Three-parameter Viscoelastic Model Research Articles

Comparative Study on the Dynamic Response of Asphalt Pavement Structures: Analysis Using the Classic Kelvin, Maxwell, and Three-Parameter Solid Models

This study addressed the complex problems of selecting a constitutive model to objectively characterize asphalt mixtures and accurately determine their viscoelastic properties, which are influenced by numerous variables. Inaccuracies in model or parameter determination can result in significant discrepancies between the calculated and measured results of the pavement’s structural dynamic response. To address this, the research utilized the physical engineering principles of asphalt pavement structure to perform dynamic modulus tests on three types of high-content rubberized asphalt mixtures (HCRAM) within the surface layer. The research aimed to investigate the influencing factors of the dynamic modulus and establish a comprehensive master curve. This study also critically evaluated the capabilities of three viscoelastic models—the three-parameter solid model, the classical Maxwell model, and the classical Kelvin model—in depicting the dynamic modulus of HCRAM. The findings indicated a negative correlation between the dynamic modulus of the asphalt mixture and temperature, while a positive association exists between the loading frequency and temperature, with the impact of the loading frequency diminishing as the temperature increases. Notably, the three-parameter solid model was identified as the most accurate in describing the viscoelastic properties of the HCRAM. Furthermore, the dynamic response calculations revealed that most indexes in the surface layer’s dynamic response are highest when evaluated using the three-parameter viscoelastic model, underscoring its potential to enhance the pavement performance’s predictive accuracy. This research provides valuable insights into optimizing the material performance and guiding the pavement design and maintenance strategies.

Creep settlement analysis of pile foundations using viscoelastic model by incorporating nonlinear soil behaviour

ABSTRACT This study utilizes a nonlinear three-parameter viscoelastic model (a nonlinear spring in series with a Kelvin-Voigt element) to study the time-dependent creep behaviour in a single pile and group of piles. The method is based on modified Mindlin’s approach; and Laplace transforms have been utilized to simplify the viscoelastic problem into an equivalent elastic problem. The soil nonlinearity has been modelled by using a hyperbolic stress-strain relationship. The effects of parameters such as pile spacing, slenderness ratio and pile load factor on shear stress distribution, displacement of pile elements relative to the pile head, effects of enlargement of the pile base and interaction factors have been evaluated. The ratio of interaction factor for immediate and creep settlement is in the range of 0.4−0.9 for various pile groups. Since this study incorporates soil nonlinearity, the interaction factors increase by about 6%−10% when the pile load factor increases from 0.5 to 1.

Magnetization-affected localized flows in ferromagnetic metallic glass

In this paper, the interaction between magnetization and dynamic relaxation of heterogeneous structure in a ferromagnetic metallic glass (MG) is investigated. It is found that the magnetic state of the MG can be changed through wearing its surface. Accompanying with the change of magnetic state, the local dynamic mechanical behavior of the MG was detected by nanoindentation varies. Through analyzing with combination of the three-parameter viscoelastic model and state-transition theory, it is discovered that the microstructure of the glass can be apparently changed by magnetization with the effective size, viscosity of the liquid-like cores and the relaxation time increased by more than 3 times. Inversely, with cycling loading below the elastic limit of the MG using nanoindentation, it is revealed that localized flows of nano-liquid in the glass erase the effect of magnetization. The interaction between magnetization and localized flows relates to spin-orbit coupling in the MG; the change of magnetic state and liquid-like regions in the MG does not affect its instantaneous shear modulus associated with its ideal glassy state. The studies help understand the dynamic magneto-mechanical properties of amorphous magnetic materials, and have technological importance for their applications.

Effect of Cross-linking Density on Creep and Recovery Behavior in Epoxy-Based Shape Memory Polymers (SMEPs) for Structural Applications

Epoxy-based shape memory polymers (SMEPs) are gaining importance in the area of aerospace structures due to their high strength and stiffness which is a primary requirement for an SMEP in structural applications. The understanding of viscoelastic behavior of SMEPs is very essential to assess their shape memory effect. In the present work, three types of SMEPs with varying cross-linking densities were developed by curing an aromatic epoxy resin with aliphatic amines. Glass transition temperature (Tg) was measured for these SMEPs using advanced rheometric expansion system, and from the Tg measurements, a range of temperatures from glassy to rubbery regimes were chosen. At selected temperatures, creep-recovery tests were performed in order to evaluate the viscoelastic behavior of SMEPs and also to investigate the effect of temperature on creep-recovery. Further, a three-parameter viscoelastic model (Zener) was used to fit the data obtained from experiments. Model parameters like moduli of the springs and viscosity of the dashpot were evaluated by curve fitting. Results revealed that Zener model was well suited to describe the viscoelastic behavior of SMEPs as a function of test temperatures.

A non-linear viscoelastic model for sediments flocculated in the presence of seawater salts

A new empirical three-parameter viscoelastic model is proposed for describing the rheological behavior of linear and nonlinear materials. In particular, the model succesfully reproduced experimental creep curves at various constant stresses for flocculated suspensions of alumina in the presence of different types of seawater salts. The new model is compared to the classical standard linear solid model and to an extension of this, also proposed here, to represent nonlinear materials. Based on the goodness of fit, the new model is found to be the most appropriate for the experimental system studied. A sensitivity analysis of the parameters to applied stress and type of salt in the sediments reveals that the new model, originally proposed as an ansatz, has three components, constant, linear and nonlinear, as inferred from the behaviour of each model parameter with the applied stresses. The linear contribution follows a correlation with the applied stresses for salts that enhance the hydrogen network of water, so called maker salts, and another for the salts that weaken the network, so called breaker salts. Even more interesting, the nonlinear contribution is characterized by large exponential decay lengths for breaker salts and small exponential decay lengths for maker salts. The existence of linear and nonlinear components may enable applying the model to a variety of systems.

A New Hybrid Viscoelastic Soft Tissue Model based on Meshless Method for Haptic Surgical Simulation

This paper proposes a hybrid soft tissue model that consists of a multilayer structure and many spheres for surgical simulation system based on meshless. To improve accuracy of the model, tension is added to the three-parameter viscoelastic structure that connects the two spheres. By using haptic device, the three-parameter viscoelastic model (TPM) produces accurate deformationand also has better stress-strain, stress relaxation and creep properties. Stress relaxation and creep formulas have been obtained by mathematical formula derivation. Comparing with the experimental results of the real pig liver which were reported by Evren et al. and Amy et al., the curve lines of stress-strain, stress relaxation and creep of TPM are close to the experimental data of the real liver. Simulated results show that TPM has better real-time, stability and accuracy.

Viscoelastic Indentation and Resistance to Motion of Conveyor Belts Using a Generalized Maxwell Model of the Backing Material

Abstract A one-dimensional Winkler foundation and a generalized viscoelastic Maxwell solid model of the belt backing material are used to determine the resistance to motion of a conveyor belt over idlers. The viscoelastic material model is a generalization of the three-parameter Maxwell model that has previously been used to predict the effective frictional coefficient of the rolling motion. Frequency, or loading rate, and temperature dependence of the material properties are incorporated with the time/temperature correspondence principle of linear viscoelastic materials. As a consequence of the Winkler foundation model, a normalized indentation resistance is independent of the primary belt system parameters - carrying weight per unit width, idler diameter and backing thickness - as is the case for a three-parameter viscoelastic model. Example results are provided for a typical rubber compound backing material and belt system parameters.

DYNAMIC STABILITY OF A VISCOELASTIC BEAM SUBJECTED TO HARMONIC AND PARAMETRIC EXCITATIONS SIMULTANEOUSLY

In this paper the dynamic stability is studied of a simply supported viscoelastic beam, which is subjected to harmonic and parametric excitations simultaneously. Considering the viscoelastic differential constitutive law, the large deflection curvature and the non-linear effects of inertia, stiffness and damping, the generalized differential governing equation of the viscoelastic beam is obtained. By choosing a simple example of the three-parameter viscoelastic model and using the Galerkin approximation, the governing equation is reduced to a third order non-linear ordinary differential equation. The Stevens method is followed to analyze the stability of the linear system and apply both the method of variation of parameters and the method of averaging to analyze the non-linear system, with the assumption of small harmonic excitation. In this paper, the Routh-Hurwitz criterion is used to investigate the stability of steady state solutions of the parametric resonance, and the non-linear effects of the spring, mass and damping terms of the subsystem are also studied.

Stress relaxation and attenuation of fluid-saturated sandstone at low frequency

The authors studied the attenuation and modulus dispersion of fluid-saturated sandstone by changing the viscosity of fluid, tried to find out the relationship between attenuation, exciting frequency and resonance amplitude to identify the difference of attenuation when the sandstone was saturated with different fluids. The authors also select three-parameter viscoelastic model and Cole-Cole distribution to explain the observed experimental phenomena.

Experimental determination of short-term creep of femoral sheep bones and theoretical estimation of the dissipated energy during walking

The short-term creep of ten fresh femoral sheep bones was determined through an analysis of their strain response in the time interval 10-2–103 s, under constant load corresponding to 100% body weight. The strain in the direction of minimum principal stress was measured by strain gauges attached at two points located on the ventral dorsal level at one-half and three-quarters of the bone's length, beginning from the knee joint. The experimental data were analysed using a three-parameter viscoelastic model consisting of a spring and a Kelvin element in series, and the material constants were calculated. The results indicate that the viscoelastic behaviour of femoral compact bone presents a transition phase with a time constant comparable with that of the normal walking period. Approximating the stress developed under walking conditions by a sinusoidal function, the corresponding strain time function and the dissipated energy due to viscoelastic mechanisms were estimated. According to our estimations the dissipated energy during normal walking conditions (speed 2.5 km h-1 and 60 steps min-1) was about 12%.

Viscoelastic crack analysis by the boundary integral equation method

The linear viscoelastic three-dimensional crack problem is analyzed by combining the correspondence principle and the boundary integral equation method. In a general crack analysis the usual boundary integral equations lead to a nonunique formulation of the problem, because they do not involve information about the loading on the crack surface. Here, the boundary integro-differential equations are applied to the numerical calculation of the crack opening displacement of a penny-shaped crack in an infinite linear viscoelastic body. Moreover, the influence of several parameters of the three-parameter viscoelastic model on the crack opening displacement and the incubation time is shown.

A comparison of the dynamic response of the ACS and SLS models for linear viscoelasticity

Using asymptotic analysis and numerical computation, we compare the behaviour of the three-parameter viscoelastic model proposed by Achenbach and Chao (ACS) with that of the Standard Linear Solid (SLS) in one-dimensional wave propagation. Our study shows that the models behave very similarly in both the near and far fields and that the much simpler form of the fundamental solution for the Achenbach-Chao model may take it preferable in many applications.

A three-parameter viscoelastic model particularly suited for dynamic problems

I n this paper a stress-strain relation is proposed for a linearly viscoelastic solid of the threeparameter type. The mechanical model representation includes a mass. An analysis of the creep function and the elastic modulus shows the similarity of these functions with those of the standard linear solid. As opposed to the stress-strain relation of the standard linear solid the present relation leads to simple solutions of dynamic problems. A wave propagation example is treated.