment. Further simplification of the moment-curvature response to a bilinear model, and the use of the moment-area method results in another set of closed-form solutions to calculate midspan deflection of a beam under three- and four-point bending tests. Model simulations are correlated with a variety of test results available in literature. The simulation of a three- and four-point bending test reveals that the direct use of uniaxial tensile response underpredicts the flexural response.     

A process model for friction welding of AlMgSi alloys and AlSiC metal matrix composites—I. Haz temperature and strain rate distribution

The present investigation is concerned with the development of an overall process model for the microstructure and strength evolution during continuous drive friction welding of AlMgSi alloys and AlSiC metal matrix composites. In Part I the different components of the model are outlined and analytical solutions presented which provide quantitative information about the HAZ temperature distribution for a wide range of operational conditions. Moreover, a general procedure for modelling the HAZ strain rate distribution has been developed by introducing a series of kinematically admissible velocity equations which describe the material flow fields in the radial, the rotational, and the axial direction, respectively. Calculations performed for both types of materials show that the effective strain rate may exceed 1000 s⁻¹ in positions close to the contact section due to the high rotational velocities involved. Application of the model for evaluation of the response of AlMgSi alloys and AlSiC metal matrix composites to the imposed heating and plastic deformation is described in an accompanying paper (Part II).     

Bond between Carbon Fiber Reinforced Polymer Bars and Concrete. I: Experimental Study

The bond characteristics of four different types of carbon fiber reinforced polymer (CFRP) rebars (or tendons) with different surface deformations embedded in lightweight concrete were analyzed experimentally. In a first series of tests, local bond stress-slip data, as well as bond stress-radial deformation data, needed for interface modeling of the bond mechanics, were obtained for varying levels of confining pressure. In addition to bond stress and slip, radial stress and radial deformation were considered fundamental variables needed to provide for configuration-independent relationships. Each test specimen consisted of a CFRP rebar embedded in a 76-mm-(3 in.)-diam, 102-mm-(4 in.)-long, precracked lightweight concrete cylinder subjected to a constant level of pressure on the outer surface. Only 76 mm (3 in.) of contact were allowed between the rebar and the concrete. For each rebar type, bond stress-slip and bond stress-radial deformation relationships were obtained for four levels of confining axisymmetric radial pressure. It was found that small surface indentations were sufficient to yield bond strengths comparable to that of steel bars. It was also shown that radial pressure is an important parameter that can increase the bond strength almost threefold for the range studied. In a second series of tests, the rebars were pulled out from 152-mm-(6 in.)-diam, 610-mm-(24 in.)-long lightweight concrete specimens. These tests were conduced to provide preliminary data for development length assessment and model validation (Part II).     

Water Migration Phenomenon Model in Cracked Concrete.?II: Calibration

The material parameters to express the degree of discontinuity of hydraulic gradient in the developed model (Part I) are calibrated based on the sensible analysis of the experimental results, and then the applicability of the calibrated parameters is discussed. As a result, the material parameters are calibrated by the sensible analysis, and then its relevance can be confirmed by another experiment. Moreover, it can be seen that the normalized permeability of concrete as a nonhomogeneous material by the initial permeability (homogeneous material) can be regressed with three straight lines in the crack width axis with the logarithm. Then the intersection point at the crack width axis shows the critical width at which leakage will not occur. The intersection point at the last two straight lines shows the critical Reynolds number at which flow becomes laminar to turbulent according to the experimental result.     

Microplane Model M5 with Kinematic and Static Constraints for Concrete Fracture and Anelasticity. II: Computation

Following the formulation of the constitutive model in the preceding Part I in this issue, the present Part II addresses the problems of computational algorithm and convergence of iterations. Typical numerical responses are demonstrated and the parameters of the model are calibrated by test data from the literature.     

A Material Model for TRIP‐Steels and its Application to a CrMnNi Cast Alloy

A material model is presented that accounts for strain rate dependent inelastic deformation and strain‐induced phase transformation in TRIP‐steels. Modifications for the kinetics equations of the strain‐induced phase transformation, introduced by Stringfellow, are proposed to overcome a drawback of Stringfellow's model. A parameter identification strategy that relies on Gauss‐Markov estimates is used to determine the model parameters from experimental data of a recently developed cast TRIP‐steel. Good agreement is observed between experimental results of the compression test and the corresponding finite element simulation employing the proposed model. This forms the basis for future applications of the material model in the design of composites and structures.     

Statistical Damage Constitutive Model of Quasi-Brittle Materials

Recent studies have shown that statistical damage mechanics is one effective method to study the failure process of quasi-brittle materials. There are two key problems in setting up the statistical damage constitutive model of quasi-brittle materials, namely, determining the microunit strength and the parameters of statistical distribution that the microunit strength obeys. The four-parameter criterion is a failure criterion consisting of four unknown parameters. When the four parameters equal appropriate values, it may become the Drucker–Prager criterion (for rock), Mohr–Coulomb criterion (for rock), and Hsieh–Ting–Chen criterion (for concrete), so the four-parameter criterion may be used to simulate the elastoplastic behavior of rock and concrete quasi-brittle materials. In the paper, microunit strength is determined with the four-parameter criterion, thus the statistical damage constitutive model suits rock and concrete. The deficiencies of existing methods in determining the distribution parameters are investigated, and a new method for determining the distribution parameters is proposed. First, the theoretical relationships between the parameters and the strain and stress at the peak point of material failure curve are derived; second, the approximate relations between the strain and stress at the peak point of material failure curve and confining pressure are established through the curve fitting method; finally, the relations between the parameters and confining pressure are established. The proposed statistical damage softening constitutive model of quasi-brittle materials has universal meaning, the determination of distribution parameters has strict theoretical basis, and the distribution parameters can be conveniently obtained with general triaxial tests. Numerical examples are also presented to validate the model.     

Scale Transition in Steel-Concrete Interaction. I: Model

This paper deals with the analysis of reinforced concrete (RC) structures with special emphasis on modeling of the interaction between concrete and reinforcement. A new mode for consideration of the response of the composite material at the member (structural) scale is proposed. It is obtained from extension of the fracture energy concept, originally developed for the simulation of cracking of plain concrete, to reinforced concrete. Hereby, the fracture energy related to the opening of primary cracks is increased in order to account for bond slip between steel and concrete. This increase is determined from the distribution of bond slip by means of a one-dimensional composite model introduced at the bar scale. The model consists of steel bars and the surrounding concrete. Between these two components, a nonlinear bond stress–bond slip relation is considered. The obtained results at the bar scale, such as the average crack spacing between adjacent cracks and the load-displacement response of the composite material, form the basis for determination of the increase of the fracture energy at the member scale. The performance of the proposed transition of the steel-concrete interaction from the bar scale to the member scale is assessed by means of reanalysis of experiments performed on RC bars. The application of the respective material model for reinforced concrete to real-life engineering structures is reported in Part II of this series.     

Material Model Describing Cyclic Elastic‐Plastic Deformation of Roller Levelling and Straightening Processes

The presented material model describes the elastic‐plastic stress‐strain course of cyclic tension‐compression deformation with variable amplitudes. The result is a hysteresis curve. Each hysteresis curve consists at maximum of three parts. Part I starts on a linear course originating from elastic strain or elastic recovery and ends at a defined point N. When the strain runs past this point, part II then follows as a non‐linear function where the superposition of a logarithmic function with a parabola proved to be in good coincidence with the real material behaviour. When the strain reaches a point T, linear hardening begins as part III. For the application of the model in practice, a file of data from special tests with cyclic tension‐compression deformations is necessary. The material model can be applied as a subsystem in a roller straightening process model. It has been successfully used in practice. The detrimental residual stresses were significantly reduced as well as the straightness of the rails was improved.     

Development of New Peak Shear-Strength Criterion for Anisotropic Rock Joints

The roughness of a natural rock joint was measured in different directions using a laser profilometer. Two stationary roughness parameters and a nonstationary roughness parameter (all fractal based) were used to quantify anisotropic roughness. A plaster of Paris based model material was used to make model material replicas of the natural rock joint. Direct shear tests were performed at five different normal stresses, in each of the directions that were used for the roughness measurements, to measure the anisotropic peak shear strength of the model joint. Required observations and experiments were conducted to estimate (1) the asperity shear area as a proportion of the total surface area of the joint, for each tested joint; (2) the basic friction angle of the model material; and (3) the joint compressive strength. Tests were also conducted to develop a peak shear-strength criterion for the intact model material. Part of the direct shear test data was used to develop a new peak shear-strength criterion for joints including the aforementioned parameters. The other part of the data was used for model validation.     

Coupled Environmental-Mechanical Damage Model of RC Structures

The evaluation of strength reduction of RC structures subjected to mechanical damage process and chemical attack is carried out, with regard to concrete deterioration and steel corrosion. A coupled environmental-mechanical damage model, developed as an extension of that previously published is presented. Two independent scalar mechanical damage parameters are introduced, each of them representing the degradation mechanisms occurring under tensile and compressive stress conditions. The stiffness recovery upon loading reversal, which is manifest when passing from tension into compression, is fully captured by the proposed model. The environmental damage is strongly related to the diffusion process, as well as to the evolution of the chemical reaction between pollutant and cementitious constituents. An enhanced local method is proposed to regularize the problem of nonobjectivity of the finite-element solution due to the strong strain softening behavior of concrete material. The splitting test of a concrete specimen and a static analysis of an RC frame subjected to mechanical loads and chemical attacks are carried out, and the damage evolution is analyzed in detail.     

Model for Analysis of Short Columns of Concrete Confined by Fiber-Reinforced Polymer

This paper presents a numerical model for evaluating the behavior of axially loaded rectangular and cylindrical short columns of concrete confined by fiber-reinforced polymer (FRP) composites. The proposed formulation considers, for unconfined and confined compressed concrete, a uniaxial constitutive relation that utilizes the area strain as a parameter of measure of the material secant axial stiffness. For unconfined concrete, the model adopts an explicit relationship between axial strain and lateral strain, while for confined concrete, an implicit relation is considered. For this last case, the model employs a simple iterative-incremental approach that describes the entire stress-strain response of the columns. The behavior of the FRP is considered linear elastic until the rupture. To validate the model, a number of columns were analyzed and the numerical results were compared with experimental values published by other authors. This comparison between experimental and numerical results indicates that the model provides satisfactory predictions of the stress-strain response of the columns.     

Microvoid Damage Model with Material Dilation for Ductile Fracture

A constitutive model that incorporates material dilation and the concept of continuum damage mechanics is developed to predict ductile fracture of steel under monotonic quasi-static loading due to microvoids. In this model, damage is assumed to be isotropic and is a function of the state of stress and the plastic strain increment. Material dilation is assumed to vary with the state of damage. Fracture occurs when the damage limit is reached. Parameters for the model are calibrated using data obtained from tension coupon tests. The constitutive model and the process used to determine its parameters are described. Analyses have been carried out to illustrate the effect of incorporating material dilation. The model is able to closely predict the load versus deformation curve of the tension test. Additional test data required for verifying the model have also been outlined.