Viscoelastic Body Research Articles

The fractal scale-invariant structure of a temporal hierarchy in the relaxation and energy dissipation processes in a visco-elastic/capillary-porous medium

The phenomena of elastic aftereffects during loading/unloading of viscoelastic and capillary-porous bodies, relaxation of their stresses is accompanied by the energy accumulation and dissipation to be taken into account in the theory of oscillations which also considers the behavior of materials when the force is applied to them. The elastic aftereffect and stress relaxation forms ostensibly opposite energy processes. In the first case, under constant load deformation, the work increases in course of time, and in the second case, under constant load deformation, the work (energy) decreases. While researching on the energy dissipation in the conditions of oscillations application, i.e. within the frame of internal friction theories, one can find that some theories are based on the dependence of friction on the oscillations’ velocity, other ones establish the dependence of friction on the amplitude. Research papers are based on the hypothesis of M.M. Davydenkov, according to which the energy when subjected to oscillations depends on the amplitude and does not depend on the velocity. According to E.S. Sorokin, the theory of internal friction is poorly consistent with the theories describing the inherited properties of materials (viscoelastic and capillary-porous ones). A tendency is observed: the better a theory reflects hereditary properties, the worse this theory is adapted to describe energy losses due to oscillations.In this paper, an attempt has been made to harmonize both these theories and numerous experiments on the destruction of materials described in the academic literature. It turns out that in order to remove contradictions, it is necessary to take into account the dependence of body deformation changing in the course of time.It is shown that the hierarchy of times determining shear and bulk relaxation in viscoelastic/capillary-porous medium has a fractal (scale-invariant) structure. It was observed that the presence of time fractality eases the modeling of viscoelastic/capillary-porous bodies resulting in the universal relaxation function of a rather simple kind. In particular, for the scale-invariant distribution of relaxation characteristics medium, the application of algebraic relaxation law for viscoelastic/capillary-porous materials is possible: this resulting in rheological models and state equations with the derivatives of fractional order.

Modelling of rolling contact fatigue under various interface conditions

This study presents the results of modelling the rolling contact of the elastic sphere and the elastic half-space in the presence of a thin intermediate viscoelastic layer which properties are described by an elastic nonlinear Winkler body in the normal direction and a viscoelastic Maxwell body in the tangential direction. The analytical–numerical approach for the estimation of contact fatigue damage, accumulated in the elastic half-space under rolling friction conditions, is developed. The proposed model can be used, in particular, to study the effect of mechanical properties of the friction modifiers (elastic moduli and relaxation times) and its thickness as well as the relative slippage on the formation of the surface and under surface contact fatigue cracks in rails. The results of the analysis can also be applied for the estimation of efficiency of solid lubricants in rolling contacts under given operating conditions.

Thermoelectromechanical behavior of three-dimensional layered piezoelectric viscoelastic cylindrical panel under forced vibrations

The paper presents a numerical technique for solving problems of forced vibrations and dissipative heating of viscoelastic three-dimensional piezoelectric bodies of revolution. Finding a solution to such problems is reduced to solving a sequence of linear problems of electroviscoelasticity with complex electromechanical characteristics and problems of non-stationary thermal conductivity with a known heat source. The developed technique for solving the specified linear problems of electromechanics and heat conduction is based on the method of finite elements in the variational formulation. The results of numerical modeling of the thermoelectromechanical behavior of a three-layer viscoelastic piezoelectric cylindrical panel in the case of rigid fixation of its ends under mechanical harmonic loading are presented. The influence of the magnitude of the mechanical load on the amplitude-frequency and temperature-frequency characteristics in the vicinity of the first resonance was investigated.

A note on constitutive relationships for viscoelastic bodies with density-dependent material properties

A note on constitutive relationships for viscoelastic bodies with density-dependent material properties

A mathematical model for intracellular NO and ROS dynamics in vascular endothelial cells activated by exercise-induced wall shear stress

Vascular endothelial cells (ECs) residing in the innermost layer of blood vessels are exposed to dynamic wall shear stress (WSS) induced by blood flow. The intracellular nitric oxide (NO) and reactive oxygen species (ROS) in ECs modulated by the dynamic WSS play important roles in endothelial functions. Mathematical modeling is a popular methodology for biophysical studies. It can not only explain existing cell experiments, but also reveal the underlying mechanism. However, the previous mathematical models of NO dynamics in ECs are limited to the static WSS induced by constant flow, while arterial blood flow is a periodic pulsatile flow with varying amplitude and frequency at different exercise intensities. In this study, a mathematical model of intracellular NO and ROS dynamics activated by dynamic WSS based on the in vitro cell experiments is developed. With the hypothesis of the viscoelastic body, the Kelvin model is adopted to simulate the mechanosensors on EC. Thus, the NO dynamics activated by dynamic shear stresses induced by constant flow, pulsatile flow, and oscillatory flow are analyzed and compared. Moreover, the roles of ROS have been considered for the first time in the modeling of NO dynamics in ECs based on the analysis of cell experiments. The predictions of the proposed model coincide fairly well with the experimental data when ECs are subjected to exercise-induced WSS. The mechanism is elucidated that WSS induced by moderate-intensity exercise is most favorable to NO production in ECs. This study can provide valuable insights for further study of NO and ROS dynamics in ECs and help develop appropriate exercise regimens for improving endothelial functions.

Degeneration of flow pattern in acousto-elastic flow through sharp-edge microchannels

Acoustic streaming (AS) is the steady time-averaged flow generated by acoustic field, which has been widely used in enhancing mixing and particle manipulation. Current researches on acoustic streaming mainly focus on Newtonian fluids, while many biological and chemical solutions exhibit non-Newtonian properties. The acoustic streaming in viscoelastic fluids has been studied experimentally for the first time in this paper. We found that the addition of polyethylene oxide (PEO) polymer to the Newtonian fluid significantly altered the flow characteristics in the microchannel. The resulting acousto-elastic flow showed two modes: positive mode and negative mode. Specifically, the viscoelastic fluids under acousto-elastic flow exhibit mixing hysteresis features at low flow rates, and degeneration of flow pattern at high flow rates. Through quantitative analysis, the degeneration of flow pattern is further summarized as time fluctuation and spatial disturbance range reduction. The positive mode in acousto-elastic flow can be used for the mixing enhancement of viscoelastic fluids in the micromixer, while the negative mode provides a potential method for particle/cell manipulation in viscoelastic body fluids such as saliva by suppressing unstable flow.

The creep model based on nonlinear Newton body under different temperature conditions

Mastering the creep deformation characteristics of rock under different temperature conditions is of great significance for studying the long-term stability and deformation mechanism of geotechnical engineering. Based on the classical Burgers model, the creep model under different temperature conditions is established by introducing a nonlinear Newton body. The parameters of the creep model are identified and the influence law of different parameters on rock creep deformation is analyzed. The relationship between model parameters and temperature is quantitatively expressed. The results show that the newly established model can describe the characteristics of the rock in the decay creep stage and the constant creep stage, especially can quantitatively characterize the relationship between the strain and the time of the rock in the tertiary creep under different temperatures conditions. The model fitting curve is highly consistent with the test data, and the correlation coefficient R2 is above 0.98, which thoroughly verifies the accuracy and rationality of the model. It is found that when the temperature is constant, the creep increases with the increase of the shear modulus of the elastomer G1, the shear modulus of the viscoelastic body G2, and the viscosity coefficient of the viscous body η1 in the constant creep stage. The decay creep property of rock is more obvious with the increase of the viscosity coefficient η2, and the axial strain tends to a constant value. The achievement can be used to predict the deformation trend of geotechnical engineering with time under different temperature conditions and provide the theoretical basis for long-term stability analysis.

A nonsmooth optimization approach for time-dependent hemivariational inequalities

This paper is devoted to the study of time-dependent hemivariational inequality. We prove the existence and uniqueness of its solution, provide a fully discrete scheme, and reformulate this scheme as a series of nonsmooth optimization problems. The introduced theory is later applied to a sample quasistatic contact problem that describes a viscoelastic body in frictional contact with a foundation. This contact is governed by a nonmonotone friction law with dependence on the normal component of displacement and the tangential component of velocity. Finally, computational simulations are performed to illustrate the obtained results.

Fatigue in a class of viscoelastic solids

We study fatigue (weakness induced by cyclic loading) in a viscoelastic body described by a generalization of the Kelvin-Voigt constitutive relation, employing a novel damage initiation criterion developed by Alagappan et al. [13-15]. The main premise is that damage is a consequence of the inhomogeneity of the material which leads to some locations in the body being naturally weaker, say for instance due to the density being lower and the material moduli depending on the density and decreasing with density, leading ultimately to failure at that location. This approach has been used successfully for polymers, elastomers and concrete subject to monotonic loading. In this study, we consider the initiation of damage due to cyclic loading, which is referred to as fatigue. Since the body under consideration is viscoelastic, it dissipates energy in each cycle which leads to an increase in temperature. We shall not take the effect of the temperature of the material moduli, instead we assume that the material moduli depend on the density and the rate of dissipation. In the case of our specific study the shear modulus of the material depends on the density and dissipation (in the case of the constitutive relation considered the shear rate), and the structure of the shear modulus is such that it decreases with decrease in density and decreases with increase in dissipation (tantamount to the assumption that it decreases with increasing shear rate for the constitutive relation under consideration) leading to damage of the material. We find that after sufficient number of cycles, the body under consideration undergoes significant loss in load carrying capacity due to fatigue.

Development of a fast and stable dynamics algorithm for soft robots including viscoelastic body

In recent years, research and development of robots that exist in the same space as humans and can collaborate with humans have been actively carried out. If the body of a robot is made of a hard material, it may cause injury. Therefore, attempts have been made to make a robot with a soft body using rubber or resin. In order to accelerate such research on soft robotics, it is necessary to establish fast and stable simulation algorithm for robots containing viscoelastic bodies such as rubber and resin. Therefore, in this study, we consider to approximate viscoelastic bodies with finite rigid body segments and connect them with joints and linear viscoelastic elements such as Voigt model, Maxwell model and generalized Maxwell model to approximate viscoelastic properties. The recursive dynamics algorithm is used to speed up the calculation, and the generalized-α method is used to stabilize the numerical integration. In particular, we propose a new method on how to incorporate the Maxwell model and generalized Maxwell model into recursive dynamics algorithm and generalized-α method. The effectiveness of the proposed method is confirmed by some numerical examples. In addition, the effectiveness of the proposed method is verified on a real system by applying Particle Swarm Optimization (PSO) to identify the dynamic parameters in linear viscoelastic elements.

粘弾性体落下衝撃における材料係数の同定

This paper deals with the material modulus estimation for the impact of dropped viscoelastic material bodies. A bar model was investigated firstly as it is easy to understand the impact phenomena. Besides the fundamental material modulus of impact, Young's modulus and density, two dimensionless viscoelastic material parameters, the ratio of the long-term elastic modulus to the short-term one and the relaxation modulus to the wave propagation time along a bar, were found to be the other key parameters. The dropped viscoelastic spheres were investigated secondly and shown to have similar impact characteristics to bars regarding these two key parameters. We can estimate the material modulus very quickly in the computation analysis by tuning these parameters. And this approach is very useful to design the impact source of dropped sphere from the point of view of the viscoelastic materials.

ON PROBLEM OF PROPERTIES OPTIMIZING FOR VISCOELASTIC MATERIALS USING THE BEGLEY-TORVIK EQUATION

Recently, fractional calculus has been the focus of attention of many researchers in the field of science and technology, since a more detailed study of physical processes leads to the need to complicate the mathematical models that describe them, and, consequently, to the study of the behavior of solutions of differential equations containing, along with " ordinary", or "classical", derivative, also fractional. Processes of this kind can include: studies of continuous media with memory, fluid filtration in media with fractal geometry, physical aspects of stochastic transfer and diffusion, mathematical models of a viscoelastic body, models of damped oscillations with fractional damping (for example, vibrations of rocks during earth-quakes or vibrations nanoscale sensors), models of non-local physical processes and phenomena of a fractal nature; climate models, etc. The paper studies boundary value problems for the equation of motion of an oscillator with viscoelastic damping (the Begley-Torvik equation) in the case when the damping order is greater than zero but less than two. Such problems model many physical processes, in particular, the vibration of a string in a viscous medium, the change in the deformation-strength characteristics of polymer concrete under loading, etc. This paper is devoted to optimizing the parametric control of the Begley-Torvik model. A fundamentally new, efficient algorithm is proposed that allows estimating the parameters of a model of real material.

Research Progress of High-Temperature Resistant Functional Gel Materials and Their Application in Oil and Gas Drilling.

With the development of oil exploration, the number of complex situations encountered in the drilling process is continuously increasing. During the operation of large displacement and horizontal wells, the safe density window of drilling fluid is narrow in complex formations and the lost circulation problem is becoming increasingly prominent. This can easily cause the drilling fluid to enter the formation from inside the well through lost circulation channels, which will prolong the drilling cycle, increase drilling costs, affect geological logging, and could cause a series of malignant accidents (such as blowout, sticking of a drilling tool, borehole collapse, and well abandoned). According to the severity, common lost circulation can be classified into three types: fractured lost circulation, karst cave lost circulation, and permeability lost circulation. Currently, researchers are developing different types of lost circulation materials (LCMs) for various lost circulation situations. Compared with conventional lost circulation control methods, the polymer gel lost circulation control technique applies a three-dimensional cage-like viscoelastic body formed via the crosslinking reaction of polymer gels. These materials have strong deformability and can enter fractures and holes through extrusion and deformation without being restricted by lost circulation channels. They then settle in the lost circulation formation and form a plugging layer through a curing reaction or swelling effect. Among the polymer gel LCMs, high-temperature resistant polymer gels can either be used alone or in combination with other LCMs, bringing the advantages of adjustable gelation time, strong lost circulation control ability, and strong filtration ability of the plugging slurry. Moreover, they are suitable for the lost circulation control of microporous leaky layer and have limited influence on the performance of drilling fluids. Therefore, the high-temperature resistant polymer gel lost circulation control technique is increasingly becoming a hot spot in the research of LCMs nowadays. This paper summarizes the research progress into high-temperature resistant functional gels for profile control and water shutoff, lost circulation prevention and control, and hydraulic fracturing. Furthermore, the current application status of high-temperature resistant gels and high-temperature resistant gel temporary plugging agents is demonstrated, followed by a detailed overview of the gel-breaking methods. Overall, this research lays the theoretical foundation for the application and promotion of high-temperature resistant gels.

A normal contact force model for viscoelastic bodies and its finite element modeling verification

A novel normal contact force model considering the energy dissipation for viscoelastic bodies is presented. By solving the differential equation through applying Laplace transform and its inverse transform, the relationship of the stress and strain is established. The model is transformed from the stress-strain relation using the Stieltjes convolution. The proposed model involves the viscosity and relaxation time which represent dominating characteristics of viscoelastic bodies. A means to verify the model using the finite element method (FEM) is performed with a specify two-sphere model for FEM simulations and a user material subroutine applied to define viscoelastic material properties. The validity of the novel model is verified with FEM simulations by comparing the force-time and force-displacement relations. The comparisons indicate that results obtained by the model agree well with the outcomes of FEM simulations. In addition, results of the proposed model are compared with the former experimental data and results obtained by other viscoelastic contact models, which manifests that results predicted by this model fit the experimental data well in general, especially in the restitution phase.

Динамическое деформирование сферического вязкоупругого тела с упруговязкопластическим заполнителем

На основе модели упрочняющегося упруговязкопластического тела и вязкоупругого тела исследовано напряженно-деформированное состояние кусочно-неоднородного сферического тела под действием нагрузок, постоянной внешней, и зависящей от времени внутренней. Получены решения для полей напряжений и перемещений. Based on the model of a hardening elastic-plastic body and a viscoelastic body, the stress-strain state of a piecewise inhomogeneous spherical body under the action of loads, constant external and time-dependent internal, is investigated. Solutions for stress and displacement fields are obtained.

EVALUATION OF THE AGING OF BITUMEN-MASTIC INSULATION OF GAS PIPELINES ON THE BASE OF THE MECHANICAL CHARACTERISTICS CHANGING

Phenomenological models for describing the process of straining of bitumen-mastic insulation used for protection of the natural gas pipelines from electrochemical corrosion is proposed. The viscoelastic characteristics of insulation at different temperatures and after aging are determined. It is shown that the viscosity and stiffness coefficients determined on the basis of the accepted rheological model of the Maxwell viscoelastic body can be used to assess the degree of degradation of insulation.

Compression Relaxation of Multi-Structure Polymer Composites in Penetrating Liquid Medium.

Multi-structural polymer composites are widely used in the mechanical engineering, automotive, aviation and oil refining industries, as well as in the printing industry as a shock-absorbing deckle on the offset cylinders of printing machines. During offset printing, composites come into contact with inks and washing solutions, the components of which penetrate the material and cause the polymers to swell. This process degrades the print quality, and for this reason the study of its features is relevant. The prerequisites for this work are the study of the fundamental laws of diffusion and sorption of liquids by polymers with different micro- and macro-structures in different physical states and in different forms (e.g., films, sheets, fibers and fabrics). The combination of polymer materials in the composition of multi-structural fabric blankets makes it possible to obtain materials with unique mechanical properties and high resistance to liquid penetrating media and to use them in high-tech processes of multi-color printing with high resolution and color rendering. This article reports for the first time the kinetics and thermodynamics results obtained from the swelling of multi-structural polymeric blankets in solvents used in printing, and the effect of sorption of different polar liquids on the viscoelastic strain under compression during the operation of the damping systems of printing machines. Using mathematical models of activated liquid diffusion in polymers and deformation of a viscoelastic body, the swelling rate constants, solvent diffusion coefficients (the kinetic characteristics of the swelling process) and Flory−Huggins parameters (the thermodynamic characteristics of the interaction of the solvent with the composite) for composite−solvent systems with several chemical composition variants were determined. The elastic modulus and the viscosity coefficient of the composite under liquid saturation were calculated based on the experimental cyclic compression data. The range of change in the compression and restoration times of the polymeric blankets (0.09 s ÷ 0.78 s) was determined. It was shown that the composite swelled to a limited extent in all the studied liquids. All solvents used were thermodynamically poor (χ > 0.5). It has been established that rubber−fabric blankets coated with nitrile rubber are the least resistant to the action of dichloroethane, and that blankets with layers of polyolefins are not resistant to ethyl acetate. Water significantly affects the physicochemical properties of rubber−fabric blankets with a large proportion of cotton fabric layers. The data obtained can serve as a basis for optimizing the compositions of inks and cleaning solutions, as well as a theoretical basis for the thermodynamics of composite−solvent systems.

A Magneto-Viscoelasticity Problem with Aging.

This study addresses a magneto-viscoelasticity problem, considering the one-dimensional case. The system under investigation is given by the coupling a non-linear partial differential equation with a linear integro-differential equation. The system models a viscoelastic body whose mechanical behavior, described by the linear integro-differential equation, is also influenced by an external magnetic field. The model here investigated aims to consider the concomitance of three different effects: viscoelasticity, aging and magnetization. In particular, the viscoelastic behavior is represented via an integro-differential equation whose kernel characterizes the properties of the material. In a viscoelastic material subject to the effects of aging, all changes in the response to deformation are due not only to the intrinsic memory of the material but also to deterioration with the age of the material itself. Thus, the relaxation function is not assumed to depend on the two times, present and past, via their difference, but to depend on both the present and past times as two independent variables. The sensibility to an external magnetic field is modeled by a non-linear partial differential equation taking its origin in the Landau-Lifschitz magnetic model. This investigation is part of a long-term research project aiming to provide new insight in the study of materials with memory and, in particular, viscoelastic materials. Specifically, the classical model of viscoelastic body introduced by Boltzmann represents the fundamental base from which a variety of generalizations have been considered in the literature. In particular, the effects on the viscoelastic body due to interaction with an external magnetic field are studied. The new aspect under investigation is the combined presence of the external magnetic field with the effect of aging. Indeed, the coupling of viscoelasticity, which takes into account the deterioration of the material with time, with the presence of an external magnetic field, was never considered in previous research. An existence and uniqueness result is proved under suitable regularity assumptions.

Zener Model with General Fractional Calculus: Thermodynamical Restrictions

We studied a Zener-type model of a viscoelastic body within the context of general fractional calculus and derived restrictions on coefficients that follow from the dissipation inequality, which is the entropy inequality under isothermal conditions. We showed, for a stress relaxation and a wave propagation, that the restriction that follows from the entropy inequality is sufficient to guarantee the existence and uniqueness of the solution. We presented numerical data related to the solution of a wave equation for several values of parameters.

Indenting viscoelastic thin layers: A numerical assessment

Normal indentation of viscoelastic bodies is a technique widely employed to characterize the viscoelastic material properties. Here, a numerical Boundary Element methodology is developed to model the indentation process also when the solids in contact are thin layers. Specifically, two boundary conditions for the thin slabs are considered: the case of a confined layer, perfectly bonded to a rigid substrate, and that one of a free layer, supported by a constant pressure. Numerical analyses focus, firstly, on creep and relaxation indentation tests and show that finite values of the contacting layers thickness produce dramatic quantitative changes in comparison with what obtained under the half-plane (HP) assumption. Similar effects are found also in the case of loading and deformation indentation cycles: this results crucial for vibrational phenomena and confirms the opportunity of introducing the numerical technique here presented.