Viscoelastic Coefficients Research Articles

Creep characteristics of a fracturing fluid-softened shale investigated by microindentation

The creep of shales affects the fracture conductivity, well production rate, and hence ultimate recovery of hydrocarbons from reservoir formations. This paper presents an experimental study of the creep characteristics of a shale softened by thermo-hydro-mechano-chemical (THMC) treatments that mimic the rock-fluid interactions affected by high temperature, high pressure, and hydraulic fracturing fluids. Microindentation was conducted to characterize the creep behavior of the THMC-treated specimens with the data analyzed by the Kelvin-Voigt (KV) and compliance methods, while X-ray diffraction and scanning electron microscopy were performed to analyze the compositional and microstructural changes respectively to aid interpretation of indentation measurements. Results show that the THMC treatments increase the creep rate by 46–162%, owing to the treatment-induced softening that varies with the treatment time and distance from the fluid-rock interface, while the Young's modulus and hardness decrease with both the THMC-treatment and creep durations. The softened zones become more viscous, as reflected by the decreased KV model's viscoelastic coefficients for the softened specimens. The higher creep rate of the softened zones is primarily attributed to the weakening in cementation bond and increase in microscale porosity due to the dissolution of carbonates. The findings help understand the mechanisms for creep deformation and pertinent proppant embedment in fractured shales, and hence can be used to predict shale gas production and optimize fracturing fluid additives and stimulants.

Research on Time Delay Feedback Control of Lateral Vibration Axially Moving Viscoelastic Beam

The nonlinear dynamic behavior of a viscoelastic beam in axially variable motion under time delay is studied. Considering that the axial velocity pulsation and radial tension change periodically with time under the action of time delay, the viscous damping and finite support stiffness are taken into account, and the viscoelastic constitutive relationship adopts Kelvin model. A mathematical model of lateral vibration of an axially moving viscoelastic beam with changes in axial velocity and tension under time delay is established, and a partial differential-integral control equation describing the lateral nonlinear vibration of an axially moving beam is given. Based on the Galerkin truncation method, the control equations established based on the mechanical model are discretized, so that the direct multi-scale method obtains the numerical solution of the lateral nonlinear vibration of the axially moving beam under the action of time delay, and determines the nonlinear dynamic behavior of the system under the action of time delay. By analyzing the numerical solution of the vibration displacement and velocity at the midpoint of the beam, the whole process of the average velocity of the axially moving structure along the axis, the amplitude of the disturbance tension and the change of the viscoelastic coefficient is simulated. It provides a numerical theoretical basis for the study of the nonlinear dynamic behavior of axially moving beams under time delay.Through the research in this article, the introduction of time delay is studied, and the time delay is used to analyze the axial force that changes along the radial direction of the beam caused by the speed pulsation, and the theoretical framework for nonlinear vibration analysis of the axially moving viscoelastic beam is constructed to expand the time delay. The application scope of the nonlinear vibration theory and nonlinear dynamics theory, the development and improvement of the approximate analysis and numerical solution of the nonlinear continuum (especially the gyro body) under the action of time delay, to provide a theoretical basis for the analysis and design of the corresponding engineering system and technical reserves.

Dynamic Stability Analysis of Size-Dependent Viscoelastic/Piezoelectric Nano-Beam

This paper analyzes the dynamic stability of an isotropic viscoelastic Euler–Bernoulli nano-beam using piezoelectric materials. For this purpose, the size-dependent theory was used in the framework of the modified couple stress theory (MCST) for piezoelectric materials. In order to capture the geometrical nonlinearity, the von Karman strain displacement relation was applied. Hamilton’s principle was also employed to obtain the governing equations. Furthermore, the Galerkin method was used in order to convert the governing partial differential equations (PDEs) to a nonlinear second-order ordinary differential one. Dynamic stability analysis was performed and the effects of such parameters as viscoelastic coefficients, size effect, and piezoelectric coefficient were investigated. The results showed that in this system, saddle points, central points, Hopf bifurcation points, and fork bifurcation points could be created, and the phase portraits connecting these equilibrium points exhibit periodic orbits, heteroclinic orbits, and homoclinic orbits.

Design, inverted vat photopolymerization 3D printing, and initial characterization of a miniature force sensor for localized in vivo tissue measurements

BackgroundTissue healthiness could be assessed by evaluating its viscoelastic properties through localized contact reaction force measurements to obtain quantitative time history information. To evaluate these properties for hard to reach and confined areas of the human body, miniature force sensors with size constraints and appropriate load capabilities are needed. This research article reports on the design, fabrication, integration, characterization, and in vivo experimentation of a uniaxial miniature force sensor on a human forearm.MethodsThe strain gauge based sensor components were designed to meet dimensional constraints (diameter ≤3.5mm), safety factor (≥3) and performance specifications (maximum applied load, resolution, sensitivity, and accuracy). The sensing element was fabricated using traditional machining. Inverted vat photopolymerization technology was used to prototype complex components on a Form3 printer; micro-component orientation for fabrication challenges were overcome through experimentation. The sensor performance was characterized using dead weights and a LabVIEW based custom developed data acquisition system. The operational performance was evaluated by in vivo measurements on a human forearm; the relaxation data were used to calculate the Voigt model viscoelastic coefficient.ResultsThe three dimensional (3D) printed components exhibited good dimensional accuracy (maximum deviation of 183μm). The assembled sensor exhibited linear behavior (regression coefficient of R2=0.999) and met desired performance specifications of 3.4 safety factor, 1.2N load capacity, 18mN resolution, and 3.13% accuracy. The in vivo experimentally obtained relaxation data were analyzed using the Voigt model yielding a viscoelastic coefficient τ=12.38sec and a curve-fit regression coefficient of R2=0.992.ConclusionsThis research presented the successful design, use of 3D printing for component fabrication, integration, characterization, and analysis of initial in vivo collected measurements with excellent performance for a miniature force sensor for the assessment of tissue viscoelastic properties. Through this research certain limitations were identified, however the initial sensor performance was promising and encouraging to continue the work to improve the sensor. This micro-force sensor could be used to obtain tissue quantitative data to assess tissue healthiness for medical care over extended time periods.

Nonlinear Viscoelastic‐Plastic Creep Model of Rock Based on Fractional Calculus

A rock creep constitutive model is the core content of rock rheological mechanics theory and is of great significance for studying the long‐term stability of engineering. Most of the creep models constructed in previous studies have complex types and many parameters. Based on fractional calculus theory, this paper explores the creep curve characteristics of the creep elements with the fractional order change, constructs a nonlinear viscoelastic‐plastic creep model of rock based on fractional calculus, and deduces the creep constitutive equation. By using a user‐defined function fitting tool of the Origin software and the Levenberg–Marquardt optimization algorithm, the creep test data are fitted and compared. The fitting curve is in good agreement with the experimental data, which shows the rationality and applicability of the proposed nonlinear viscoelastic‐plastic creep model. Through sensitivity analysis of the fractional order β2 and viscoelastic coefficient ξ2, the influence of these creep parameters on rock creep is clarified. The research results show that the nonlinear viscoelastic‐plastic creep model of rock based on fractional calculus constructed in this paper can well describe the creep characteristics of rock, and this model has certain theoretical significance and engineering application value for long‐term engineering stability research.

Measuring viscoelasticity and friction of tempuras for robotic handling

Automation in the food industry is not as developed as that in the automotive industry because of the difficulties in handling food products that vary significantly in shape, size, and mechanical properties. Food properties have been studied in terms of product processing, nutrition, and eating. However, the investigation of mechanical properties, such as the viscoelasticity and friction coefficient under different grasping forces and velocities, which are crucial for robotic handling, is currently insufficient. In this study, we propose a measuring apparatus reproducing a robotic grasping scenario and methods for measuring the viscoelasticity and friction coefficient of food materials. The standard linear solid model was employed to represent the viscoelasticity of food materials, and the model parameters were estimated through a grasping test conducted using the proposed method. The friction coefficient was calculated using the measured normal and shear forces during an induced slippage. Finite element (FE) simulation was conducted to validate the friction coefficient calculation. Finally, experimental tests on four kinds of tempuras suggested that the proposed apparatus and methods can estimate the viscoelasticity and friction properties of food materials, and the grasping force, velocity, and contact area influence the estimated properties. • An apparatus was developed to measure viscoelasticity and friction coefficient of food materials for robotic handling. • Approaches for estimating viscoelasticity and friction coefficient of food materials were established. • Experiments on four tempuras were conducted under different conditions of grasping force and velocity. • Results reveal that grasping force, velocity and contact area influence the estimated properties. • Friction coefficient of tempura is 0.3–0.4 at normal force 0.5–1.0 N grasped by robotic hand with flat stainless fingers.

Variational approach for recovering viscoelasticity from MRE data

This paper deals with an inverse problem for recovering the viscoelasticity of a living body from MRE (Magnetic Resonance Elastography) data. Based on a viscoelastic partial differential equation whose solution can approximately simulate MRE data, the inverse problem is transformed to a least square variational problem. This is to search for viscoelastic coefficients of this equation such that the solution to a boundary value problem of this equation fits approximately to MRE data with respect to the least square cost function. By computing the Gateaux derivatives of the cost function, we minimize the cost function by the projected gradient method is proposed for recovering the unknown coefficients. The reconstruction results based on simulated data and real experimental data are presented and discussed.

Continuous dependence and convergence for a Kelvin\u2013Voigt fluid of order one

It is shown that the solution to the boundary - initial value problem for a Kelvin–Voigt fluid of order one depends continuously upon the Kelvin–Voigt parameters, the viscosity, and the viscoelastic coefficients. Convergence of a solution is also shown.

An analytical approach of filament bundle swinging dynamics, Part II: identifying equivalent dynamic constitutive parameters of filament bundles

A filament bundle is a type of yarn, which is composed of nearly parallel and highly oriented polymer monofilaments. Due to its nonlinearity both in material constitutive properties and structure, the filament bundle possesses nonlinear viscoelastic properties. It is important to study the dynamic behavior of the filament bundle accurately during its high-speed movement. Therefore, an accurate expression of the constitutive relation of the filament bundle is an essential prerequisite for its dynamic simulation and analysis. Continued the previous study in Part I: modeling filament bundle method, in this paper, an approach was proposed to identify the equivalent dynamic constitutive parameters of the filament bundle considering frequency-dependent characteristics. Firstly, the identification formulas of the dynamic elastic modulus and viscoelastic coefficients were derived based on the Kelvin model. Then, a testing method of the cross-sectional parameters of the filament bundle under a certain tension was proposed, and the testing device was developed to obtain the area of the filament bundle; The dynamic loading test of the bundle filament was conducted in a DMA Q800 dynamic mechanical tester. Thirdly, the equivalent dynamic elastic modulus and viscoelastic coefficients were obtained through the experimental test. Finally, an analytical method was proposed to verify the correctness of experimental results through simulation. The results show that the excitation frequency has a significant influence on the dynamic elastic modulus and viscoelastic coefficient, and the curves of the equivalent dynamic elastic modulus and viscoelastic coefficient present nonlinear variation characteristics.

Improvement of Torque Estimation for Series Viscoelastic Actuator Based on Dual Extended Kalman Filter

Adding damping such as viscoelastic element in series elastic actuators (SEA) can improve the force control bandwidth of the system and suppression of high frequency oscillations induced by the environment. Thanks to such advantages, series viscoelastic actuators (SVA) have recently gained increasing research interests from the community of robotic device design. Due to the inconvenience of mounting torque sensors, employing the viscoelastic elements to directly estimate the output torque is of great significance regarding the real-world applications of SVA. However, the nonlinearity and time-varying properties of viscoelastic materials would degrade the torque estimation accuracy. In such a case, it is paramount to simultaneously estimate the output torque state and viscoelastic model coefficients in order to enhance the torque estimation accuracy. To this end, this paper first completed the design of a rubber-based SVA device and used the Zenner linear viscoelastic model to model the viscoelastic element of the rubber. Subsequently, this paper proposed a dual extended Kalman filter- (DEFK) based torque estimation method to estimate the output torque and viscoelastic model coefficients simultaneously. The noisy observations of two Kalman filters were provided by motor current-based estimated torque. Moreover, the dynamic friction of harmonic drive of the designed SVA was modeled and compensated to enhance the reliability of current-based torque estimation. Finally, a number of experiments were carried out on SVA, and the experimental results confirmed the DEFK effectiveness of improving torque estimation accuracy compared to only-used rubber and only-used motor current torque estimation methods. Thus, the proposed method could be considered as an effective alternative approach of torque estimation for SVA.

Dynamic Response of Bi-Directional Functionally Graded Materials (BDFGMs) Beams Rested on Visco-Pasternak Foundation Under Periodic Axial Force

Since the temperature or stress distribution in some advanced machines such as modern aerospace shuttles and craft develops in two or three directions, the need for a new type of FGMs is felt whose properties vary in two or three directions. On the other hand, dynamic buckling behavior of structures is a complicated phenomenon which should be investigated through the response of equations of motion. In this paper, dynamic response of beams composed of bi-directional functionally graded materials (BDFGMs) rested on visco-Pasternak foundation under periodic axial force is investigated. Material properties of BDFGMs beam vary continuously in both the thickness and longitudinal directions based on the two types of analytical functions (e.g. exponential and power law distributions). Hamilton's principle is employed to derive the equations of motion of BDFGMs beam according to the Euler-Bernoulli and Timoshenko beam theories. Then, the generalized differential quadrature (GDQ) method in conjunction with the Bolotin method is used to solve the differential equations of motion under different boundary conditions. It is observed that a good agreement between the present work and the literature result. Various parametric investigations are performed for the effects of the gradient index, length-to-thickness ratio and viscoelastic foundation coefficients on the dynamic stability region of BDFGMs beam. The results show that the influence of gradient index of material properties along the thickness direction is greater than gradient index along the longitudinal direction on the dynamic stability of BDFGMs beam for both exponential and power law distributions.

Instrumentation and methods for rapid estimation of selected viscoelastic parameters in foods.

A new method to estimate the selected viscoelastic parameters of foods using damped vibration analysis is presented for the evaluation of fruits and baked products. A flat disk is attached to the flat sample surface using a laser rangefinder that measures the sample thickness in advance, and it is locked by a trigger. Next, the trigger is released to allow the probe to press the sample through the force of gravity. The damped vibration of the probe caused by the deformation of the food is measured by monitoring the displacement of the probe via a linear encoder. The bulk modulus and viscosity are estimated using the fractional Zener model and mass. Young's modulus (E) is estimated independently by determining the maximum velocity of the probe using Hooke's law. Poisson's ratio (ν), and the shear modulus and viscosity are calculated by employing the estimated E and bulk modulus. The bulk modulus, bulk viscosity, shear modulus, shear viscosity, and E of apples were found to be higher than those of bananas. The bulk modulus, bulk viscosity, E, and shear modulus for white bread were lower than those for pound cake, but the ν values were higher, whereas those of sponge cake were intermediate. After drying the baked products for 1 day, most of the parameters of the samples increased, but the value of ν for white bread decreased. The proposed free-falling device estimated the four viscoelastic coefficients, Poisson's ratio, and Young's modulus of the food sample in less than 1s.

Micromechanics modeling of viscoelastic asphalt-filler composite system with and without fatigue cracks

Fatigue cracking of viscoelastic asphalt composite materials is one of the major distresses in asphalt pavements. To quantify the weakening effect of the fatigue cracks on the mechanical properties of the viscoelastic asphalt composite materials, this study takes an asphalt-filler composite system as an example, and micromechanics models are proposed by combining Eshbely’s equivalent inclusion theory and Mori-Tanaka approach. Dynamic shear rheometer (DSR) tests are performed on the viscoelastic asphalt-filler composite systems with two volumetric contents of inclusion (10% and 27%) at different frequencies (0.1–100 Hz), temperatures (15℃, 20℃, 25℃) and strain levels (0.01%-0.1% for nondestructive DSR tests; 5%, 6%, 7% for destructive DSR tests). Results show that the predicted shear modulus results by a modified viscoelastic strengthening coefficient (VSC) model match with the test results at both low and high filler contents. Then a viscoelastic strengthening coefficient with fatigue cracks (VSC-f) model is proved being capable of accurately predicting the shear modulus for the viscoelastic asphalt-filler composite systems at different strain levels, temperatures, filler contents and damage levels. Both the VSC and the VSC-f model are derived to be dependent of loading frequency, temperature and filler content, but independent of strain level.

On the tri-dimensional constitutive theory identification of linearly viscoelastic solids based on Bayesian framework

Linearly viscoelastic constitutive theories are usually expressed as a Prony series involving fourth order tensors and retardation times. Obtaining the numerical values of the terms involved in such constitutive models from experiments is an ill-posed problem in the sense that many parameter sets can adequately fit experimental data. Considering that the computational time involved in the simulation of the response of viscoelastic structures scales with the number of viscoelastic coefficients, it would be of considerable interest to devise identification strategies yielding the minimum number of parameters. We propose in this work a framework based on the Bayesian inference to reach this objective. We have applied our methodology to three-dimensional experimental data and validated the obtained constitutive theory on an independent data set, for two different viscoelastic materials. Our results demonstrated the robustness and adequacy of our method.

Aeroelastic stability and nonlinear flutter analysis of viscoelastic heated panel in shock-dominated flows

In recent years, new composite materials, functional materials and intelligent materials have been widely used in the structural design of supersonic vehicle panels, and these new materials generally have viscoelastic properties. This paper analyzes aeroelastic stability and nonlinear flutter of a viscoelastic heated panel in shock-dominated flows by using theoretical analysis methods and numerical computations, respectively. The governing equations, based on von-Kármán large deflection theory of isotropic flat plates, are constructed with viscoelastic structural damping of Kelvin's model included. Local first-order piston theory is employed in the region before and after shock to estimate the aerodynamic loadings. The results show that the introduction of viscoelastic structural damping reduces the aeroelastic stability of the panel in shock-dominated flows. The presence of the oblique shock reduces the aeroelastic stability of the viscoelastic panel. Generally, as the viscoelastic damping or the shock strength increases, the critical flutter dynamic pressure decreases. However, at the strong shock strength, the critical flutter dynamic pressures and stability boundaries remain unchanged as the viscoelastic damping changes in a range of large viscoelastic damping coefficients. It is also found that for a flexible panel in shock-dominated flows, chaotic motion can be effectively regulated as periodic motions by the additive structural viscoelastic damping. This investigation has important theoretical and practical values in the aeroelastic design of thin panel structures of supersonic and hypersonic vehicles.

Hygro-thermo-mechanical bending behavior of advanced functionally graded ceramic metal plate resting on a viscoelastic foundation

In this work, the bending behavior of an advanced functionally graded ceramic–metal plate subjected to a hygro-thermo-mechanical load and resting on a viscoelastic foundation is studied using a simple higher-order integral shear deformation theory. The power-law function in terms of volume fraction is used to vary the elastic material constituents through the plate's thickness. The in-plane displacement field uses a sine shape function which changes linearly through the plate thickness to calculate the out-of-plane shear deformation. Both the linear and nonlinear influence of temperature and moisture concentration on the bending response are investigated. For the first time, a three-parameter viscous foundation model is used to study the bending response utilizing the damping coefficient in addition to Winkler’s and Pasternak’s parameters. The governing equations are derived using the principle of virtual displacement, and the analytical solution is obtained by the Navier method. Non-dimensional numerical results is validated by existing results in the literature. A parametric investigation is established to discuss the effects of the power-law gradient index, temperature rise and moisture concentration, elastic foundation coefficients, and the viscoelastic damping coefficient on the FGM plate's bending response.

Eringen’s nonlocal and modified couple stress theories applied to vibrating rotating nanobeams with temperature effects

This study develops a comprehensive vibrational analysis of rotating nanobeams on visco-elastic foundations with thermal effects based on the modified couple stress and Eringen’s nonlocal elasticity theories. This approach accurately simulates the nonlocal stress and size effects. Higher-order shear deformation beam theory and the generalized differential quadrature method are used to obtain the numerical results. The effects of nonlocal parameters, length scale, Winkler–Pasternak coefficients, thermal gradient, slenderness ratios, rotating velocity, and viscoelastic coefficient are demonstrated and discussed in detail. Mode switching and the importance of the correct choice of theory and associated size effect parameters are highlighted.

Prediction of Adhesion Friction Coefficient Using Two Different Models for Tire Tread Rubber Compounds

ABSTRACT Two proposed methods to determine the adhesion friction coefficient were validated by experimental results of two types of rubber compounds at different sliding velocities under dry conditions. The experimental results were measured from a linear friction tester, while the viscoelastic friction coefficient was estimated using the Persson's contact theory. Adhesive friction (model 1) was derived from the deconvolution of dry friction coefficient in two Gaussian-like curves. Interesting results were obtained using the deconvoluted method in the range of intermediate sliding velocities where preponderant contribution to the adhesion friction is replaced by the viscoelastic friction. Fitting parameter results were in good general agreement with values derived from the literature, confirming the influence of the mechanical properties of the compound and substrate texture on the proposed adhesion frictional method. The second adhesive friction model (model 2) was based on the confinement rheology of rubber chains on the contact with the asperities of the road surface. We demonstrated that acceptable adhesion friction results were achieved from a dynamic viscosity test at low frequencies, confirming the applicability of the proposed rheological model. Moreover, the relationship between the rubber composition and the modified contact layer along with the likely interphase reaction are also discussed.

Critical thresholds for mode-coupling instability in viscoelastic sliding contacts

Mode-coupling instabilities are known to trigger self-excited vibrations in sliding contacts. Here, the conditions for mode-coupling (or “flutter”) instability in the contact between a spherical oscillator and a moving viscoelastic substrate are studied. The work extends the classical 2-Degrees-Of-Freedom conveyor belt model and accounts for viscoelastic dissipation in the substrate, adhesive friction at the interface and nonlinear normal contact stiffness as derived from numerical simulations based on a boundary element method capable of accounting for linear viscoelastic effects. The linear stability boundaries are analytically estimated in the limits of very low and very high substrate velocity, while in the intermediate range of velocity the eigenvalue problem is solved numerically. It is shown how the system stability depends on externally imposed parameters, such as the substrate velocity and the normal load applied, and on contact parameters such as the interfacial shear strength tau _{0} and the viscoelastic friction coefficient. In particular, for a given substrate velocity, there exist a critical shear strength tau _{0,crit} and normal load F_{n,crit}, which trigger mode-coupling instability: for shear stresses larger than tau _{0,crit} or normal load smaller than F_{n,crit}, self-excited vibrations have to be expected.

Continuous and elastically consistent viscoelastic reflection and transmission coefficient curves for plane inhomogeneousPandSwaves

SUMMARYFor inhomogeneous plane waves in dissipative media, correctly selecting the vertical slowness (q) is the key requirement to obtain physically acceptable reflection/transmission (R/T) coefficients (e.g. both continuous curves as a function of incidence angle, and consistency with the elastic coefficients at very low attenuation). Based on the fundamental branch-cut theory, the continuity criterion ensures the continuity of the R/T coefficient curves. The elastic consistence is obtained due to the definition of the mixed principal values and the consistent assumptions of time dependence of the harmonic plane wave, the Z-direction of the spatial coordinate system and the particle motion (polarization) vectors. The elastic consistence of R/T coefficients is checked by both elastic models with zero dissipation factor (1/Q) and the equal-Q model in which the Q values of the incident wave and the R/T waves are non-zero but equal for the P and S waves on both sides of the interface. In particular, the previously reported 180° phase difference between the viscoelastic coefficients with arbitrarily small attenuation but the same ratio of Q across the interface and the corresponding elastic coefficients is circumvented by introducing the mixed principal value. The continuity criterion is implemented directly in the complex vertical slowness squared (q2) plane in which the branch-cut is defined. Furthermore, the loci of q2 and several ‘critical angles’ defined for anelastic waves are clearly investigated and clarified. The loci of q2 are expressed as a function of the incidence angle and the incident wave inhomogeneity parameter D. The plots of wave inhomogeneity parameter (D and/or attenuation angle γ) versus incidence angle are calculated from the slowness vectors. The resultant D values, especially their equality for all vertically propagating R/T waves, are examined using the complex Snell's law to provide extra support to the correctness of the slowness vectors and thus of the R/T coefficients. It is worth noting that phase angle of the R/T waves from an inhomogeneous incident wave may exhibit rapid changes at vertical incidence because near-vertical reflection is still the dominant application of the exploration seismic method. To the best of our knowledge, this research is the first time it has been possible to obtain continuous and elastically consistent viscoelastic R/T coefficients.