Viscoelastic Rheological Model Research Articles

Viscoelastic Rheological Modelling of the Lateral Dynamic Response of Ballasted Railway Tracks

This article presents a novel methodology for evaluating the response of ballasted railway tracks under train-induced loading along lateral directions. The main focus of this study is the development of a computational technique that can capture the lateral response of ballasted railway tracks, which has been ignored in past studies. The proposed approach employs a viscoelastic rheological track model in which three substructure layers are simulated using discrete masses, Hooke’s (springs) and Newtonian elements (dampers). The methodology is successfully validated against the data from experimental and analytical investigations published in the literature. Subsequently, parametric investigations are conducted to study the influence of axle load, train speed, and granular layer thickness on the track response. The results indicate that as the axle load (20 to 40 t) and train speed (70 to 200 km/h) are increased, there is a corresponding increase in track displacements (both lateral and vertical) by 100% and 26.2%, respectively. However, an increase in the granular layer thickness (0.1 to 0.75 m) reduces ballast top displacement (lateral and vertical) by 20–30%. The results demonstrate the capability of the proposed computational approach to capture the transient response of railway tracks and the influence of neighbouring layer properties on the track response. The proposed methodology can be helpful to practising railway engineers for assessing the performance of ballasted railway tracks along lateral directions.

Modeling of temperature effect on electromechanical properties of dielectric elastomer minimum energy structures

Due to the characteristics of large deformation and fast response to excitation voltage, dielectric elastomer minimum energy structures (DEMES) can actively adjust its shape to adapt to the complex environments, which is a research hotspot in the field of soft robotics. The electromechanical properties of DEMES are sensitive to temperature variation. However, the analysis of the effect of temperature on the viscoelastic dynamic behavior of DEMES is incomplete in existing studies. In this paper, an analytical framework for investigating the electromechanical performances of DEMES actuator is presented. By introducing the effects of temperature on the dielectric constant and elastic modulus of DEMES actuator, the governing equations of motion for the underlying non-conservative system affected by temperature are established by combining the DE viscoelastic rheological model and the Euler-Lagrange equation. The proposed model is used for building insights into the effect of temperature on the stiffness, equilibrium state, actuation range and the evolution law of the dynamic response under the DC and AC excitations of DEMES. The results show that a significant enhancement in the equilibrium angle attained by the structure with the improving of the temperature is observed, indicating a favorable impact of ambient temperature. Phase paths and Poincaré maps are presented for assessing the temperature effect on the stability and periodicity of the nonlinear oscillations. The frequency responses of the actuator for the AC loads indicate that a suitable temperature can significantly improve the dynamic performance and stability of DEMES actuator. The proposed analytical model and results presented in this study can provide guidance for the design and development of DEMES based soft robot subjected to harsh environments.

A Comparative Study of Viscoelastic Rheological Models Using Finite-Difference Method and an Evaluation of the Seismic Attenuation in the Búzios Field Data

A Comparative Study of Viscoelastic Rheological Models Using Finite-Difference Method and an Evaluation of the Seismic Attenuation in the Búzios Field Data

Viscoelastic rheological models for guided acoustic waves: Single mode at high frequency and second harmonic generation of Lamb and SH modes

The previous published work by Othmani et al. invites a further useful discussion on how the viscoelastic rheological model affects the second harmonic and single modes of guided waves. However, this paper has two main objectives. The first objective is to establish a simple relationship between the Rayleigh waves velocity (VR), fundamental Lamb modes (A0 and S0), and the shear wave velocity (VS) in unidirectional viscoelastic carbon–epoxy at high frequency. The second objective is to study the second harmonic Lamb modes. Numerical codes based on Legendre polynomial and Newton–Raphson methods are developed and implemented to predict dispersion and attenuation curves. The second harmonic generation was investigated with the hysteretic and Kelvin–Voigt viscoelastic models. Results showed that rheological models have a much larger effect on the attenuation curves than the ones on the dispersion trajectories. Additionally, the optimal angles of Lamb and SH modes in unidirectional carbon–epoxy under Snell‐Descartes law was investigated. The present numerical results may render as a useful message for the rheological community.

Experimental evidence of shear waves in fractional viscoelastic rheological models.

Fractional viscoelastic rheological models, such as the Kelvin Voigt Fractional Derivative model, have been proposed in the literature for modelling shear wave propagation in soft tissue. In this article, our previously developed wave propagation model for transluminal propagation based on a Kelvin Voigt Fractional Derivative wave equation is experimentally validated. The transluminal procedure uses the transmission and detection of shear waves through the luminal wall. The model was compared against high-speed camera observations in translucent elastography phantoms with similar viscoelastic properties to prostate tissue. An ad hoc cross-correlation procedure was used to reconstruct the angular displacement from the high-speed camera observations. Rheometry and shear wave elastography were used for characterising the shear wave velocity dispersion curve for the phantoms. Fractional viscoelastic properties were derived after fitting the dispersion curve to its analytical expression. Propagation features and amplitude spectra from simulations and high-speed camera observations were compared. The obtained results indicate that the model replicates the experimental observations with acceptable accuracy. The model presented here provides a useful tool to model transluminal procedures based on wave propagation and its interaction with the mechanical properties of the tissue outside the lumen.

Size-dependent translational velocity of phospholipid-coated bubbles driven by acoustic radiation force

This study investigates how the translational velocity of phospholipid-coated bubbles caused by acoustic radiation force depends on their size. The translations of bubbles with mean radii of 0.9–5 μm were experimentally evaluated at five ultrasound frequency conditions (3.5, 5, 7.5, 10, and 15 MHz). We compared experimental data with theoretical prediction using a viscoelastic interfacial rheological model and a model suitable for high amplitude oscillation. The results suggested that the translation of bubbles could be enhanced for a mean radius of 1–3 μm but echo intensity could not.

Simulating Airborne Ultrasound Vibrations in Human Skin for Haptic Applications

The ability to focus high amplitude ultrasound onto human skin and elicit a tactile sensation in mid-air poses a number of scientific opportunities and challenges. For example, a common issue with mid-air haptics is the relatively low forces generated on the user’s skin, thus limiting the dynamic range of vibrotactile sensations that can be induced. To that end, we develop a viscoelastic rheological finite element model and apply it to show that different acoustic radiation patterns can generate varying forces, displacements, and oscillatory patterns on the targeted skin and its nearby vicinity. Our framework allows for the high resolution computational exploration of a wide range of mid-air stimulus sensations saving time and resources spent on running expensive experiments while.

Stability bounds of a delay visco-elastic rheological model with substrate friction.

Cells and tissues exhibit sustained oscillatory deformations during remodelling, migration or embryogenesis. Although it has been shown that these oscillations correlate with intracellular biochemical signalling, the role of these oscillations is as yet unclear, and whether they may trigger drastic cell reorganisation events or instabilities remains unknown. Here, we present a rheological model that incorporates elastic, viscous and frictional components, and that is able to generate oscillatory response through a delay adaptive process of the rest-length. We analyse its stability as a function of the model parameters and deduce analytical bounds of the stable domain. While increasing values of the delay and remodelling rate render the model unstable, we also show that increasing friction with the substrate destabilises the oscillatory response. This fact was unexpected and still needs to be verified experimentally. Furthermore, we numerically verify that the extension of the model with non-linear deformation measures is able to generate sustained oscillations converging towards a limit cycle. We interpret this sustained regime in terms of non-linear time varying stiffness parameters that alternate between stable and unstable regions of the linear model. We also note that this limit cycle is not present in the linear model. We study the phase diagram and the bifurcations of the non-linear model, based on our conclusions on the linear one. Such dynamic analysis of the delay visco-elastic model in the presence of friction is absent in the literature for both linear and non-linear rheologies. Our work also shows how increasing values of some parameters such as delay and friction decrease its stability, while other parameters such as stiffness stabilise the oscillatory response.

Nonlinear IGABEM formulations for the mechanical modelling of 3D reinforced structures

The adequate coupling of dissimilar materials and structural element types provides effective engineering designs. Particularly, it enables high stiffness and low weight mechanical components, which are largely desired in numerous applications. Besides, Isogeometric Analysis (IGA) has recently stood out as a robust and accurate approach for the mechanical modelling of complex 3D engineering designs directly from Computer-Aided Design (CAD) tools. In this context, this study presents nonlinear Isogeometric Boundary Element Method (IGABEM) formulations for the effective mechanical modelling of nonhomogeneous 3D structural systems reinforced by embedded fibres. The IGABEM based on NURBS surfaces represents the solid whereas the 1D approach of BEM models the reinforcements, which characterises a 1DBEM/IGABEM coupling technique. The sub-region technique enables the nonhomogeneous system modelling whereas connection 1DBEM elements allow for crossing reinforcements along boundary interfaces without the need for surfaces remeshing. Thus, the CAD model information can be straightforwardly used in the mechanical model. Nonlinear time independent formulations are presented accounting for both elastoplastic and bond-slip behaviours. Besides, linear and nonlinear time dependent formulations are presented herein applying the Kelvin-Voigt and Boltzmann viscoelastic rheological models. Five applications illustrate the accuracy and robustness of the proposed formulations. The IGABEM formulations lead to accurate and stable results, in addition to efficient modelling. Besides, it demonstrates excellent performance considering the computational time consuming and the total number of degrees of freedom in each application.

Analysis of the Influence of Fatigue Strength of Prototype Under Ballast Mats (UBMs) on the Effectiveness of Protection against Vibration Caused by Railway Traffic.

The present paper focuses on laboratory tests of fatigue strength of prototype under ballast mats (UBMs), carried out according to the procedure described in the new European standard EN 17282, which was released in October 2020. The mineral wool-based mat revealed significant differences in the values of static and dynamic characteristics, measured before and after the fatigue tests. The elastomeric mats based on recycled materials (SBR granulate and fibers) turned out to have had sufficient durability and effectiveness of protection against vibration caused by railway traffic. The values of static and dynamic bedding moduli, determined before and after the fatigue tests, were used to develop a viscoelastic rheological model of the vibration isolator with the use of fractional derivatives. Using this original model of the ballasted track system with four degrees of freedom, a significant influence of cyclic loading on the level of vibration suppression (insertion loss factor) was demonstrated. The analytical model confirmed that the mats with variations of bedding moduli exceeding 10% should not be used as resilient elements.

Research on viscoelastic fluid unsteady flow model based on torque loss correction

To address the complexity of unsteady shear flow in the initial start-up stage of rheometers, a model considering torque losses in motors and fixtures was developed based on the true torque balance relationship at the rotor boundary of the rheometer and the constitutive equation of the viscoelastic rheological model. The viscoelastic fluid transient flow model was established, and the real wall stress expression of unsteady shear flow of the viscoelastic fluid in the initial stage was obtained. The reliability of the model was verified by comparing the result from the analytical model with numerical calculation. The impact of the geometric dimensions of the test system and the material viscoelastic characteristics on the transient test was analyzed. The results show that the non-uniform velocity distribution has little effect on the initial strain response in the gap of the actual test system of the rheometer. The oscillation curves of strain and stress obtained by numerical and analytical methods coincide completely, proving the reliability of the model in characterizing the transient flow. For a Jeffery fluid, the elastic modulus G mainly affects the oscillation period and amplitude, the parallel viscosity pots η1 mainly impact the amplitude and oscillation attenuation speed, and the series clay pots η2 mainly influence the slope of the strain curve. The greater the system inertia, the more significant the creep oscillation in the unsteady flow process. The coupling between the test system inertia and the viscoelasticity fluid is the essential cause of the creep oscillation. Combined with the mechanical response characteristics of rheometer, a Jeffery model based on short term correction and torque loss was established. The model can accurately describe the strain time curve of gelled crude oil in the initial unsteady flow stage. The results of this study can help understand the rheological properties of materials in the transient start-up process.

Flow dynamics of vitreous humour during saccadic eye movements

In this work, we reveal the flow dynamics of Vitreous Humour (VH) gel and liquid phases during saccadic movements of the eye, considering the biofluids viscoelastic character as well as realistic eye chamber geometry and taking into account the saccade profile. We quantify the differences in the flow dynamics of VH gel and liquid phases using viscoelastic rheological models that are able to model the VH shear rheology, considering different amplitudes of saccadic movements (10∘, 20∘, 30∘ and 40∘). For this purpose, the computational fluid dynamics (CFD) open source software OpenFOAM® was used. The results portray a distinct flow behaviour for the VH gel and liquid phases, with inertial effects being more significant for the VH liquid phase. Moreover, the Wall Shear Stress (WSS) values produced by the VH gel phase are more than twice of those generated by the VH liquid phase. Results also show that for different amplitudes of eye movement both the velocity magnitude in the vitreous cavity and the shear stresses on the cavity walls rise with increasing saccadic movement displacement.

Study on Consolidation Behaviors of Peaty Soils Using a Viscoelastic Rheological-Consolidation Model in Kunming, China

Due to the presence of organic matters, peaty soils have a highly compressible nature, and the consolidation process is complicated by the occurrence of rheological deformation. This paper presents the behaviors of the peaty soils sampled from the city of Kunming, the capital of Yunnan province in southwestern China. A series of one-dimensional compression tests are carried out on the peaty soil specimens with different organic matter contents. Considering the rheological properties of peaty soils, the three-element viscoelastic rheological model is introduced into the consolidation equation, then the analytical solution is derived for the viscoelastic rheological-consolidation model. Finally, the influences of consolidation pressures and organic matter contents on the model parameters determined by test data fitting are investigated. It has been shown that the model is coinciding fairly well with test results, and the consolidation pressure and organic matter content have a remarkable effect on the model parameters.

Rate‐dependent fracture simulation of viscoelastic material by the phase‐field method

AbstractThe phase‐field method has been studied for fracture analysis during the last decade. Based on the classical GRIFFITH‐type brittle fracture, good agreements are obtained by comparing to other numerical methods as well as experiments. Furthermore, phase‐field modelling does not depend on any explicit criterion and gets rid of discontinuous displacement tracing. Regarding most elastomers exhibiting both elastic and viscous behaviour simultaneously, it yields a rate‐dependent mechanical response. Investigated by experiments, the fracture process is shown to be rate‐dependent as well. In this work, a viscoelastic rheological model based on REESE & GOVINDJEE [1] is coupled to the phase‐field approach to investigate rate‐dependent fracture evolution within elastomers. The fracture mechanism is based on the volumetric‐isochoric split and the driving force for fracture is defined to be the elastic strain energy potential by both the equilibrium and the non‐equilibrium branches. Representative numerical models are simulated and related findings and potential subsequent perspectives are summarized to close the paper.

Fracture simulation of viscoelastic polymers by the phase-field method

The phase-field model has been employed for fracture analysis over the last decade. One of the main advantages is that the fracture evolution does not depend on any explicit criterion. Good agreement is obtained by comparing the results of simulations and experiments. Most elastomers exhibit both elastic and viscous behavior simultaneously, which yields rate-dependent properties for both the mechanical and fracture responses. In this contribution, a viscoelastic rheological model based on Reese and Govindjee (Int J Solids Struct 35:3455–3482, 1998) is coupled to phase-field modeling to investigate rate-dependent fracture within elastomers. The elastic strain energy potential supposed to evolve fracture is provided by both the equilibrium and non-equilibrium branches. The fracture mechanism is characterized by a volumetric–isochoric split, which specifies a varying driving force in the case of tensile or compressive deformation. Representative numerical examples are studied and related findings and potential perspectives are summarized to close the paper.

The Influence of Viscoelastic Crustal Rheologies on Volcanic Ground Deformation: Insights From Models of Pressure and Volume Change

AbstractInelastic rheological behavior, such as viscoelasticity, is increasingly utilized in the modeling of volcanic ground deformation, as elevated thermal regimes induced by magmatic systems may necessitate the use of a mechanical model containing a component of time‐dependent viscous behavior. For the modeling of a given amplitude and footprint of ground deformation, incorporating a viscoelastic regime has been shown to reduce the magma reservoir overpressure requirements suggested by elastic models. This phenomenon, however, is restricted to pressure‐based analyses and the associated creep behavior. Viscoelastic materials exhibit additional constitutive time‐dependent behaviors, determined by the stress and strain states, that are yet to be analyzed in the context of volcanic ground deformation. By utilizing a mechanically homogeneous model space and distinct reservoir evolutions, we provide a comparison of three viscoelastic rheological models, including the commonly implemented Maxwell and Standard Linear Solid configurations, and their time‐dependent behaviors from a fundamental perspective. We also investigate the differences between deformation time series resulting from a pressurization or volume change, two contrasting approaches that are assumed to be equivalent through elastic modeling. Our results illustrate that the perceived influence of viscoelasticity is dependent on the mode of deformation, with stress‐based pressurization models imparting enhanced deformation relative to the elastic models, thus reducing pressure requirements. Strain‐based volumetric models, however, exhibit reduced levels of deformation and may produce episodes of apparent ground subsidence induced by source inflation or vice versa, due to the relaxation of crustal stresses, dependent on whether the reservoir is modeled to be expanding or contracting, respectively.

Modeling the viscoelastic behavior of wheat flour dough prepared from a wide range of formulations

The viscoelastic behavior of wheat flour dough has been characterized using constitutive models of varying degrees of complexity. Modeling characterizations of the viscoelasticity of dough have not always demonstrated the general applicability of their models to a wide range of dough strengths and formulations. Therefore, the objective of this study was to use two extrema in viscoelastic rheological models (i.e., a power-law gel and the four-element Burgers models) to characterize the linear and non-linear shear behavior of wheat flour doughs. A wide range of breadmaking strength and formulations were employed, particularly those with varying salt content (to ascertain model applicability to strategies to reduce sodium in bread). The power-law gel model fitted all the experimental data well for oscillatory rheometry and creep-recovery tests. The power-law gel model was better at describing the linear viscoelasticity of wheat flour dough compared to the Burgers model, but was poorer at characterization of the recovery phase. Gel strength parameters derived from power-law gel models are recommended for defining the effects of changes in wheat cultivar, water and salt content on both the linear and non-linear viscoelasticity of dough rheology.

New Method for Computing Postseismic Deformations in a Realistic Gravitational Viscoelastic Earth Model

AbstractAfter extensive development of the dislocation theories regarding static deformations that are due to earthquakes, coseismic deformations can be well explained by the present elastic dislocation theories. However, it is difficult to separate and interpret the contributions from interseismic and postseismic deformations, because various mechanisms are involved, including the coupling of the fault interface, aftershock activity, porous‐elastic rebound, and viscoelastic relaxation. It is only possible to infer the dominant mechanism for an earthquake via multiobservation of postseismic deformations in regions that have a dense geodetic network. Accurately simulating a process in a realistic Earth model is a unique way to overcome this difficulty. Here, we present a new robust, accurate, and antioscillational method for modeling the postseismic deformations that are due to viscoelastic relaxation in a realistic gravitational spherical Earth model with linear viscoelastic rheological models. The viscoelastic dislocation Love numbers are evaluated by comparing the results of Sun and Okubo (1993, https://doi.org/10.1029/95JB03536), those of Tanaka et al. (2006 https://doi.org/10.1111/j.1365-246X.2005.02821.x, 2007, https://doi.org/10.1111/j.1365-246X.2007.03486.x), and our newly derived analytical results. The satisfactory consistency between our new results and previous ones demonstrates that our proposed method is highly accurate. This robust and accurate forward modeling approach is helpful for investigating and separating the major mechanism of the postseismic deformations and will greatly benefit the inverse investigation of the ground viscoelastic parameters from geodetic observations.

An experimental study on gravity waves through a floating viscoelastic cover

We report the results of a laboratory study conducted to investigate the dispersion relation and attenuation of surface waves under viscoelastic floating covers. The study uses oil-doped polydimethylsiloxane (PDMS) with different viscoelastic properties quantified in-situ using a rheometer. An additional test is made with a floating PVC film to estimate possible attenuation in the boundary layer under the cover. Within the frequency range tested, the wavelength deviates from open water case negligibly under the PVC film. But for the PDMS covers, depending on the material property, cover thickness and incident wave period, both wave lengthening and shortening are observed. With thin PDMS covers, the measured wavelength matches well with three theoretical predictions based on different viscoelastic rheological models, while the thick cover shows some discrepancy especially for shorter wave periods. In terms of wave attenuation, however, large discrepancies are observed between the measured data and theoretically predicted results for all PDMS covers. Various mechanisms that could contribute to the discrepancies are considered. The most important mechanism is the boundary layer effect, as demonstrated by the measured wave attenuation from the PVC film. The overall results indicate that the attenuation due to the oscillatory boundary layer underneath the floating cover, which has not been included in the viscoelastic theories, contributes significantly to the discrepancies. Direct measurement of the fluid flow under a periodically flexing cover and the related attenuation rate is a challenging but highly important future study.

Rheological properties of lignosulfonate intercalated layered double hydroxides modified bitumen before and after ultraviolet aging

Rheological property of bitumen is closely related to the service life of bituminous pavement, which is mainly affected by temperature, vehicle load and ultraviolet (UV) ray. In this paper, lignosulfonate intercalated layered double hydroxides modified bitumen (LLMB) were researched by Fourier transform infrared (FTIR) spectrometer characterization, aging index and storage stability test. Meanwhile, rheological properties of LLMB before and after UV aging were investigated by temperature susceptibility, dynamic viscoelastic properties and rheological model analyses. The results showed that the introduction of lignosulfonate intercalated layered double hydroxide (LS-LDHs) could strengthen the anti-UV aging ability of bitumen more effectively and had better high temperature storage stability than layered double hydroxides (LDHs). From rheological performance measurement, LS-LDHs could weaken the temperature susceptibility of bitumen observably. Compared with pristine bitumen (PB), the values including loss tangent (tanδ), complex modulus (G∗) and rutting factor (G∗/sinδ) of LLMB got higher. According to rheological model analyses, the addition of LS-LDHs affected the models of bitumen hardly, but restrained instantaneous elastic, delayed elastic and viscous deformation. Therefore, LS-LDHs could enhance rigidity, high temperature performance and resistance to deformation of bitumen significantly. After UV aging, the rheological parameters variations and deformation arguments amplitudes of LLMB were lowest among PB, layered double hydroxides modified bitumen (LMB) and LLMB, which demonstrated that LS-LDHs improved the UV aging resistance of bitumen prominently.