Voigt Viscoelastic Model Research Articles

PH‐Dependent Growth Laws and Viscoelastic Parameters of Poly‐l‐Lysine/Hyaluronic Acid Multilayers

The layer‐by‐layer formation of polyelectrolyte multilayer films based on poly(l‐lysine) and hyaluronic acid (PLL/HA) is investigated in situ as a function of the pH value employing the quartz crystal microbalance with dissipation. By the use of the Kelvin–Voigt viscoelastic model, the film thickness, the complex viscosity, and the complex shear modulus are obtained as a function of the single layer number and pH. For all investigated pH values, PLL/HA films show an exponential growth behavior. However, in different pH regimes the exponentiality, represented by the exponential factor of the respective fit function, is more or less pronounced. Toward low or high pH values, PLL interdiffusion causing exponential growth is less relevant for the increase in mass coverage, though in the high (pH > 9) and the low (pH < 5) pH range thicker (PLL/HA)4 multilayers form. Here, the films are less viscous and less elastic compared to polyelectrolyte multilayers formed at intermediate pH (5 ≤ pH ≤ 9) conditions. Film thickness, viscosity, and elasticity do not only change with pH but also with the kind of the terminating layer. This odd–even effect is caused by the diffusion of PLL into and out of the multilayer film.

Macroscopic rheological behavior of suspensions of soft solid particles in yield stress fluids

In this study, we present a homogenization model for the macroscopic rheological behavior of non-colloidal suspensions of initially spherical, viscoelastic particles in yield stress fluids, which are subjected to uniform flow conditions. The constitutive behavior of the suspending fluid is characterized by the Herschel–Bulkley (HB) model, and the particles are assumed to be neutrally buoyant solids characterized by the finite-strain Kelvin–Voigt viscoelastic model. We make use of the “linear comparison composite” variational technique of Ponte Castañeda (1991) to approximate the instantaneous response of the suspensions of viscoelastic particles in the HB fluid by that of a fictitious suspension consisting of the same particles distributed identically in a Newtonian fluid with a suitably-chosen viscosity. The response of the latter suspension is then estimated by the homogenization model recently developed by Avazmohammadi and Ponte Castañeda (2015), which, when combined with appropriate evolution laws for the relevant microstructural variables, provides a complete characterization of the time-dependent response of the actual suspensions. With the objective of illustrating the key features of our model, we consider the particular case of suspensions of elastic particles in HB fluids under shear flow conditions. The results provide a broad picture of the influence of the HB fluid and particle constitutive properties, as well as of the particle volume fraction on the effective time-dependent and steady-state behaviors of the suspensions. For the special case of non-deformable particles, our model predicts that the suspensions behave like HB fluids with modified properties, consistent with the results of Chateau et al. (2008).

Employing DEM to study the impact of different parameters on the screening efficiency and mesh wear

Discrete element method (DEM) was employed in modeling vibrating screen, in order to study the effects of different parameters on the process efficiency and the mesh wear. A review was provided about modeling the contact force between colliding bodies. However, Hertz elastic and Kelvin–Voigt viscoelastic models were combined for the purpose of this study. Gear's approach was used in the numerical integration of the governing equations. The required programs were developed to perform the simulations using an open source code. Factors affecting numerical computations were tuned to achieve suitable values and obtain reliable results in the numerical studies. In the section of numerical studies, several simulations were built to reveal the effects of mesh slope, vibration frequency and excitation direction on the screening efficiency and wear of the screen mesh. Results related to the dependence of the efficiency on vibration frequency, excitation angle and mesh inclination were in agreement with those of data reported in open literature. However, no comparable data was seen with regards to the wear of the screen mesh. It was observed that most of the introduced parameters affect the efficiency and wear. The results were appropriately discussed and were presented graphically using diagrams and graphs. The conclusions and methodology of this study can be employed in both practical and theoretical fields.

Investigation of guided waves propagation in orthotropic viscoelastic carbon–epoxy plate by Legendre polynomial method

The effect of viscoelasticity on the guided waves propagation in viscoelastic plate has been investigated according to multi-aspect. To this purpose, an extension of the Legendre polynomial method is proposed to formulate the guided waves equation in orthotropic viscoelastic plate composed of carbon–epoxy. The validity of the proposed Legendre polynomial method is illustrated by comparison with available data. The convergence of the method is discussed through a numerical example. The hysteretic and Kelvin–Voigt viscoelastic models are used to integrate the imaginary part of the complex stiffness matrix associated with the viscoelastic plate in this study. Accordingly, both viscoelastic models do not affect on the dispersion curves results. However, appreciable effects are seen in the attenuation curves. Also, the sensitivity of the guided waves propagation caused by variations of elastic and viscoelastic modulus has been studied in detail. Finally, the advantages of the Legendre polynomial method are described.

Optimal error estimates for semidiscrete Galerkin approximations to equations of motion described by Kelvin–Voigt viscoelastic fluid flow model

In this paper, a finite element Galerkin method is applied to equations of motion arising in the Kelvin–Voigt viscoelastic fluid flow model, when the forcing function is in L∞(L2). Some a priori estimates for the exact solution, which are valid uniformly in time as t↦∞ and even uniformly in the retardation time κ an κ↦0 are derived. It is shown that the semidiscrete method admits a global attractor. Further, with the help of a priori bounds and Sobolev–Stokes projection, optimal error estimates for the velocity in L∞(L2) and L∞(H1)-norms and for the pressure in L∞(L2)-norm are established. Since the constants involved in error estimates have an exponential growth in time, therefore, in the last part of the article, under certain uniqueness condition, the error bounds are established which are valid uniformly in time. Finally, some numerical experiments are conducted which confirm our theoretical findings.

Nonconservative stability of viscoelastic rectangular plates with free edges under uniformly distributed follower force

Dynamic stability of viscoelastic rectangular plates under a uniformly distributed tangential follower load is studied. Two sets of boundary conditions are considered, namely, clamped in one boundary and free in other boundaries (CFFF) and two opposite edges simply supported and other two edges free (SFSF). By considering the Kelvin–Voigt model of viscoelasticity, the equation of motion of the plate is derived. The differential quadrature method is employed to obtain the numerical solution and it is verified against known results in the literature. Numerical results are given for the real and imaginary parts of the eigenfrequencies to investigate the divergence and flutter instabilities. It is observed that the type of stability differs for CFFF and SFSF plates indicating the strong influence of the boundary conditions on the dynamic stability of viscoelastic plates. In particular it is found that CFFF plates undergo flutter instability and SFSF plates divergence instability. One consequence is that SFSF plates become unstable at a load less than the load for CFFF plates as the effects of viscoelasticity as well as the aspect ratio are found to be minor for SFSF plates.

Large Time Approximation for Shearing Motions

Small- and large-amplitude oscillatory shear tests are widely used by experimentalists to measure, respectively, linear and nonlinear properties of viscoelastic materials. These tests are based on the quasi-static approximation according to which the strain varies sinusoidally with time after a number of loading cycles. Despite the extensive use of the quasi-static approximation in solid mechanics, few attempts have been made to justify rigorously such an approximation. The validity of the quasi-static approximation is studied here in the framework of the Mooney--Rivlin Kelvin--Voigt viscoelastic model by solving the equations of motion analytically. For a general nonlinear model, the quasi-static approximation is instead derived by means of a perturbation analysis.

Quantification of the Mass and Viscoelasticity of Interfacial Films on Tin Anodes Using EQCM-D.

Electrochemical quartz crystal microbalance coupled with dissipation (EQCM-D) is employed to investigate the solid electrolyte interphase (SEI) formation and Li insertion/deinsertion into thin film electrodes of tin. Based on the frequency change we find that the initial SEI formation process is rapid before Li insertion but varies significantly with increasing concentration of the additive fluoroethylene carbonate (FEC) in the electrolyte. The extent of dissipation, which represents the film rigidity, increases with cycle number, reflecting film thickening and softening. Dissipation values are almost twice as large in the baseline electrolyte (1.2 M LiPF6 in 3:7 wt % ethylene carbonate:ethyl methyl carbonate), indicating the film in baseline electrolyte is roughly twice as soft as in the FEC-containing cells. More importantly, we detail how quantitative data about mass, thickness, shear elastic modulus, and shear viscosity in a time-resolved manner can be obtained from the EQCM-D response. These parameters were extracted from the frequency and dissipation results at multiple harmonics using the Sauerbrey and Voigt viscoelastic models. From these modeled results we show the dynamic mass changes for each half cycle. We also demonstrate that different amounts of FEC additive influence the SEI formation behavior and result in differences in the estimated mass, shear modulus and viscosity. After three cycles, the film in baseline electrolyte exhibits a 1.2 times larger mass change compared with the film in the FEC-containing electrolyte. The shear elastic modulus of films formed in the presence of FEC is larger than in the baseline electrolyte at early stages of lithiation. Also with lithiation is a marked increase in film viscosity, which together point to a much stiffer and more homogeneous SEI formed in the presence of FEC.

Wave propagation in fluid-conveying viscoelastic carbon nanotubes based on nonlocal strain gradient theory

The governing equation of wave motion of fluid-conveying viscoelastic single-walled carbon nanotubes is formulated on the basis of the nonlocal strain gradient theory and the Kelvin–Voigt viscoelastic model. Based on the formulated equation of wave motion, the closed-form dispersion relation between the wave frequency (or phase velocity) and the wave number is derived. It is found that, the effects of nonlocal parameters and small scale material parameters on the dispersion relation between the phase velocity and the wave number are significant at high wave numbers, however, may be ignored at low wave numbers. The upstream phase velocities decrease as increasing flow velocity, whereas the downstream phase velocities firstly increase as increasing flow velocity and then decrease as increasing flow velocity. The effect of damping coefficient on the phase velocity of both upstream and downstream waves is negligible at low wave numbers, however, is remarkable at high wave numbers.

A new approach for modeling of magnetorheological elastomers

This article presents a novel model to portray the behavior of magnetorheological elastomer in oscillatory shear test. The dynamic behavior of an isotropic magnetorheological elastomer is experimentally investigated at different input conditions. A modified Kelvin–Voigt viscoelastic model is developed to describe relationships between shear stress and shear strain of magnetorheological elastomers based on input frequency, shear strain, and magnetic flux density. Unlike the previous models of magnetorheological elastomers, the coefficients of this model, calculated by nonlinear regression method, are constant at various harmonic shear loads and different magnetic flux densities. The results show that the new phenomenological model can effectively predict the viscoelastic behavior of magnetorheological elastomers. Also, the results demonstrate that the trend of shear storage modulus of magnetorheological elastomer based on the frequency is nonlinear from 0.1 to 8 Hz, which is predicted by the present model. The proposed model is beneficial to simulate vibration control strategies in magnetorheological elastomer base devices under harmonic shear loadings.

A Bayesian approach for characterization of soft tissue viscoelasticity in acoustic radiation force imaging.

Biomechanical imaging techniques based on acoustic radiation force (ARF) have been developed to characterize the viscoelasticity of soft tissue by measuring the motion excited by ARF non-invasively. The unknown stress distribution in the region of excitation limits an accurate inverse characterization of soft tissue viscoelasticity, and single degree-of-freedom simplified models have been applied to solve the inverse problem approximately. In this study, the ARF-induced creep imaging is employed to estimate the time constant of a Voigt viscoelastic tissue model, and an inverse finite element (FE) characterization procedure based on a Bayesian formulation is presented. The Bayesian approach aims to estimate a reasonable quantification of the probability distributions of soft tissue mechanical properties in the presence of measurement noise and model parameter uncertainty. Gaussian process metamodeling is applied to provide a fast statistical approximation based on a small number of computationally expensive FE model runs. Numerical simulation results demonstrate that the Bayesian approach provides an efficient and practical estimation of the probability distributions of time constant in the ARF-induced creep imaging. In a comparison study with the single degree of freedom models, the Bayesian approach with FE models improves the estimation results even in the presence of large uncertainty levels of the model parameters.

Influence of interfacial interactions on deformation mechanism and interface viscosity in α-chitin–calcite interfaces

The interfaces between organic and inorganic phases in natural materials have a significant effect on their mechanical properties. This work presents a quantification of the interface stress as a function of interface chemical changes (water, organic molecules) in chitin–calcite (CHI–CAL) interfaces using classical non-equilibrium molecular dynamics (NEMD) simulations and steered molecular dynamics (SMD) simulations. NEMD is used to investigate interface stress as a function of applied strain based on the virial stress formulation. SMD is used to understand interface separation mechanism and to calculate interfacial shear stress based on a viscoplastic interfacial sliding model. Analyses indicate that interfacial shear stress combined with shear viscosity can result in variations to the mechanical properties of the examined interfacial material systems. It is further verified with Kelvin–Voigt and Maxwell viscoelastic analytical models representing viscous interfaces and outer matrix. Further analyses show that overall mechanical deformation depends on maximization of interface shear strength in such materials. This work establishes lower and upper bounds of interface strength in the interfaces examined.

Carbohydrate-derived amphiphilic macromolecules: a biophysical structural characterization and analysis of binding behaviors to model membranes.

The design and synthesis of enhanced membrane-intercalating biomaterials for drug delivery or vascular membrane targeting is currently challenged by the lack of screening and prediction tools. The present work demonstrates the generation of a Quantitative Structural Activity Relationship model (QSAR) to make a priori predictions. Amphiphilic macromolecules (AMs) “stealth lipids” built on aldaric and uronic acids frameworks attached to poly(ethylene glycol) (PEG) polymer tails were developed to form self-assembling micelles. In the present study, a defined set of novel AM structures were investigated in terms of their binding to lipid membrane bilayers using Quartz Crystal Microbalance with Dissipation (QCM-D) experiments coupled with computational coarse-grained molecular dynamics (CG MD) and all-atom MD (AA MD) simulations. The CG MD simulations capture the insertion dynamics of the AM lipophilic backbones into the lipid bilayer with the PEGylated tail directed into bulk water. QCM-D measurements with Voigt viscoelastic model analysis enabled the quantitation of the mass gain and rate of interaction between the AM and the lipid bilayer surface. Thus, this study yielded insights about variations in the functional activity of AM materials with minute compositional or stereochemical differences based on membrane binding, which has translational potential for transplanting these materials in vivo. More broadly, it demonstrates an integrated computational-experimental approach, which can offer a promising strategy for the in silico design and screening of therapeutic candidate materials.

On the forward and backward in time problems in the Kelvin–Voigt thermoviscoelastic materials

This paper studies the uniqueness of solutions to the forward and backward in time boundary value problems associated with the Kelvin–Voigt viscoelastic model of the thermoelastic materials. For thermoviscoelastic materials with a center of symmetry, it is shown the uniqueness of solutions to the forward in time boundary value problems without any assumptions upon the thermoviscoelastic constitutive coefficients other than the symmetry properties and those induced by the dissipation inequality. While for the final boundary value problems two uniqueness theorems are presented: the first one is essentially based on the assumption that the specific heat is of negative definite sign, while the second is established in the class of displacement–temperature variation fields whose dissipation energy has a temporal behavior lower than an appropriate growing exponential.

Aeroelastic analysis and active flutter suppression of an electro-rheological sandwich cylindrical panel under yawed supersonic flow

Supersonic flutter control of a three-layered sandwich curved panel of rectangular plan form with an adaptive electro-rheological fluid (ERF) core layer is investigated. The panel is excited by an arbitrary transient transverse load along with an arbitrary airflow yaw angle. The problem formulation is based on Kirchhoff–Love thin shell theory, the first order Kelvin–Voigt viscoelastic material model, and the linear quasi-steady Krumhaar's modified supersonic piston theory that accounts for both the panel curvature and flow yaw angle. The classical Hamilton's principle and the Galerkin method are used to set up the equations of motion which are then put in the state-space form. The effects of applied electric field, panel aspect ratio, panel shallowness angle, and airflow direction on the critical free stream static pressure are studied. Also, the aeroelastic response of the cylindrical panel excited by an impulsive central point load is calculated using the Runge–Kutta time integration scheme. Subsequently, a Sliding Mode Control (SMC) methodology is implemented to actively attenuate the structural response in the supersonic flow regime. Numerical simulations establish the effectiveness of the applied control configuration in successful suppression of the structural oscillations. The validity of results is demonstrated by rigorous comparisons with the existing data.

Monitoring viscosity changes from time‐lapse seismic attenuation: case study from a heavy oil reservoir

ABSTRACTHeating heavy oil reservoirs is a common method for reducing the high viscosity of heavy oil and thus increasing the recovery factor. Monitoring of these viscosity changes in the reservoir is essential for delineating the heated region and controlling production. In this study, we present an approach for estimating viscosity changes in a heavy oil reservoir. The approach consists of three steps: measuring seismic wave attenuation between reflections from above and below the reservoir, constructing time‐lapse Q and Q−1 factor maps, and interpreting these maps using Kelvin–Voigt and Maxwell viscoelastic models. We use a 4D relative spectrum method to measure changes in attenuation. The method is tested with synthetic seismic data that are noise free and data with additive Gaussian noise to show the robustness and the accuracy of the estimates of the Q‐factor. The results of the application of the method to a field data set exhibit alignment of high attenuation zones along the steam‐injection wells, and indicate that temperature dependent viscosity changes in the heavy oil reservoir can be explained by the Kelvin–Voigt model.

Computational and Theoretical Justification of Foundation Design Solutions for Equipment Subject to Dynamic Loads

The solution to the problem of foundation vibration jointly with the subgrade soil caused by dynamic loads generated by equipment is considered. Soil and foundation behavior, which has anti-vibration pads, can be described by the Voigt model of viscoelasticity. The explicit scheme was used in the algorithm of numerical calculation in time domain. Spatial discretization is carried out by finite element method. The analysis of the solution was conducted in order to compare this method with known analytical methods of foundation designing.

On a two-grid finite element scheme combined with Crank–Nicolson method for the equations of motion arising in the Kelvin–Voigt model

In this paper, we present a second order accurate Crank–Nicolson scheme applied to a system arising from Galerkin finite element two-grid approximations to the equations of motion described by the Kelvin–Voigt viscoelastic fluid flow model. Optimal error estimates in L∞(L2)-norm and L∞(H1)-norm for velocity and L∞(L2)-norm for pressure are established. These estimates are shown to be uniform in time. Numerical results are provided to verify the theoretical estimates.

Construction and Modeling of Concatemeric DNA Multilayers on a Planar Surface as Monitored by QCM-D and SPR

The sequential hybridization of a 534 base pair DNA concatemer layer was monitored by QCM-D and SPR, and the QCM-D data were analyzed by Voigt viscoelastic models. The results show that Voigt-based modeling gives a good description of the experimental data but only if shear viscosity and elasticity are allowed to depend on the shear frequency. The derived layer thickness, shear viscosity and elasticity of the growing film give a representation of the DNA film in agreement with known bulk properties of DNA, and reveal a maximum in film viscosity when the molecules in the layer contain 75 base pairs. The experimental data during construction of a 3084 bp DNA concatemer layer were compared to predictions of the QCM-D response of a 1 μm thick film of rod-like polymers. A predicted nonmonotonous variation of dissipation with frequency (added mass) is in qualitative agreement with the experiments, but with a quantitative disagreement which likely reflects that the flexibility of such long DNA molecules is not included in the model.

Quantitative analysis of liver fibrosis in rats with shearwave dispersion ultrasound vibrometry: Comparison with dynamic mechanical analysis

Ultrasonic elastography, a non-invasive technique for assessing the elasticity properties of tissues, has shown promising results for disease diagnosis. However, biological soft tissues are viscoelastic in nature. Shearwave dispersion ultrasound vibrometry (SDUV) can simultaneously measure the elasticity and viscosity of tissue using shear wave propagation speeds at different frequencies. In this paper, the viscoelasticity of rat livers was measured quantitatively by SDUV for normal (stage F0) and fibrotic livers (stage F2). Meanwhile, an independent validation study was presented in which SDUV results were compared with those derived from dynamic mechanical analysis (DMA), which is the only mechanical test that simultaneously assesses the viscoelastic properties of tissue. Shear wave speeds were measured at frequencies of 100, 200, 300 and 400Hz with SDUV and the storage moduli and loss moduli were measured at the frequency range of 1–40Hz with DMA. The Voigt viscoelastic model was used in the two methods. The mean elasticity and viscosity obtained by SDUV ranged from 0.84±0.13kPa (F0) to 1.85±0.30kPa (F2) and from 1.12±0.11Pas (F0) to 1.70±0.31Pas (F2), respectively. The mean elasticity and viscosity derived from DMA ranged from 0.62±0.09kPa (F0) to 1.70±0.84kPa (F2) and from 3.38±0.32Pas (F0) to 4.63±1.30Pas (F2), respectively. Both SDUV and DMA demonstrated that the elasticity of rat livers increased from stage F0 to F2, a finding which was consistent with previous literature. However, the elasticity measurements obtained by SDUV had smaller differences than those obtained by DMA, whereas the viscosities obtained by the two methods were obviously different. We suggest that the difference could be related to factors such as tissue microstructure, the frequency range, sample size and the rheological model employed. For future work we propose some improvements in the comparative tests between SDUV and DMA, such as enlarging the harmonic frequency range of the shear wave to highlight the role of viscosity, finding an appropriate rheological model to improve the accuracy of tissue viscoelasticity estimations.