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Overflow is usually used to keep fluid continuously flowing to avoid the fluid from changing flow direction and subsequently inducing large stresses. To explore the mechanism of flow-induced stress evolution, a flow model was established in terms of compressible, non-isothermal, and viscoelastic flow. Based on the Leonov model and the mid-plane approach, a pseudo-Poisson type equation for pressure was derived to decouple the interdependence between velocity and pressure. To improve computational efficiency, a numerical approach involving double iterations was proposed to solve the flow problem. Two kinds of mold cavities, with and without overflow, were designed and manufactured. Molding experiments were conducted, and corresponding simulations based on the proposed model and algorithm were performed. The results show that the simulated contours of flow-induced stress are in good agreement with the photoelastic streaks. The use of overflow can significantly reduce flow-induced stresses. If the slot thickness is set to a proper value, the flow-induced stress can be reduced by more than 80%. On the other hand, a slot that is too thick does not have significant reducing effects. Therefore, using overflow to reduce flow-induced stresses during transparent part production is a promising approach if the material cost is worthy of the quality. Highlights * A double iteration method is proposed for viscoelastic flow problem. * Overflow can reduce the stress as much as 80% if the dimension is properly set. * The simulated stress streaks are in good agreement with photoelasticities. KEYWORDS finite element method, flow-induced stress, Leonov model, overflow, viscoelastic, 1 | INTRODUCTION Injection molding (IM) is the most efficient mass-production technology for manufacturing polymers in complex and detailed geometries with high precision. In view of these advantages, most transparent [...]

Polymerie materials are widely used in structural components and systems, and the accurate prediction of their complex time-dependent behavior is critical. Several constitutive models are available for different types of mechanical behaviors and loading conditions. However, selecting the model and the correct calibration of its parameters is often a challenge. This paper evaluates the applicability of the two-layer viscoplasticity (TLV) model to predict the viscoplastic behavior of polyvinylidene fluoride (PVDF) in a large range of strain rates and complex states of strain. The setting of parameters and model validation was made by performing experimentally and numerically uniaxial compression tests and relaxation tests. The model parameters were also analyzed in performing microindentation tests. The TLV model using the same set of parameters selected well predicted the PVDF behavior in a wide variety of compressive loading conditions. KEYWORDS elastoplastic-viscoelastic model, finite element analysis, instrumented indentation test, polyvinylidene fluoride, two-layer viscoplasticity model, 1 | INTRODUCTION Flexible pipelines are multilayered structures that transport fluids between wells and floating units in offshore oil fields. [1] They are composed of helical armoring layers and polymer [...]

This paper aims to develop asphalt binder fatigue models by time sweep tests under constant strain. By investigating the fatigue life in neat and modified asphalts under linear and nonlinear viscoelastic responses, results were analyzed in terms of strain levels, asphalt type, and additive content. The dissipated energy and dissipated energy ratio concepts were utilized to develop the phenomenological models for estimating fatigue lives of asphalt binders. Results showed that the dissipated energy ratio-based equations give relatively identical fatigue models irrespective of the strain level or asphalt binder type. Moreover, statistical analyses were performed to investigate the contribution of each parameter in the fatigue model prediction. A comparison was made between fatigue life predictions by means of traditional and energy-based methods. Results proved that the fatigue life prediction models based on the concept of dissipated energy ratio follow a similar trend. Key words: asphalt binder, fatigue, time sweep, dissipated energy, viscoelasticity. Le but vise de cet article est de developper des modeles de fatigue de liants d'asphalte au moyen d'essais de balayage temporel sous contrainte constante. En examinant la longevite a la fatigue des asphaltes purs et modifies selon les reponses viscoelastiques lineaires et non lineaires, les resultats ont ete analyses sur le plan des niveaux de deformation, du type d'asphalte et de la teneur en additif. Les concepts d'energie dissipee et de rapport d'energie dissipee ont servi a elaborer les modeles phenomenologiques permettant d'estimer la longevite a la fatigue des liants d'asphalte. Les resultats ont montre que les equations fondees sur le rapport d'energie dissipee donnent des modeles de fatigue relativement identiques quel que soit le niveau de deformation ou le type de liant d'asphalte. De plus, des analyses statistiques ont ete effectuees afin d'etudier la contribution de chaque parametre dans la prevision du modele de fatigue. Une comparaison a ete faite entre les predictions de la longevite a la fatigue au moyen de methodes traditionnelles et fondees sur l'energie. Les resultats ont demontre que les modeles de prediction de la longevite a la fatigue fondes sur le concept de rapport d'energie dissipee suivent une tendance similaire. [Traduit par la Redaction] Mots-cles : liant asphaltique, fatigue, balayage temporel, energie dissipee, viscoelasticite., Introduction Fatigue is the dominant mode of distress in flexible pavements at intermediate temperatures. It has been reported that the crack initiation and(or) propagation in asphalt pavements often originate from [...]

Most industrial process lines involve mixing complex dispersions, which can include non-Newtonian liquids and viscoelastic particles. Knowledge of the parameters of these components may provide a key for understanding how dispersions are formed and how equipment should be designed. One parameter is the shear modulus, which describes the ability of particles to resist mechanical stresses. This parameter may play the main role in the mixing process, when a dispersion is formed by the mechanical influence of a rotor (slice or shear in a rotor-stator mixer). In this work, two methods were chosen for measuring the shear modulus: the evaluation method, based on the Warner-Bratzler cut test, and the oscillatory method. Both methods were used for measuring viscoelastic clusters of particles, and the results were adjusted for the purposes of the comparison. The comparison shows that the shear modulus values obtained from Warner-Bratzler are higher than the values obtained from the oscillatory test for the same conditions. This difference can be explained by differences in the mechanical processes during the experiments. KEYWORDS frequency sweep, shear modulus, viscoelasticity, Warner-Bratzler test, 1 | INTRODUCTION Viscoelastic materials are involved in many processes, for example, mixing, blending, and extrusion. Measurements of the viscoelastic characteristics of these materials are essential for the adjustment of [...]

A series of statistical copolymers of 4-vinylbiphenyl and styrene were prepared via free radical polymerization to investigate the effect of the comonomer ratio on their microstructure and rheological properties. The glass transition temperature of the copolymers follows a nonlinear monotonic decreasing dependence with increasing styrene content which is well described by the GordonTaylor equation. WAXS measurements reveal that both the backbone to backbone and the inter-phenyl distances (dx and [d.sub.2], respectively) are decreasing functions of the styrene content in the copolymers. The apparent monomeric friction coefficient, calculated from dynamic frequency sweeps in the linear viscoelastic regime, decreases exponentially with the styrene content in the copolymer. We postulate that the strong effect of the copolymer composition on the friction coefficient is due to the larger overlapping distance between phenyl rings of adjacent polymer chains (d0Veriap)> giving rise to stronger aromatic n-n interactions, which in turn results in stronger friction between adjacent chains. The increase in doveriap and monomeric friction coefficient also leads to a significant increase in the extensional strain hardening measured during extensional startup flow measurements. KEYWORDS copolymerization, differential scanning calorimetry (DSC), glass transition, polystyrene, rheology, WAXS, 1 | INTRODUCTION The viscoelastic response of thermoplastics is intimately related to the polymer chain conformation as well as to the local structure (at the monomer level). From a practical [...]

In this work, a new constitutive equation for the description of the nonlinear viscoelastic response of polymeric materials is presented, by proposing modifications on a model developed in previous works. This time-dependent equation has been derived on the basis of transient model, and a new assumption regarding the kinetics of active molecular chains due to the imposed deformation. The present treatment was proved to be more flexible, given that it contains a relaxation function that has been derived by considering, instead of first-order kinetics, a fractional derivative that controls the rate of molecular chain detachment from their junctions. It has been further explored that the potential of this equation to be employed for the evaluation of the dynamic modulus master curve, once the experimental data of the compliance modulus of a polymeric structure have been matched., INTRODUCTION The extended application of polymers and polymer matrix composites as engineering materials in aerospace, automotive industry, and civil engineering structures demands for their correct characterization with regard to the [...]

This work investigates the transient slip flow of viscoelastic fluids in a slit micro-channel under the combined influences of electro-osmotic and pressure gradient forcings. We adopt the generalized second-grade fluid model with fractional derivative as the constitutive equation and the Navier linear slip model as the boundary conditions. The analytical solution for velocity distribution of the electro-osmotic flow is determined by employing the Debye-Huckel approximation and the integral transform methods. The corresponding expressions of classical Newtonian and second-grade fluids are obtained as the limiting cases of our general results. These solutions are presented as a sum of steady-state and transient parts. The combined effects of slip boundary conditions, fluid rheology, electro-osmotic, and pressure gradient forcings on the fluid velocity distribution are also discussed graphically in terms of the pertinent dimensionless parameters. By comparison with the two cases corresponding to the Newtonian fluid and the classical second-grade fluid, it is found that the fractional derivative parameter [beta] has a significant effect on the fluid velocity distribution and the time when the fluid flow reaches the steady state. Additionally, the slip velocity at the wall increases in a noticeable manner the flow rate in an electro-osmotic flow. Key words: generalized second-grade fluid, electro-osmotic flow, fractional calculus, slip velocity, analytical solutions. Nous etudions ici l'ecoulement glissant transitoire de fluides viscoelastiques dans un micro-canal a fente sous l'influence combinee de forces electro-osmotique et de gradient de pression. Nous adoptons le modele generalise du fluide de grade deux avec derivee fractionnaire comme loi de comportement et le modele de glissement lineaire de Navier comme conditions limites. Utilisant l'approximation de Debye-Hukel et les methodes de transformation integrale, nous obtenons la solution analytique pour la distribution de vitesse d'ecoulement electro-osmotique. Les expressions correspondantes pour des fluides newtoniens classiques et de grade deux sont obtenues comme cas limites de nos resultats generaux. Ces solutions sont presentees comme la somme de deux termes, decrivant un etat stationnaire et un autre transitoire. Les effets combines des conditions limites de glissement, de la rheologie du fluide, des forces electro-osmotique et de gradient de pression sur la distribution de vitesse du fluide sont aussi discutes graphiquement en fonction des parametres sans dimension pertinents. En comparant avec les resultats correspondants pour des fluides newtonien et de grade deux, nous trouvons que le parametre de la derivee fractionnaire [beta] a un effet significatif sur la distribution de vitesse du fluide et sur le temps que prend le fluide pour atteindre l'etat stationnaire. De plus, la vitesse de glissement a la paroi augmente de facon notable le taux d'ecoulement d'un ecoulement electro-osmotique. [Traduit par la Redaction] Mots-cles : fluide generalise de grade deux, ecoulement electro-osmotique, calcul fractionnaire, vitesse de glissement, solutions analytiques., 1. Introduction Today, fractional calculus has obtained more and more attention because of its demonstrated applications in many diverse fields of science and engineering. For an extensive bibliography on fractional [...]

Argillaceous rocks are candidate host and (or) cap formations for the geological disposal of nuclear wastes in many countries, including Canada, France, and Switzerland. The understanding of the long-term mechanical behaviour of such rocks is an essential requirement for the assessment of their performance as a barrier against radionuclide migration. The French Institute for Radiological Protection and Nuclear Safety (IRSN) operates an Underground Research Laboratory (URL) in Tournemire, France, in a rock formation known as the Tournemire shale. Many types of experiments are conducted at the Tournemire URL to better understand the physical and chemical behaviour of this shale and its interaction with seal materials intended to be used in the geological disposal of radioactive wastes. The Canadian Nuclear Safety Commission (CNSC) collaborates with the IRSN and CanmetMINING laboratories to perform experimental and theoretical research on the mechanical behaviour of the Tournemire shale. Using data from creep tests, and monotonic and cyclic triaxial tests performed at CanmetMINING Laboratories, we developed constitutive relationships for the mechanical behaviour of the Tournemire shale. The model is based on the theory of plasticity, and takes into consideration the inherent anisotropy due to the existence of bedding planes, hardening behaviour before the peak strength, and viscosity. Key words: shale, viscoelastoplasticity, anisotropy, triaxial test, geological disposal. Dans de nombreux pays comme le Canada, la France ou la Suisse, les roches argileuses sont des formations candidates pour le stockage geologique des dechets nucleaires. La comprehension du comportement mecanique a long terme de ces roches est une condition essentielle pour l'evaluation de leur performance comme une barriere contre la migration des radionucleides. L'Institut de Radioprotection et de Surete Nucleaire (IRSN) exploite un Laboratoire de recherche souterrain (LRS) a Tournemire, France, dans une formation rocheuse connue sous le nom de schiste Tournemire. De nombreux types d'experiences sont menees au LRS de Tournemire afin de mieux comprendre le comportement physique et chimique de ce schiste et son interaction avec les materiaux d'etancheite destines a etre utilises dans le stockage geologique des dechets radioactifs. La Commission canadienne de surete nucleaire (CCSN) collabore avec l'IRSN et les laboratoires de CanmetMINING pour effectuer des recherches experimentales et theoriques sur le comportement mecanique du schiste Tournemire. En utilisant les donnees des essais de fluage, et des essais triaxiaux monotones et cycliques effectuees aux Laboratories de CanmetMINING, nous avons developpe des relations constitutives du comportement mecanique du schiste Tournemire. Le modele est base sur la theorie de la plasticite, et prend en consideration l'anisotropie inherente en raison de l'existence de plans de stratification, le comportement au durcissement avant la resistance de pointe, et la viscosite. [Traduit par la Redaction] Mots-cles: schiste, viscoelastoplasticite, anisotropie, essai triaxial, stockage geologique., Introduction Deep geological disposal is being proposed for the long-term management of nuclear wastes in many countries, including Canada, France, and Switzerland. Sedimentary rock formations are one of the host [...]

HDPE pipes are frequently laid in buried or submerged conditions and are often subjected to considerable internal pressure. This context requires the consideration of HDPE as a structural material and demands constitutive models to predict failure possibilities in short and long terms. This article presents an approximate procedure to simulate the viscoelastoplastic nature of HDPE's material behavior under creep conditions. While a generalized Kelvin-Voigt model based on Prony series is used to model viscoelasticity, the power law of Zapas-Crissman is adopted to account for viscoplastic effects. The associated material parameters are obtained from experimental creep-recovery tests evaluated at different stress levels and constant temperature. As this type of test allows an uncoupled procedure for identifying the viscoelastic and viscoplastic material parameters, this task is divided into two stages: (i) a constrained nonsmooth optimization problem is defined and solved for the viscoelastic parameters, and (ii) the viscoplastic parameters are determined by linear regression. Thereafter, the viscoelastic and viscopiastic parameters obtained for each experimental stress level are interpolated linearly for intermediate stress conditions. Finally, a numerical-experimental example is presented, showing that the proposed procedure is able to reproduce adequately more complex loading conditions., INTRODUCTION Motivated by ever more challenging industrial requirements, technological advancements have thrusted the development of nontraditional structural materials, which frequently show improved multifunctional properties with respect to those of conventional [...]

A thermodynamically consistent rate-type viscoelastic-viscoplastic constitutive model is developed in the framework of isothermal and small deformation to describe the nonlinear and time-dependent deformation behaviors of polymers, e.g., ratchetting, creep, and stress relaxation. The model is proposed on the base of a one-dimensional Theological model with several springs and dashpot elements. The strain is divided into viscoelastic and viscoplastic parts, and the stress is also decomposed into two components. Each stress component is further divided into elastic and viscoelastic sub-components. The viscoelasticity is described by introducing pseudo potentials, and the ratchetting is considered by the viscoplastic flow which is derived by the codirectionality hypotheses. The capability of the proposed model to describe the nonlinear and time-dependent deformation of polymers is then verified by comparing the simulations with the corresponding experimental results of polycarbonate (PC) polymer. It is shown that the nonlinear and time-dependent stress-strain responses of the PC can be reasonably predicted by the proposed model., INTRODUCTION Nowadays, polymeric materials have been widely applied in many areas, such as aerospace, automotive industry, biomedicine, and civil engineering, etc., due to their low cost, high specific stiffness, capability [...]

Clays exhibit creep in compression and shear. In one-dimensional compression, creep is commonly known as 'secondary compression' even though it is also a significant component of deformations resulting from shear straining. It reflects viscous behaviour in clays and therefore depends on load duration, stress level, the ratio of shear stress to compression stress, strain rate, and temperature. Research described in the paper partitions strains into elastic (recoverable) and plastic (nonrecoverable) components. The plastic component includes viscous strains defined by a creep rate coefficient ψ that varies with plasticity index and temperature (T), but not with stress level or overconsolidation ratio (OCR). Earlier elastic-viscoplastic (EVP) models have been modified so that ψ = ψ(T) in a new elastic-thermoviscoplastic (ETVP) model. The paper provides a sensitivity analysis of simulated results from undrained (CIU) triaxial compression tests for normally consolidated and lightly overconsolidated clays. Axial strain rates range from 0.15%/day to 15%/day, and temperatures from 28 to 100°C. Key words: clay, creep, viscosity, compression, shear, creep rate coefficient, strain rate, load duration, temperature. Les argiles ont une tendance au fluage en compression et au cisaillement. En compression unidimensionelle, le fluage est communement appele << compression secondaire >>, meme si c'est aussi une composante importante des deformations resultant d'un effort de cisaillement. Il reflete un comportement visqueux dans les argiles et depend donc de la duree de charge, le niveau de stress, le rapport entre la contrainte de cisaillement a la contrainte de compression, la vitesse de deformation et la temperature. La recherche decrit les deformations de partitions de papier en composants elastiques (recuperable) et en plastiques (non recuperable). Le composant en plastique comprend des deformations visqueuses definies par un coefficient de taux de fluage ft qui varie avec l'indice de plasticite et la temperature (T), mais pas avec le rapport de surconsolidation ou du niveau de contrainte (OCR--Overconsolidation Ratio). Les modeles anterieurs elasto viscoplastiques (EVP) ont ete modifies afin que ψ = ψ(T) se retrouve dans un nouveau modele elastique-thermoviscoplastique (ETVP). Le document fournit une analyse de sensibilite de resultats simules d'essais de compression triaxiale non draines (CIU) pour l'argile normalement consolidee et legerement surconsolidee. Les taux de deformation axiale varient de 0,15%/jour a 15%/jour et les temperatures de 28 a 100°C. [Traduit par la Redaction] Mots-cles : argile, fluage, viscosite, compression, cisaillement, coefficient de taux de fluage, vitesse de deformation, duree de charge, temperature., Introduction Creep, or more formally 'viscous behaviour', is an inherent property of interparticle relationships in most natural clays, particularly if they contain bentonite, montmorillonite, and organic material; or less significantly, [...]

In this article, visco-hyperelastic constitutive model is developed to describe the rate-dependent behavior of transversely isotropic functionally graded rubber-like materials at finite deformations. Zener model that consists of Maxwell element parallel to a hyperelastic equilibrium spring is used in this article. Steady state response is described by equilibrium hyperelastic spring and rate-dependence behavior is modeled by Maxwell element that consists of a hyperelastic intermediate spring and a nonlinear viscous damper. Modified and reinforced neo-Hookean strain energy function is proposed for the two hyperelastic springs. The mechanical properties and material constants of strain energy function are graded along the axial direction based on exponential function. A history-integral method has been used to develop a constitutive equation for modeling the behavior of the model. The applied history integral method is based on the Kaye-BKZ theory. The material constant parameters appeared in the formulation have been determined with the aid of available uniaxial tensile experimental tests for a specific material and the results are compared to experimental results. It is then concluded that, the proposed constitutive equation is quite proficient in forecasting the behavior of rubber-like materials in different deformation and wide ranges of strain rate., INTRODUCTION Elastomeric materials are frequently used to diminish damage caused by impulsive or impact loads because of their low modulus, high damping, and large extensibility. For instance, buildings and bridges [...]

In this paper, a modified viscoelastic-plastic constitutive model has been proposed on the framework of Anand's work to describe the uniaxial ratcheting behavior of polycarbonate (PC) under tension-tension cyclic loading. The experimental observation illustrates that the previously accumulated deformation has an assignable influence on the subsequent material response during the ratcheting process of PC. Thus, the deformation resistance in the viscoelastic micromechanism is assumed to be evolving with the local accumulated inelastic strain rather than keeping unchanged in the original Anand's model. The proposed model is validated firstly by the monotonic tension and creep experiment results of PC. Then, its capability to describe the uniaxial ratcheting behaviors is compared with Anand model. Finally, the modified model is adopted to study the effect of mean stress, stress amplitude, loading rate, and peak holding time on the ratcheting behaviors of PC. It is shown that the proposed model can predict reasonably the uniaxial tension-tension ratcheting behavior of polymer., INTRODUCTION Polycarbonate (PC) has been extensively utilized in automatic vehicle, civil engineering and aerospace industry due to its excellent mechanical properties [1, 2], The structural components made by PC are [...]

An analysis was carried out to study the effect of thermal radiation on magnetohydrodynamic boundary layer flow and heat transfer characteristics of a non-Newtonian viscoelastic fluid near the stagnation point of a vertical stretching sheet in a porous medium with internal heat generation-absorption. The flow is generated because of linear stretching of the sheet and influenced by the uniform magnetic field that is applied horizontally in the flow region. Using a similarity variable, the governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations, which are solved numerically using an accurate implicit finite difference scheme. A comparison of the obtained results with previously published numerical results is done and the results are found to be in good agreement. The effects of the viscoelastic fluid parameter, magnetic field parameter, nonuniform heat source-sink, and the thermal radiation parameter on the heat transfer characteristics are presented graphically and discussed. The values of the skin friction coefficient and the local Nusselt number are tabulated for both cases of assisting and opposing flows. PACS Nos.: 44.35.+c, 44.20.+b, 44.30.+v, 46.35.+Z. Nous completons une etude de l'effet de la radiation thermique sur l'ecoulement de la couche limite magnetohydrodynamique et les caracteristiques du transfert de chaleur d'un fluide viscoelastique non newtonien pres du point d'arret d'une feuille verticale en extension dans un milieu poreux avec generation-absorption interne de chaleur. L'ecoulement est genere par l'extension lineaire de la feuille et influence par le champ magnetique uniforme applique horizontalement dans la region d'ecoulement. Utilisant une variable de similarite, nous transformons les equations directrices non lineaires aux derivees partielles en un ensemble d'equations differentielles ordinaires couplees et non lineaires qui sont solutionnees numeriquement a l'aide d'un schema precis de differences finies. Une comparaison indique que nos resultats sont en bon accord avec des resultats deja publies. Nous presentons graphiquement et discutons les effets du parametre de viscoelasticite du fluide, du parametre de champ magnetique, de la non uniformite de la source-puits de chaleur et du parametre de radiation thermique, sur les caracteristiques du transfert de chaleur. Nous affichons en tableau le coefficient de frottement superficiel et le nombre de Nusselt local pour les deux cas d'ecoulements en opposition et assistant. [Traduit par le Redaction], 1. Introduction The study of heat transfer on a surface embedded in a saturated porous medium has attracted considerable attention in recent decades because of many engineering applications, such as [...]

The viscoelastic continuum damage model, developed based on Schapery's correspondence principle and the continuum damage mechanics, has received a great deal of attention because of its mathematical soundness and effectiveness in describing damage growth in viscoelastic media and has been used to make reliable estimations on the fatigue lives of asphalt mixtures. Its applications to field mixtures, however, have been limited because the model requires performing the uniaxial tension test. As an alternative, this study developed an analytical methodology for applying the model to the indirect tension test, which has been successfully used in testing both laboratory-made and field-cored mixtures. From the results of the indirect tension tests conducted on asphalt mixture at three different crosshead-controlled rates, it was found that the stress-pseudostrain curves could be superimposed onto one equality line in the linear viscoelastic range of the given mixture, and its rate dependency was successfully eliminated in the [C.sub.1] and [S.sub.1] plots. This indicates that the methodology developed for the indirect tension test has a capability of evaluating damage development in asphalt mixtures through the viscoelastic continuum damage model. It would be potentially of great benefit to pavement engineers who want to estimate the remaining lives of field mixtures. DOI: 10.1061/(ASCE)EM.1943-7889.0000094 CE Database subject headings: Asphalts; Mixtures; Poisson ratio; Viscoelasticity; Cyclic tests; Biaxial tests; Stiffness; Tensile strength; Damage; Temperature effects. Author keywords: Asphalts; Mixtures; Poisson ratio; Viscoelasticity; Cyclic tests; Biaxial tests; Stiffness; Tensile strength; Damage.

This paper presents a viscoelastic model of asphalt mixtures with the discrete element method, where the viscoelastic behaviors of asphalt mastics (fine aggregates, fines, and asphalt binder) are represented by a Burger's model. Aggregates are simulated with irregular shape particles consisting of balls bonded together by elastic contact models, and the interplaces between aggregates are filled with halls bonded with viscoelastic Burger's model to represent asphalt mastic. Digital samples were prepared with the image analysis technique. The micromechanical model was developed with four constitutive laws to represent the interactions at contacts of discrete elements (balls) within an aggregate, within mastic, between an aggregate and mastic, and between two adjacent aggregates. Each of these constitutive laws consists of three parts: a stiffness model, a slip model, and a bonding model in order to provide a relationship between the contact force and relative displacement and also in order to describe slipping and tensile strength at a particular contact. The relationship between the microscale model input and macroscale material properties was derived, and an iterative procedure was developed to fit the dynamic modulus test data of asphalt mastic with Burger's model. The favorable agreement between the discrete element prediction and the lab results on dynamic moduli and phase angles indicates that the viscoelastic discrete element model developed in this study is very capable of simulating constitutive behavior of asphalt mixtures. CE Database subject headings: Asphalts; Mixtures; Discrete elements; Viscoelasticity; Simulation.

We propose a micromechanics model for aging basic creep of early-age concrete. Therefore, we formulate viscoelastic boundary value problems on two representative volume elements, one related to cement paste (composed of cement, water, hydrates, and air), and one related to concrete (composed of cement paste and aggregates). Homogenization of the 'nonaging' elastic and viscoelastic properties of the material's contituents involves the transformation of the aforementioned viscoelastic boundary value problems to the Laplace-Carson (LC) domain. There, formally elastic, classical self-consistent and Mori-Tanaka solutions are employed, leading to pointwisely defined LC-transformed tensorial creep and relaxation functions. Subsequently, the latter are back- transformed, by means of the Gaver-Wynn-Rho algorithm, into the time domain. Temporal derivatives of corresponding homogenized creep and relaxation tensors, evaluated for the current maturation state of the material (in terms of current volume fractions of cement, water, air, hydrates, and aggregates; being dependent on the hydration degree, as well as on the water-cement and aggregate-cement ratios) and for the current time period since loading of the hydrating composite material, allow for micromechanical prediction of the aging basic creep properties of early-age concrete. CE Database subject headings: Micromechanics; Viscoelasticity; Concrete; Creep.

A one-dimensional model of the two-temperature generalized magneto-viscoelasticity with two relaxation times in a perfect conducting medium is established. The state space approach is adopted for the solution of one-dimensional problems for any set of boundary conditions. The resulting formulation together with the Laplace transform techniques are applied to a specific problem of a half-space subjected to thermal shock and traction-free surface. The inversion of the Laplace transforms is carried out using a numerical approach. Numerical results are given and illustrated graphically for the problem. Some comparisons have been shown in figures to estimate the effects of the temperature discrepancy and the applied magnetic field. PACS No: 62.40.+i Nous construisons un modele a une dimension de la magnetoviscoelasticite generalisee a deux temperatures avec deux temps de relaxation dans un milieu parfaitement conducteur. Nous appliquons ce formalisme, avec l'aide de la transformee de Laplace, a l'etude du proble'me d'un demi-espace sujet a un choc thermique et une surface sans traction. Les transformees inverses de Laplace sont evaluees numeriquement. Nous presentons nos resultats numeriques pour ce probleme et les illustrons graphiquement. Des figures montrent des comparaisons qui ont ete faites pour estimer les effets de l'ecart de temperature et du champ magnetique applique. [Traduit par la Redaction], 1. Introduction Linear viscoelasticity remains an important area of research not only due the advent and use of polymers, but also because most solids when subjected to dynamic loading exhibit [...]

A nonlinear rubber material model is presented, where influences of frequency and dynamic amplitude are taken into account through fractional order viscoelasticity and plasticity, respectively. The problem of simultaneously modeling elastic, viscoelastic, and friction contributions is removed by additively splitting them. Due to the fractional order representation mainly, the number of parameters of the model remains low, rendering an easy fitting of the values from tests on material samples. The proposed model is implemented in a general-purpose finite element (FE) code. Since commercial FE codes do not contain any suitable constitutive model that represents the full dynamic behavior of rubber compounds (including frequency and amplitude dependent effects), a simple approach is used based on the idea of adding stress contributions from simple constitutive models: a mesh overlay technique, whose basic idea is to create a different FE model for each material definition (fractional derivative viscoelastic and elastoplastic), all with identical meshes but with different material definition, and sharing the same nodes. Fractional-derivative viscoelasticity is implemented through user routines and the algorithm for that purpose is described, while available yon Mises' elastoplastic models are adopted to take rate-independent effects into account. Satisfactory results are obtained when comparing the model results with tests carried out in two rubber bushings at a frequency range up to 500 Hz, showing the ability of the material model to accurately describe the complex dynamic behavior of carbon-black filled rubber compounds. [DOI: 10.1115/1.2999454] Keywords: rubber, dynamic stiffness, viscoelasticity, Fletcher-Gent effect, FE code, vibration isolator

Following the previous paper, 'Full two-dimensional model for rolling resistance: Hard cylinder on viscoelastic foundation of finite thickness,' addressing modeling of rigid cylinder rolling against viscoelastic foundation of finite thickness, this paper focuses on the development of a rigorous full two-dimensional semianalytical model for viscoelastic rollers with layered structure rolling against a rigid ground. In this model, the polar coordinate system is used, the solution is expanded into a set of Fourier series corresponding to the angular coordinate, the frequency domain master curves of G' and G' characterizing the general viscoelastic properties for a viscoelastic material are used to relate Fourier coefficients, and a special condensed structure model based on the Fourier series is developed to handle viscoelasticity and the rolling contact boundary condition. Examples are given to show the model capabilities to efficiently handle rolling resistance and contact stresses, and capture major characteristics of standing-wave phenomenon, such as sharp rise of rolling resistance, emergence of standing waves and material dynamic softening as the rolling speed approaches a critical value. The methodology may be of interest to industrial roller designers. DOI: 10.1061/(ASCE)0733-9399(2009)135:1(20) CE Database subject headings: Viscoelasticity; Tires; Standing waves; Cylinders; Two-dimensional models.

Abstract: A mathematical model of the viscoelastic phenomenon, employing the fractional derivative Maxwell Model (FDMM) is analyzed in order to determine its consistency with thermodynamic principles. In particular, the development [...]

The time-dependent mechanical properties of the porcine esophagus were investigated experimentally and theoretically. It was hypothesized that the viscoelasticity was quasilinear, i.e., the time and strain effects were independent. In order to verify the separability of time and strain effects, the stress-relaxation test was conducted at various strains and the data were fitted with the Fung's quasilinear viscoelastic (QLV) model. By using the material parameters obtained from the stress relaxation test, the cyclic peak stress and hysteresis were predicted. Results showed that the stress relaxed by 20-30% of the peak stress within the first 10 s and stabilized at ~50% at the time of 300 s. The relative stress relaxation [R.sub.2] (i.e., the difference of stress at a particular time to the final equilibrium stress normalized by the total difference of the peak and final stress) was not different significantly for various strains. It was also found that, by using the stress-time data during both the ramp and relaxation phases, the correlation between parameters was substantially reduced. The model could also predict the cyclic peak stress and hysteresis except for the underestimate of valley stress. We conclude that the QLV model could be used as the material characterization of the esophageal tissue. [DOI: 10.1115/1.2372473] Keywords: quasilinear viscoelasticity (QLV), incremental stress relaxation test, cyclic test, hysteresis, esophagus

We have measured the time-resolved adsorption kinetics of the mussel adhesive protein (Mefp-1) on a nonpolar, methyl-terminated (thiolated) gold surface, using three independent techniques: quartz crystal microbalance with dissipation monitoring (QCM-D), surface plasmon resonance, and ellipsometry. The QCM-D and ellipsometry data shows that, after adsorption to saturation of Mefp-1, cross-linking of the protein layer using NaI[O.sub.4] transforms it from an extended (~20 nm), water-rich, and hydrogel-like state to a much thinner (~5 nm), compact, and less water-rich state. Furthermore, we show how quantitative data about the thickness, shear elastic modulus, and shear viscosity of the protein film can be obtained with the QCM-D technique, even beyond the Sauerbrey regime, if frequency (f) and energy dissipation (D) measurements measured at multiple harmonics are combined with theoretical simulations using a Voight-based viscoelastic model. The modeling result was confirmed by substituting [H.sub.2]O for [D.sub.2]O. As expected, the [D.sub.2]O substitution does not influence the actual adsorption behavior, but resulted in expected differences in the estimated effective density and shear viscosity. These results provide new insight and understanding about the adsorption kinetics and cross-linking behavior of Mefp-1. They also demonstrate how the above three techniques complement each other for biomolecule adsorption studies.

The problem of a smooth rigid indentor under variable loading moving across a viscoelastic half-space in one direction with variable speed is considered. The motion is assumed to be frictionless and the standard linear model is adopted to describe the viscoelastic material response. An integral equation is derived and a numerical algorithm for its solution subject to appropriate subsidiary conditions is constructed. The contact interval length, pressure, and coefficient of hysteretic friction are presented and the results discussed. [DOI: 10.1115/1.1354622]

Analysis of the irradiated Zircaloy-4 cladding tube data on biaxial tensile, creep, and relaxation tests demonstrate radiation hardening and creep strain reduction. Also presented is a viscoplastic model to simulate uni- and biaxial tensile, creep, and relaxation tests at temperatures between 350 C and 400 C and fluences.

Traction measurements for two kinds of synthetic naphthenic traction oils were carried out, using a two-roller machine. The Eyring stress and shear modulus of test oils were estimated simultaneously by a curve-fitting procedure based on the nonlinear viscoelastic model introduced by Johnson and Tevaarwerk. As a consequence, it has been found that the Eyring stress decreases with an increase in contact pressure, and it increases with oil temperature. It has been also clarified that the effective shear modulus, including the effect of the roller compliance, decreases with an increase in contact pressure. At higher pressure it decreases as the oil temperature increases, whereas at lower pressure it increases with the oil temperature. In addition, the influences of operating conditions such as the kind of oil, pressure, and oil temperature upon the Eyring stress, shear modulus, and traction coefficient were also investigated. It has been shown that under the operating conditions where the effect of oil viscosity is predominant, the accuracy of the shear modulus calculation deteriorates when the shear modulus is estimated by assuming that the oil is perfectly elastic.

Nonlinear viscoelastic analysis was used to characterize the time-dependent behavior of mesenchymal gap tissue generated during distraction osteogenesis. Six (n = 6) lengthened tibiae were harvested from New Zealand white rabbits at 18 days. This gap tissue was subjected to a series of step displacement tests of increasing magnitude, and force relaxation behavior was monitored. Isochrones in stress-strain space were fit to odd cubic functions of strain. An analytic expression, linear in both e and e3, was developed to predict stress accumulation within the gap tissue as a function of time during distraction. Stress relaxation functions were described well by two-term Prony series. The two time constants determined from mechanical testing results were consistent, suggesting the presence of two fundamental physiologic relaxation processes. Gap tissue stresses were predicted to rise considerably during early stages of lengthening when distraction magnitudes exceeded the clinical norm of 0.25 mm. These differences in tension accumulation were less pronounced by the time lengthening was completed. Specifically, these results may in part explain clinical observations of decreased bone regeneration and altered tissue proliferation and differentiation at higher distraction rates. More generally, this work provides a framework for the rigorous characterization of the viscoelastic properties of biologic tissues ordinarily exposed to step strains.

A computational method is proposed for simulating rheological phenomena of a body composed of a material such as soft soil, powder, and granular material under large excitations. These phenomena are considered to be elastic-viscoplastic (E-VP) flows with moving boundaries. Fundamental equations for the dynamics are constructed from the Eulerian viewpoint. The constitutive laws for pressure volume and deviatoric stress strain are E-VP and are expressed by differential equations. The pressure and deviatoric stress are combined to satisfy yield conditions. The equations construct the first-order partial differential equation system. A domain containing an E-VP body is divided into cells by applying a finite difference method to the partial differential equation system. The locations of markers distributed in the body are calculated to trace the moving free boundaries. The collapse of an E-VP square body is shown as an application example.

A viscoelastic constitutive model of asphalt mixtures that accounts for the rate-dependent damage growth and microdamage healing is presented in this paper. An elastic continuum damage model, which is based on thermodynamics of irreversible processes with internal state variables, is first reviewed and extended to a corresponding viscoelastic model using an elastic-viscoelastic correspondence principle. A rate-type internal state evolution law is employed to describe the damage growth and microdamage healing in asphalt concrete. An analytical representation of the model is established for the uniaxial loading condition. Tensile uniaxial cyclic tests were performed under the controlled-strain mode with different strain amplitudes to determine model parameters. The resulting constitutive model successfully predicts the damage growth and recovery in asphalt concrete under multilevels of loading, varying rates of loading, different modes of loading (controlled-strain and controlled-stress), and random rest periods.

The transient elastic and viscoelastic thermal stresses that take place during laser drilling of ceramics were investigated using numerical simulation methods. Elastic and viscoelastic thermal stress models were integrated into a two-dimensional drilling code to examine the mechanism of thermal stresses that account for cracks and decrease in strength. It was found that elastic and viscoelastic thermal stresses develop and decay during the drilling process as shown by drill geometry and temperature field calculations.

A constitutive model is derived for the viscoelastic behavior of physically aged amorphous polymers under non-isothermal loading. The model is based on the concept of transient reversible networks, where a polymeric material is treated as a network of active chains (adaptive links) that break and reform because of micro-Brownian motion. The breakage and reformation rates for active chains in an aged medium are assumed to depend on the current temperature and the time after cooling below the glass transition temperature. To validate the model, the long-term viscoelastic response is predicted on the basis of data obtained in the standard short-term creep tests and compared with data from long-term experiments. Fair agreement is demonstrated between numerical results and observations. The model is used to calculate residual stresses in a polymeric spherical pressure vessel cooled down (after curing) to the room temperature. It is shown that physical aging of the polymer significantly affects stresses and displacements in the vessel., 1 INTRODUCTION The paper is concerned with the non-isothermal viscoelastic behavior of physically aged polymers. Our objective is twofold: (i) to derive a constitutive model for the long-term viscoelastic response [...]

A constitutive equation of the differential type is introduced to model the nonlinear viscoelastic response behavior of elastomeric bearings in large-scale system simulations for vibration assessment and component loads prediction. The model accounts for the nonlinear dependence of dynamic stiffness and damping on vibration amplitude commonly observed in the behavior of bearings made of particle-reinforced elastomers. A testing procedure for the identification of the model parameters from bearing component test data is described. The experimental and analytical results for predicting the behavior of four (4) different car bushings are presented. In an example application, the model is incorporated in an ADAMS simulation to study the dynamic behavior of a car rear suspension.

This paper presents a mechanistic approach to uniaxial viscoelastic constitutive modeling of asphalt concrete that accounts for damage evolution under cyclic loading conditions. Schapery's elastic-viscoelastic correspondence principle is applied as a means of separately evaluating viscoelasticity and time-dependent damage growth in asphalt concrete. The time-dependent damage growth in asphalt concrete is modeled by using a damage parameter based on a generalization of microcrack growth law. Internal state variable formulation was used in developing the analytical representation of the model. Tensile uniaxial fatigue tests were performed under the controlled-strain mode to determine model parameters. Then, the resulting constitutive equation was used to predict the stress-strain behavior of the same materials under controlled-stress mode. The constitutive equation proposed in this paper satisfactorily predicts the constitutive behavior of asphalt concrete all the way up to failure under various loading conditions including different stress-strain amplitudes, monotonic versus cyclic loadings, and different modes of loading.

Principles of continuum mechanics were utilized to create a viscoelastic model of finitely deforming rubber. This model was subjected to finite element analysis using numerical simulation and nonlinear finite element approximation. The validity of the model was verified by simulating uniaxial stretch tests at varying stretch rates. Experimental results confirmed the model's validity.

A new constitutive model is derived for the viscoelastic behavior of polymers under non-isothermal loading. The model extends the Tobolsky concept of adaptive links (entanglements) between polymeric molecules to thermoviscoelastic media. Employing this model, we calculate residual stresses built up in an epoxy resin plate under cooling from the rubber-glass transition temperature, analyze the effect of material parameters on residual stresses, and compare results of numerical simulation with experimental data., 1. INTRODUCTION This paper is concerned with constitutive relations for non-isothermal loading of viscoelastic media in the vicinity of the rubber-glass transition temperature. The subject is of essential interest because [...]

A fractional integral viscoelasticity model was developed. It consists of a single fractional integral operator which acts on stress and strains. The model was compared with the fractional derivative viscoelasticity model, which was found to have the same constitutive advantages as the latter and to have a unique relation between excitation and response. However, the requirement of stored time histories of acceleration and displacement were cited as the major drawback of the model.

The effects of temperature on the energy dissipation of viscoelastic dampers for seismic mitigation of structures are investigated. To simulate the damper behavior, an evolutionary model is proposed to describe the dependence of the mechanical properties of the damper on the deformation frequency and the temperature increase due to dissipation. Thermorheologically simple materials are considered and the influence of the deformation frequency on the storage and loss moduli is modeled using fractional derivative operators. The effect of material temperature on the force-deformation relation is modeled using the concept of evolutionary transfer function, and the proposed model is implemented using a step-by-step technique in the frequency domain. The predictions of the proposed model in the case of sinusoidal and seismic deformations show good agreement with experimental results. Finally, the response spectra of single-degree-of-freedom structures with added vis-coelastic dampers and subjected to seismic excitation are computed using the proposed evolutionary model; the results obtained show that the thermal effect due to energy dissipation is not always negligible.

A model based on the discrete element method (DEM), ASBAL, was developed by modifying the TRUBAL program to simulate hot mix asphalt (HMA). To represent asphalt cement, several viscoelastic elements (i.e., Maxwell, Kelvin-Voigt, and Burger's elements) were considered. The research results from the Strategic Highway Research Program (SHRP) were used for the selection of proper element. From these viscoelastic elements the Burger linear viscoelastic element is shown to be the most promising element for modeling asphalt binder behavior, based on mechanical responses and comparisons with physical experimental results. Therefore, Burger's elements were added in normal and tangential directions to each aggregate-asphalt-aggregate contact to simulate the asphalt binder in HMA assemblies. This new model is called ASBAL (TRUBAL for Asphalt). Several monotonic and cyclic tests were simulated to observe and fine-tune the model ASBAL. A carefully conducted physical experiment with X-ray tomographs was simulated and compared. The simulation based on the ASBAL model compared well with experimental results.

A study developed a model that can be used to predict transient stress distributions in wound rolls made of orthotropic viscoelastic materials with nonlinear moduli. The viscoelastic behavior is characterized by a generalized Maxwell model with allowance for pressure dependent radial behavior. The numerical results agree with the analytical solution for a simplified isotropic case and with other published works regarding this subject.

The analysis of viscoelastic continua and spatial frames may be related back to the study of the RLC (resistance, inductance, and capacitor lumped constant) electrical network by considering the analogy existing between the stress-strain relationships in the viscoelastic materials and the current-potential relationships in the electric circuits. The proposed analogy is also a consistent tool for the evaluation of creep in spatial structures composed of rectilinear frames. The theoretical bases of this possible application are brought out and a numerical example is presented. The main contribution of this work is the development of the electrical analogy to the solution of dynamic systems excited by time-dependent loads. The theoretical formulation of a free dynamic system is extensively discussed and a numerical example shows its easy applicability to a spatial framework. As far as the analysis of damped structures is concerned, two different models of a single-degree-of-freedom system are proposed.

The poor solutions of numerical simulations at a contraction has often been attributed to the numerical scheme used. However, the solution of a numerical simulation is also highly dependent on the constitutive equation. A study of various constitutive equations on the simulation of the 4:1 contraction flow is made in this paper, and their effects on the results analyzed. The constitutive models considered include the Upper Convected Maxwell model, the Oldroyd-B model, the White-Metzner model, the Phan-Thien-Tanner model and the Giesekus-Leonov model. It was found that although the Phan-Thien-Tanner model gave the best results, the solution at higher shear rates were still not satisfactory., INTRODUCTION With the increasing use of computers, research in the simulation of molding processes gained importance in the 1970s. Initial simulations were done using analytical solutions or the Hele-Shaw equations, [...]

In this paper the causality of linear viscoelastic models with complex coefficients is examined. Such constitutive models have been found effective in describing the response of practical dampers and other dissipation devices used for seismic protection of structures. Complex-parameter viscoelastic models must be subjected only to complex-valued excitations that are analytic functions, i.e., their imaginary and real parts are related with the Hilbert transform. First, it is shown that the resulting force from complex parameter constitutive models is also an analytic signal. Subsequently, the analyticity of the impedances of constitutive models with complex-coefficients is investigated and it is found that under certain conditions they satisfy the Kramers-Kronig relations. These relations ensure that the differential operator used in the model is causal; however, the entire model (differential operator and analytic input) is noncausal, since the Hilbert transform needed to construct the analytic input requires information from the future. Finally, a general real-valued representation of these models is developed. Real-valued representations are needed when the analysis of the response is performed in the time domain using step-by-step integration techniques. Time-domain techniques are necessary when the proposed constitutive models describe devices which are incorporated in structures that exhibit nonlinear response. The equivalence between complex-valued and real-valued representations is shown through a practical example, and the noncausality of these models is analyzed.

The implementation of a comprehensive viscoelastic modeling of the oxidation of silicon improves the numerical modeling of the local oxidation of silicon process for mass-production of integrated circuits. The model is based on the deformation of silicon and includes the viscoelastic behavior of oxide and nitride. The calculations of oxide shapes and stresses due to oxidation in silicon substrate display the predictive capacities of the model.

A general continuum model for the nonlinear viscoelastic behavior of soft biological tissues was formulated. This single integral finite strain (SIFS) model describes finite deformation of a nonlinearly viscoelastic material within the context of a three-dimensional model. The specific form describing uniaxial extension was obtained, and the idea of conversion from one material to another (at a microscopic level) was then introduced to model the nonlinear behavior of ligaments and tendons. Conversion allowed different constitutive equations to be used for describing a single ligament or tendon at different strain levels. The model was applied to data from uniaxial extension of younger and older human patellar tendons and canine medial collateral ligaments. Model parameters were determined from curve-fitting stress-strain and stress-relaxation data and used to predict the time-dependent stress generated by cyclic extensions.

A mathematical model is formulated to simulate dam-break transient debris flows, in which the debris and water mixture is assumed to be isotropic and continuous. In terms of its viscoelastoplasticity, a three-dimensional (3D) rheologic model for Bingham body is used to describe the relationship between the stress tensor and the rate of strain. Only the deformation caused by the deviatoric stress tensor is taken into account. Under the prior considerations, the governing equations for two-dimensional (2D) depth-averaged transient debris flows are obtained by integrating the equation of continuity and equations of motion over depth for 3D flows. To deal with the transient and high-speed features of dam-break debris flows, the derived governing equations are discretized and solved using the method of characteristics. The model is applied to simulate the dam-break debris flow of April 30, 1986, for the Jinshan debris reservoir in Anhui, China. The debris and water mixtures reach as far as 900 m downstream from the initial tailings dam site, with a depth of 1.7 m near the tailings dam and 1.0 m at 900 m downstream. These model results are in good agreement with the available observations.

Recently, Friedrich proposed an empirical model for linear viscoelastic fluids corresponding to a constitutive equation with fractional derivatives [Phil. Mag. Lett., 66, 287 (1992)]. For this model, the relaxation modulus, the dynamic moduli, the relaxation time spectrum, and other material functions have been explicitly calculated as a function of the few parameters that characterize a viscoelastic fluid within this model. By fitting this model to experimental data, the model parameters can be determined and other material functions, in particular the relaxation time spectrum, can be calculated immediately. This paper reports to what extent this method, which may be called analytical inversion, is appropriate for the determination of relaxation time spectra. For that purpose, the spectra of a number of very different polymeric materials are determined with this method. The spectra calculated in this way are compared with the spectra obtained by nonlinear regularization. It turns out that the empirical model describes the linear viscoelastic properties of a variety of different materials with high accuracy. Keeping in mind that the determination of the relaxation time spectrum requires the solution of an ill-posed problem, the agreement between the relaxation time spectra obtained by analytical inversion and by regularization is satisfactory for these materials., INTRODUCTION The determination of the relaxation time spectrum from experimental data for a material function is one of the oldest tasks in rheology. It is, however, not an easy task, [...]

This paper presents an analytical model for predicting the hysteretic behavior of viscoelastic dampers based on the Boltzmann's superposition principle and the method of reduced variables. The model parameters have physical meaning and they can be determined from simple time-domain and frequency-domain tests. The presented model is checked against damper tests performed under different strain inputs and shows good results. Test procedure and determination of model parameters are also discussed. Under certain conditions, it is shown that a significant simplification results in determining the frequency and temperature dependency of the shear storage and shear loss moduli of the viscoelastic material, leading to useful applications to viscoelastic damper design and structural applications. Finally, the presented model is compared with the ones based on the concept of fractional derivatives.