Micromechanical finite element framework for predicting viscoelastic properties of asphalt mixtures

A micromechanical finite element (FE) framework was developed to predict the viscoelastic properties (complex modulus and creep stiffness) of the asphalt mixtures. The two-dimensional (2D) microstructure of an asphalt mixture was obtained from the scanned image. In the mixture microstructure, irregular aggregates and sand mastic were divided into different subdomains. The FE mesh was generated within each aggregate and mastic subdomain. The aggregate and mastic elements share nodes on the aggregate boundaries for deformation connectivity. Then the viscoelastic mastic with specified properties was incorporated with elastic aggregates to predict the viscoelastic properties of asphalt mixtures. The viscoelastic sand mastic and elastic aggregate properties were inputted into micromechanical FE models. The FE simulation was conducted on a computational sample to predict complex (dynamic) modulus and creep stiffness. The complex modulus predictions have good correlations with laboratory uniaxial compression test under a range of loading frequencies. The creep stiffness prediction over a period of reduced time yields favorable comparison with specimen test data. These comparison results indicate that this micromechanical model is capable of predicting the viscoelastic mixture behavior based on ingredient properties.     

A bilinear cohesive zone model tailored for fracture of asphalt concrete considering viscoelastic bulk material

A bilinear cohesive zone model (CZM) is employed in conjunction with a viscoelastic bulk (background) material to investigate fracture behavior of asphalt concrete. An attractive feature of the bilinear CZM is a potential reduction of artificial compliance inherent in the intrinsic CZM. In this study, finite material strength and cohesive fracture energy, which are cohesive parameters, are obtained from laboratory experiments. Finite element implementation of the CZM is accomplished by means of a user-subroutine which is employed in a commercial finite element code (e.g., UEL in ABAQUS). The cohesive parameters are calibrated by simulation of mode I disk-shaped compact tension results. The ability to simulate mixed-mode fracture is demonstrated. The single-edge notched beam test is simulated where cohesive elements are inserted over an area to allow cracks to propagate in any general direction. The predicted mixed-mode crack trajectory is found to be in close agreement with experimental results. Furthermore, various aspects of CZMs and fracture behavior in asphalt concrete are discussed including: compliance, convergence, and energy balance.     

A viscoelastic continuum damage model and its application to uniaxial behavior of asphalt concrete

An existing viscoelastic constitutive model which accounts for the effects of rate-dependent damage growth is described and applied successfully to characterize the uniaxial stress, constant strain rate behavior of asphalt concrete. The special case of an elastic continuum damage model with multiaxial loading, which is based upon thermodynamics of irreversible processes with internal state variables, is first reviewed and then it is shown how this model has been extended to a corresponding viscoelastic damage model through the use of an elastic-viscoelastic correspondence principle. The general mathematical model is next specialized to uniaxial loading. A rate-type evolution law, similar in form to a crack growth law for a viscoelastic medium, is adopted for describing the damage growth within the body. Results from laboratory tests of uniaxial specimens under axial tension at different strain rates are then shown to be consistent with the theory. The discussion of data analysis describes the specific procedure used here to obtain the material parameters in the constitutive model for uniaxial loading and how the method may be generalized for multiaxial loading.     

Characterization of linear viscoelastic properties of asphalt concrete subjected to confining pressure

This paper presents a triaxial storage modulus master curve model and a continuous relaxation spectrum model for characterizing the linear viscoelastic (LVE) properties of asphalt concrete subjected to confining pressure. The triaxial master curve model relates the reduced storage modulus to the reduced frequency by performing both horizontal and vertical shifting on storage modulus test results. The horizontal shifting is used to characterize the time- and temperature-dependent behavior of asphalt concrete, while the vertical shifting is to characterize the pressure-dependent behavior. The vertical shift factor has the form of a sigmoidal function and varies with the reduced frequency and confining pressure. A relaxation spectrum model as well as a long-time equilibrium modulus model has been derived from the triaxial master curve model via integral transforms of basic LVE equations and complex algebra. The model predictions agree well with the laboratory test results of three asphalt mixtures indicating the proposed models can accurately characterize the LVE behavior of asphalt concrete under confinement.     

基于分数阶黏弹性模型的温拌改性沥青低温性能

基于分数阶黏弹性模型,通过低温弯曲梁流变试验（BBR）分析RH和Evotherm温拌剂对苯乙烯-丁二烯-苯乙烯嵌段共聚物（SBS）改性沥青低温性能的影响。结果表明：利用BBR试验数据拟合出的分数阶黏弹性模型参数可较好地预估温拌改性沥青的蠕变柔量和蠕变速率; RH温拌剂可以提高SBS改性沥青的阻尼比和耗散能比,但Evotherm温拌剂在低于-18℃时不能够提高;因7种沥青按照阻尼比和耗散能比排序相同,故也可以将阻尼比作为温拌改性沥青低温性能的一种评价指标; RH可以改善沥青的蠕变柔量,提高黏性流动柔量,且掺量越高改善效果越好,但不能提高黏弹性比,故不能用黏弹性比评价温拌SBS改性沥青的低温性能,而Evotherm温拌剂的规律性不强;两种温拌剂都在低于-24℃时对SBS改性沥青的低温性能改善不佳。     

A two-way coupled multiscale model for predicting damage-associated performance of asphaltic roadways

This paper presents a quasi-static multiscale computational model with its verification and rational applications to mechanical behavior predictions of asphaltic roadways that are subject to viscoelastic deformation and fracture damage. The multiscale model is based on continuum thermo-mechanics and is implemented using a finite element formulation. Two length scales (global and local) are two-way coupled in the model framework by linking a homogenized global scale to a heterogeneous local scale representative volume element. With the unique multiscaling and the use of the finite element technique, it is possible to take into account the effect of material heterogeneity, viscoelasticity, and anisotropic damage accumulation in the small scale on the overall performance of larger scale structures. Along with the theoretical model formulation, two example problems are shown: one to verify the model and its computational benefits through comparisons with analytical solutions and single-scale simulation results, and the other to demonstrate the applicability of the approach to model general roadway structures where material viscoelasticity and cohesive zone fracture are involved.     

Modeling the viscoelastic function of asphalt concrete using a spectrum method

A continuous spectrum method is proposed and applied for modeling the time-domain viscoelastic function of asphalt concrete materials. This technique, employing a Wiechert model for the relaxation function and a Kelvin model for the compliance function, is found to substantially enhance accuracy and consistency compared to existing methods. Furthermore, this paper shows how to determine a time-domain Prony series representation, which can be used efficiently for numerical analysis, such as finite element analysis, from the complex modulus in the frequency domain, based on the continuous spectrum method.     

Continuous relaxation and retardation spectrum method for viscoelastic characterization of asphalt concrete

This paper presents a simple and practical approach to obtain the continuous relaxation and retardation spectra of asphalt concrete directly from the complex (dynamic) modulus test data. The spectra thus obtained are continuous functions of relaxation and retardation time. The major advantage of this method is that the continuous form is directly obtained from the master curves which are readily available from the standard characterization tests of linearly viscoelastic behavior of asphalt concrete. The continuous spectrum method offers efficient alternative to the numerical computation of discrete spectra and can be easily used for modeling viscoelastic behavior. In this research, asphalt concrete specimens have been tested for linearly viscoelastic characterization. The linearly viscoelastic test data have been used to develop storage modulus and storage compliance master curves. The continuous spectra are obtained from the fitted sigmoid function of the master curves via the inverse integral transform. The continuous spectra are shown to be the limiting case of the discrete distributions. The continuous spectra and the time-domain viscoelastic functions (relaxation modulus and creep compliance) computed from the spectra matched very well with the approximate solutions. It is observed that the shape of the spectra is dependent on the master curve parameters. The continuous spectra thus obtained can easily be implemented in material mix design process. Prony-series coefficients can be easily obtained from the continuous spectra and used in numerical analysis such as finite element analysis.     

Universal linear viscoelastic approximation property of fractional viscoelastic models with application to asphalt concrete

The paper presents a comprehensive linear viscoelastic characterization of asphalt concrete using fractional viscoelastic models. For this purpose, it is shown that fractional viscoelastic models are universal approximators of relaxation and retardation spectra. This essentially means that any spectrum can be mathematically represented by fractional viscoelastic models. Characterization of asphalt concrete is performed by constructing the dynamic modulus master curve and determining the parameters of the generalized fractional Maxwell model (GFMM). This procedure is similar to the widely used one of determining the master curve of asphalt concrete using a statistical function such as the sigmoidal model. However, from the GFMM, the relaxation modulus, creep compliance, continuous relaxation spectrum, and Prony series parameters can be determined analytically. A further advantage of the GFMM is that unlike the sigmoidal model, which only gives a representation of either the dynamic modulus or the storage modulus, the GFMM gives a representation of both the storage modulus and loss modulus (and therefore also the dynamic modulus and phase angle). The procedure was successfully applied to ten different mixes used in the State of Virginia.     

Influence of de-icing agents on the viscoelastic properties of asphalt mastics

A study using dynamic mechanical analysis (DMA) and stress rheometry was done on the viscoelastic properties of different bitumen-filler blends disposed to de-icing agents. The blends were mixtures of the same bitumen, B200 (B), and four different filler grades, limestone (L) filler, Oulu (O) stone (mica-gneiss with high biotite amount), Rovaniemi (R) stone (diabase) and Hietavaara (H) stone (diabase). The de-icing agents tested were water, formic acid, potassium acetate (KAc) and potassium formate (KFo). From the DMA measurements, the elastic modulus (stiffness) at −25 °C, the glass transition temperature (T _g) of the bitumen phase, and the softening temperature were measured. The stiffness data at −25 °C proposed that all agents seem to decrease the stiffness levels of the B-O blend with biotite to a larger extent. Formic acid and 50% potassium formates significantly decreased the stiffness level of the B-L blend. The stiffness of B-H blends was not affected by the chemical treatment. A plasticizing effect of water, formic acid, and 5% potassium acetate, was found for the B-L blend. From the changes in the softening temperatures in the temperature range 15–28 °C, it was concluded that chemical treatment may have an increasing effect on the softening temperatures of all blends, although the effect of hardening could not be omitted. Oscillatory flow measurements with a shear stress rheometer demonstrated that the viscosities of the blends increased significantly after the immersion in de-icing agents.     

乳化沥青橡胶混凝土的力学性能

对用乳化沥青(Emulsified asphalt,EA)改善橡胶混凝土(Crumb rubber concrete,CRC)的力学性能进行了研究。通过抗压、抗折、劈裂抗拉和三点弯曲试验,研究了5%、10%和15% 3种橡胶掺量(等体积取代细骨料)下,EA理论计算成膜覆盖橡胶颗粒表面4层、6层和8层膜对应不同EA掺量对CRC力学性能的影响。试验结果发现,对比未预处理CRC和NaOH预处理CRC两个对照组:掺入不同掺量EA后,不同橡胶掺量的CRC的抗压强度和劈裂抗拉强度均有较大提高,CRC的峰值位移显著增大,弯曲弹性模量E_b明显降低;乳化沥青与橡胶质量比为0.15(6层EA膜)时,3种橡胶掺量下CRC较未预处理组相比抗压强度平均提高3.5%,峰值位移提高27.6%,E_b降低21.8%,乳化沥青橡胶混凝土具有较突出的力学性能复合效应。      

A nonlocal multiscale discrete‐continuum model for predicting mechanical behavior of granular materials

A three‐dimensional nonlocal multiscale discrete‐continuum model has been developed for modeling mechanical behavior of granular materials. In the proposed multiscale scheme, we establish an information‐passing coupling between the discrete element method, which explicitly replicates granular motion of individual particles, and a finite element continuum model, which captures nonlocal overall responses of the granular assemblies. The resulting multiscale discrete‐continuum coupling method retains the simplicity and efficiency of a continuum‐based finite element model, while circumventing mesh pathology in the post‐bifurcation regime by means of staggered nonlocal operator. We demonstrate that the multiscale coupling scheme is able to capture the plastic dilatancy and pressure‐sensitive frictional responses commonly observed inside dilatant shear bands, without employing a phenomenological plasticity model at a macroscopic level. In addition, internal variables, such as plastic dilatancy and plastic flow direction, are now inferred directly from granular physics, without introducing unnecessary empirical relations and phenomenology. The simple shear and the biaxial compression tests are used to analyze the onset and evolution of shear bands in granular materials and sensitivity to mesh density. The robustness and the accuracy of the proposed multiscale model are verified in comparisons with single‐scale benchmark discrete element method simulations. Copyright © 2015 John Wiley & Sons, Ltd.     

A model for predicting the evolution of multiple cracks on multiple length scales in viscoelastic composites

A model is presented herein for predicting the evolution of numerous cracks on multiple length scales, the objective of such a model being to develop the capability to predict failure of structural components to perform their intended tasks. Such a capability would then be useful as a predictive tool for designing structural components so as not to fail, but rather to succeed in performing their intended tasks. The model developed herein is somewhat involved, being based in continuum mechanics and thermodynamics, but is nevertheless expected to be cost effective (wherever sufficient accuracy permits) when compared to more costly experimental means of determining component life. An essential ingredient within the context of the model is that cracks must develop on widely differing length scales. Where this is observed to occur in nature, which is surprisingly often, there are potential simplifications over more generally described but practically untenable approaches, that can lead to (at least partly) computational multiscale algorithms capable of assimilating failure due to multiple cracking with a high degree of accuracy. The model presented herein will be briefly described within a mathematical framework, and an example problem will be presented that is representative of certain currently relevant technologies.     

A multiscale micromechanical approach to model the deteriorating impact of alkali-silica reaction on concrete

The alkali-silica reaction (ASR) in concrete is one of the most harmful deterioration processes, which leads to expansion and cracking of the material. To understand the evolution of ASR in concrete and its deteriorating impact on the material, a multiscale material model, from aggregate to concrete level, is proposed. The concrete, which at macro scale is considered a homogeneous material, is micromechanically modelled by a matrix-cracks system, in which each phase is uniform and behaves elastically. The damage criterion, associated to the cracks, is formulated on the basis of linear fracture mechanics theory. The model, which is analytically solved, is based on a limited numbers of input parameters, to be determined via micro and macro experimental investigations. The model is able to predict the non-linear behaviour of concrete subject to uniaxial loading in good agreement with code formulations, which are usually input for numerical analyses of structures. For the case of ASR-affected material, the model overestimates the degradation rate of mechanical properties as a function of the expansion. On the contrary, the relationship between stiffness and strength deterioration is correctly approximated. Various model modifications are explored suggesting that the assumption of elastic behaviour of each phase should be reconsidered.     

Is concrete a poromechanics materials?—A multiscale investigation of poroelastic properties

Materials and Structures - There is an ongoing debate, in Concrete Science and Engineering, whether cementitious materials can be viewed as poromechanics materials in the sense of the porous media...     

A model predicting carbonation depth of concrete containing silica fume

Silica fume (SF) has been used since long as a mineral admixture to improve durability and produce high strength and high performance concrete. Due to the pozzolanic reaction between calcium hydroxide and silica fume, compared with ordinary Portland cement, the carbonation of concrete containing silica fume is much more complex. In this paper, based on a multi-component concept, a numerical model is built which can predict the carbonation of concrete containing silica fume. The proposed model starts with the mix proportions of concrete and considers both Portland cement hydration reaction and pozzolanic reaction. The amount of hydration products which are susceptible to carbonate, such as calcium hydroxide (CH) and calcium silicate hydrate (CSH), as well as porosity can be obtained as associated results of the proposed model during the hydration period. The influence of water-binder ratio and silica fume content on carbonation is considered. The predicted results agree well with experimental results.     

A coupled thermo-chemo-mechanical reduced-order multiscale model for predicting process-induced distortions,residual stresses,and strength

We study residual stresses and part distortion induced by a manufacturing process of a polymer matrix composite and its effect on the component strength. Unlike most of the thermo-chemo-mechanical models in the literature where governing multiphysics equations are directly formulated on the macroscale, we present a multiscale-multiphysics approach. To address the enormous computational complexity involved, a reduced-order homogenization was originally developed for a single physics problem is employed. The proposed reduced-order two-scale thermo-chemo-mechanical model has been validated for predicting part distortion beam strength in three-point bending test. It is shown that while macroscopic stresses are relatively low, and therefore often ignored in practice, stresses at the scale of microconstituents are significant and may have an effect on the overall composite component strength.     

Development of a stress-mode sensitive viscoelastic constitutive relationship for asphalt concrete: experimental and numerical modeling

Asphalt binder is responsible for the thermo-viscoelastic mechanical behavior of asphalt concrete. Upon application of pure compressive stress to an asphalt concrete specimen, the stress is transferred by mechanisms such as aggregate interlock and the adhesion/cohesion properties of asphalt mastic. In the pure tensile stress mode, aggregate interlock plays a limited role in stress transfer, and the mastic phase plays the dominant role through its adhesive/cohesive and viscoelastic properties. Under actual combined loading patterns, any coordinate direction may experience different stress modes; therefore, the mechanical behavior is not the same in the different directions and the asphalt specimen behaves as an anisotropic material. The present study developed an anisotropic nonlinear viscoelastic constitutive relationship that is sensitive to the tension/compression stress mode by extending Schapery’s nonlinear viscoelastic model. The proposed constitutive relationship was implemented in Abaqus using a user material (UMAT) subroutine in an implicit scheme. Uniaxial compression and indirect tension (IDT) testing were used to characterize the viscoelastic properties of the bituminous materials and to calibrate and validate the proposed constitutive relationship. Compressive and tensile creep compliances were calculated using uniaxial compression, as well as IDT test results, for different creep-recovery loading patterns at intermediate temperature. The results showed that both tensile creep compliance and its rate were greater than those of compression. The calculated deflections based on these IDT test simulations were compared with experimental measurements and were deemed acceptable. This suggests that the proposed viscoelastic constitutive relationship correctly demonstrates the viscoelastic response and is more accurate for analysis of asphalt concrete in the laboratory or in situ.     

Validation of time temperature superposition principle for high modulus asphalt concrete in the linear viscoelastic and fatigue domains

Validation of time–temperature superposition principle (TTSP) in the fatigue domain for a high modulus asphalt concrete (HMAC) is presented in this paper. All tests were performed in tension-compression under strain control mode. First, TTSP was validated in the linear viscoelastic domain. Then, fatigue tests were performed under three loading conditions, 9.2°C and 5 Hz, 11.0°C and 10 Hz and 12.9°C and 20 Hz, which are equivalent regarding TTSP. Two fatigue protocols were adopted: continuous fatigue test (FT) and fatigue test with rest period (FTRP). For FT, three samples were tested at 180μm/m for each loading condition whereas for FTRP, one sample was tested at 100 μm/m. The data were analysed by comparing the dynamic modulus evolution as a function of time or the fatigue life duration. The results showed that HMAC with fatigue damage remains thermorheologically simple (i.e., respects the TTSP) in the studied temperatures range.