Computational Constitutive Model for Predicting Nonlinear Viscoelastic Damage and Fracture Failure of Asphalt Concrete Mixtures

A computational constitutive model was developed to predict damage and fracture failure of asphalt concrete mixtures. Complex heterogeneity and inelastic mechanical behavior are addressed by the model by using finite-element methods and elastic–viscoelastic constitutive relations. Damage evolution due to progressive cracking is represented by randomly oriented interface fracture, which is governed by a newly developed nonlinear viscoelastic cohesive zone model. Computational simulations demonstrate that damage evolution and failure of asphalt concrete mixtures is dependent on the mechanical properties of the mixture. This approach is suitable for the relative evaluation of asphalt concrete mixtures by simply employing material properties and fracture properties of mixture components rather than by performing expensive laboratory tests recursively, which are typically required for continuum damage mechanics modeling.     

Rate-Type Model for Bituminous Mixtures and Its Application to Sand Asphalt

A variety of hot mix asphalt mixtures are used in highway and runway pavement construction. Each mixture caters to specific needs. Mixtures differ from one another in the type and percentage of aggregates and asphalt used, and their response can be markedly different, and thus there is a need to develop constitutive models that can differentiate between the different kinds of mixtures. In this paper, we outline a general procedure for the constitutive modeling of bituminous mixtures. We illustrate the efficacy of this approach by means of an application to sand asphalt. The governing equations for this special problem reduce to a stiff nonlinear ordinary differential equation and this is solved numerically using Gear’s method. We compare the results of the predictions of the model that we have developed with the compressive creep experiments carried out by Wood and Goetz on a typical sand asphalt mixture and find them to be in good agreement.     

Constitutive Model for Concrete with Embedded Sets of Reinforcement

In this paper a constitutive relation is developed for concrete reinforced with two orthogonal sets of steel bars. The formulation incorporates a homogeneous deformation mode, prior to cracking, as well as a localized mode associated with formation of macrocracks. In the latter case, the representative volume comprises the reinforced fractured zone and the “intact” material. The stiffness of the reinforcing network is evaluated by considering the individual steel bars to be rigidly embedded in the adjacent intact material. An extensive numerical analysis is conducted examining the performance of the proposed framework in pure shear and axial tension for different reinforcement intensities and orientations. The results are compared with the available experimental data.     

Global Constitutive Model for Reinforced Concrete Plates

A new constitutive model for reinforced concrete plates using global variables is discussed in this work. It includes the modeling of concrete cracking (through damage) and the plastic yielding of steel. The yield surface, derived from limit analysis, generalizes the Johansen’s criterion by taking into account both membrane and bending behaviors in reinforced concrete plates. Compared to three-dimensional models, this stress resultant model gives reliable results and can be applied to the study of large shell structures.     

Construction Quality Control for Asphalt Concrete Hydraulic Barriers

Asphalt concrete has been used for low permeability barriers in numerous applications over many centuries. In recent times, asphalt concrete barriers have been used for waste containment applications. The hydraulic conductivity of asphalt concrete specimens can be measured in the laboratory; however, there is no expedient, efficient way of accurately measuring the in situ hydraulic conductivity of low permeability asphalt concrete shortly after its placement and compaction in the field. A method has been developed to efficiently check the in situ hydraulic conductivity of asphalt concrete in the field. Asphalt concrete specimens with varying asphalt cement contents and unit weights were prepared in the laboratory and their hydraulic conductivity measured. The measured hydraulic conductivity data were grouped into different ranges and plotted as a function of unit weight and asphalt cement content. An acceptable zone was specified for a combination of asphalt cement content and unit weight that resulted in a specified hydraulic conductivity. In the field, a quality control inspector can check the unit weight and asphalt cement content of the in-place barrier to make sure it lies within the acceptable zone. The asphalt cement content and unit weight can be readily measured, thereby allowing rapid acceptance or rejection of the asphalt concrete barrier shortly after compaction.     

Constitutive Modeling of Inherently Anisotropic Sand Behavior

A plasticity constitutive framework for modeling inherently anisotropic sand behavior is presented within a modified form of critical state soil mechanics. A second-order symmetric fabric tensor, Fij, describes the material inherent anisotropy, and a scalar-valued anisotropic state variable A is properly defined in terms of a joint invariant of Fij and the stress tensor. The location of the critical state line in the plane of void ratio and effective mean normal stress is not fixed but depends on A, rendering the soil dilatancy also a function of A. In addition, the plastic modulus is made a function of A. The incorporation of these two modifications in terms of A in an existing stress-ratio bounding surface model, achieves the successful simulation of both the contractive and dilative responses of sand over a wide range of variations in stress and density as shown by experimental data. Of particular significance are the results which exhibit the drastic effect of different principal stress orientations in reference to the material axes of anisotropy.     

Limitations in the Constitutive Modeling of Unsaturated Soils and Solutions

Over the past six decades, significant attention has been paid to the elastoplastic behavior of unsaturated soils. In the past two decades alone, elastoplastic theory for unsaturated soils has been established and experimental techniques for measuring the elastoplastic behavior of unsaturated soils have become more sophisticated. However, less effort has been directed at developing the best strategy for constitutive modeling of unsaturated soils. At present, there is no standard method for developing constitutive models for unsaturated soils from experimental data, and owing to the extreme complexity of unsaturated soil behavior, there are limitations in the existing modeling methods. If these limitations are not recognized, misleading results in the constitutive modeling of unsaturated soil behavior may occur. This paper discusses the origins of and possible solutions to these limitations. Experimental data from the recent literature are used to demonstrate the use of existing methods for the constitutive modeling of unsaturated soils and potential associated problems. A modified state-surface approach (MSSA), recently proposed to model the elastoplastic behavior of unsaturated soils under isotropic conditions, was applied to overcome the limitations and develop a constitutive model that can best represent the behavior of unsaturated soil. A comparison of the proposed method and existing methods is discussed, and from this discussion, the capability and effectiveness of the proposed method are evaluated.     

Van Der Waals Force and Asphalt Concrete Strength and Cracking

Van der Waals force between neutral molecules is employed to characterize the interaction among molecules in asphalt cement. Several important consequences emerge from the consideration. The brittle strength of the asphalt binder is shown to be linked to the well depth of the Van der Waals potential and the mesoscopic cracks present within the asphalt binder. Moreover, the elastic modulus of asphalt binder is analytically related to the potential well depth. The strength of the asphalt concrete (AC) is estimated by considering aggregate surface characteristics and the adhesion strength between asphaltenes or resins and molecules of aggregates. These predictions can help design asphalt concrete pavement. Formulas for predicting the binder strength and the interfacial breaking strength between aggregates and binders are derived. These results are supported by reported data. Furthermore, an analytic expression for the strength of AC is given at temperature below the AC glass transition point.     

Constitutive Model for Time-Dependent Behavior of FRP–Concrete Interface

A fundamental understanding of fiber-reinforced polymer (FRP) laminate bonding behavior, including bond strength and effective bonding length, is of primary importance for the development of design guidelines and codes for concrete structures strengthened with externally bonded FRP reinforcement as a bond-critical application. However, the long-term serviceability of such FRP-strengthened structures is still a concern due to a lack of both long-term performance data and a suitable model to represent these performances. This study aims at presenting a viscoelastic model describing the time-dependent behavior of the FRP–concrete interface. The proposed model has been calibrated using strain measurements of the designed specimen for the experimental investigation of the time-dependent behavior of the FRP–concrete interface, including the development of the effective bonding length. Afterward, the proposed model satisfactorily predicts the time-dependent bonding length of the FRP sheet in comparison with the experimental results. The effects, both of creep of the adhesive layer and of creep and shrinkage of the concrete, on the changes in the effective bonding length of the PFRP sheet are also discussed.     

Development of Fabric Constitutive Behavior for Use in Modeling Engine Fan Blade-Out Events

The development of a robust and reliable material model for fabrics used to prevent fan blade-out events in propulsion engines has significant importance in the design of fan-containment systems. Currently, Kevlar is the only fabric approved by the Federal Aviation Administration to be used in fan-containment systems. However, very little work has been done in building a mechanistic-based material behavior model, especially one that can be used to quantify the behavior of Kevlar when subjected to high-velocity projectiles. Experimental static and high strain rate tensile tests have been conducted at Arizona State University to obtain the material properties of Kevlar fabric. In this paper we discuss the development and verification of a constitutive model for dry fabrics for use in an explicit finite-element program. Results from laboratory tests such as tension tests including high-strain rate tests, picture frame shear tests, and friction tests yield most of the material properties needed to define a constitutive model. The material model is incorporated in the LS-DYNA commercial program as a user-defined subroutine. The validation of the model is carried out by numerically simulating actual ballistic tests conducted at NASA-GRC and fan blade out tests conducted at Honeywell Aerospace (Propulsion Engines).     

Advanced Testing and Characterization of Asphalt Concrete Materials in Tension

The modeling of asphalt concrete materials is currently handled using linear viscoelasticity (VE) and viscoplasticity (VP) with damage. Exploratory frequency sweep and creep and recovery test results indicate that the linear VE with damage theory cannot represent the material response unless damage–healing is also included in the formulation. Therefore, the concept of effective stress, used for modeling damage, is extended to include additional nonlinear effects. A new theory of nonlinear VE with damage and VP is presented for uniaxial loading conditions in tension. A special load transfer device is described. It allows very fast unloading and very long recovery periods with complete unloading. It permits better separation between VE and VP components. Using this device, a uniaxial tension creep and recovery test is conducted and analyzed. The nonlinear material response is illustrated and a calibration of the damage function is presented. The formulation is being extended to three-dimensional conditions.     

Constitutive Modeling of Fiber Reinforced Shotcrete Panels

Beam and panel specimens are commonly used to assess the flexural performance of fiber reinforced shotcrete (FRS). Constitutive modeling of the flexural performance of ASTM C-1550 panels made with FRS is useful for explaining the relationship between the performance of specimens and the behavior of in situ FRS tunnel linings. A series of analyses have therefore been undertaken using yield line theory to derive the nonlinear load-deflection response of C-1550 panels based on the flexural capacity of beams of similar composition and thickness. A Monte Carlo simulation has been incorporated into the analysis to account for the stochastic nature of the material properties. This has demonstrated that the postcracking behavior of C-1550 panels can be successfully modeled using yield line theory and moment-crack rotation relationships developed from tests on beams made of the same material. Moreover, the variation in performance of C-1550 panels is primarily caused by variations in the flexural capacity of elements comprising the panel rather than variations in the location of the radial cracks that form during a test.     

Constitutive Model for Static Liquefaction

A general, three-dimensional formulation of the elastoplastic refined Superior sand constitutive model is presented. The model is aimed at realistic simulation of liquefaction phenomena occurring in loose saturated granular materials under monotonic static loading. The isotropic hardening/softening is related to plastic deformation and distance to a reference yield surface. The nonassociated flow rule is used with the closed yield surface introduced previously in the Superior sand model. The refined model accounts for the different response of materials with different deposition densities. The model prediction of drained and undrained plane-strain compression is presented and compared with the response in triaxial compression/extension loading. Static and kinematic instability states also are discussed.     

Constitutive Model of High-Damping Rubber Materials

A mathematical model of high-damping rubber materials is developed. First the material experiments necessary for modeling are systematically conducted. Then, on the basis of the results of the material experiments, a constitutive model for rubber materials is proposed. The model is decomposed into two parts. The first part consists of an elastoplastic body with a strain-dependent isotropic hardening law and it represents the energy dissipation of the material, while the second part consists of a hyperelastic body with a damage model and it expresses the evolutional direction of the stress tensor. By comparing the experimental results with the simulation by the model, the model is found to well approximate the behaviors of high-damping rubber materials. Finally, a hybrid analysis method is proposed. In this method, the strain field of laminated rubber bearings measured by image processing is combined with the numerical analysis to confirm the applicability of the proposed model to the bearing. In addition, by this hybrid analysis method, the bulk modulus of rubber material is also computed.     

Genetic Algorithms for the Calibration of Constitutive Models for Soils

This paper presents a study that uses an innovative numerical method called the “genetic algorithm” for material parameter optimization in constitutive modeling. The paper introduces a new scheme, a fitness function, to estimate the error of predicted behavior due to a given set of material parameters. Optimization efficiency of the proposed fitness function is analyzed by changing the selected genetic algorithm parameters. The genetic algorithm and the new fitness function were found to be capable of optimizing material parameters of complex constitutive models.     

Simulation of Crack Propagation in Asphalt Concrete Using an Intrinsic Cohesive Zone Model

This is a practical paper which consists of investigating fracture behavior in asphalt concrete using an intrinsic cohesive zone model (CZM). The separation and traction response along the cohesive zone ahead of a crack tip is governed by an exponential cohesive law specifically tailored to describe cracking in asphalt pavement materials by means of softening associated with the cohesive law. Finite-element implementation of the CZM is accomplished by means of a user subroutine using the user element capability of the ABAQUS software, which is verified by simulation of the double cantilever beam test and by comparison to closed-form solutions. The cohesive parameters of finite material strength and cohesive fracture energy are calibrated in conjunction with the single-edge notched beam [SE(B)] test. The CZM is then extended to simulate mixed-mode crack propagation in the SE(B) test. Cohesive elements are inserted over an area to allow cracks to propagate in any direction. It is shown that the simulated crack trajectory compares favorably with that of experimental results.     

Constitutive Model for Municipal Solid Waste

Municipal solid waste (MSW) is a refuse composed of various materials with different properties. Some of the components are stable while others degrade as a result of biological and chemical processes. These aspects impart to MSW a complex behavior that has been modeled, with many limitations, within the concepts of soil mechanics. In this paper, a framework to model the MSW mechanical behavior is proposed based on results from laboratory tests, such as triaxial compression and confined compression of large samples. It is suggested that two different effects command MSW mechanical behavior: (a) the reinforcement of MSW by synthetic fibers (composed by many types of polymers) and (b) the behavior of the MSW paste, without fibers. Accordingly, two distinct frameworks were used to represent the main MSW characteristics: (a) a critical state framework for MSW paste and (b) an elastic perfectly plastic framework for waste fibers, with a time lag for fiber loading (function fm). The proposed model is capable of reproducing quite well the results obtained from triaxial and confined compression tests performed in the laboratory as well as the settlement recorded in a sanitary landfill.     

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.     

Unified DSC Constitutive Model for Pavement Materials with Numerical Implementation

Need for unified and mechanistic constitutive models for pavement materials for evaluation of various distresses has been recognized; however, such models are not yet available. There have been efforts to develop unified models; however, they have been based usually on ad hoc combinations of models for special properties such as elastic, plastic, creep and fracture, often without appropriate connections to various coupled responses of bound and unbound materials, they may result and in a large number of parameters, often without physical meanings. The disturbed state concept (DSC) provides a modeling approach that includes various responses such as elastic, plastic, creep, microcracking and fracture, softening and healing under mechanical and environmental (thermal, moisture, etc.) within a single unified and coupled framework. A brief review is presented to identify the advantages of the DSC compared to other available models. The DSC has been validated and applied to a wide range of materials: geologic, asphalt, concrete, ceramic, metal alloys, and silicon. It allows for evaluation of various distresses such as permanent deformations (rutting), microcracking and fracture, reflection cracking, thermal cracking, and healing. The DSC is implemented in two- and three-dimensional finite-element (FE) procedures, which allow static, repetitive, and dynamic loads including elastic, plastic, creep, microcracking leading to fracture and failure. A number of examples are solved for various distresses considering flexible (asphalt) pavements; however, the DSC model is applicable to rigid (concrete) pavements also. It is felt that the DSC and the FE computer programs provide unique and novel approaches for pavement engineering. It is desirable to perform further research and applications including validation with respect to simulated and field behavior of pavements.