Viscoelastic Model Research Articles

Vibration reduction of rotor systems using magneto-rheological elastomeric supports

Support characteristics (stiffness and dissipation) are well understood to influence the dynamic behaviour of rotors. Supports play an essential role in deciding the stability and response of the rotors. Therefore, frequency-dependent support characteristics are beneficial in determining the rotor response as the frequency of excitation keeps changing. An elegant choice of making rotor supports is by using magneto-rheological elastomeric (MRE) materials. The magnetic field application results in a change in the stiffness and dissipation behaviour of MREs and consequently influences the dynamics of the rotor–shaft system. An attempt is made in this work to conceptualize the MRE as viscoelastic sectors put between the outer race of a bearing and the bearing housing to make the rotor support. A rigorous analytical formulation is done to obtain the stiffness and dissipation of the support so formed in terms of a viscoelastic model of the material under the effect of dispersed magnetic material, the geometry of the sectors, the intensity of the magnetic field, and the frequency of forcing function the supports are subject to. The supports show promising results by reducing the vibrations at resonance by suitably applying the magnetic field. Therefore, MRE materials may be proposed as adaptive supports to both structures and rotors to induce intended dynamic behaviour.

Dynamic compressive properties and constitutive model of waste crumb rubber (CR) modified ultra-high performance engineered cementitious composites (UHP-ECC)

Ultra-high-performance engineered cementitious composites (UHP-ECC) are well-known for their outstanding mechanical properties under static and dynamic loads. However, the effect of modifying UHP-ECC with crumb rubber (CR) on its performance, especially under high strain rates, remains poorly understood. This study systematically examined the dynamic compressive behavior and characteristic failure patterns of CR-modified UHP-ECC under high strain rates using a split Hopkinson pressure bar (SHPB) system. The study focused on evaluating the dynamic compressive strength, stress-strain response, and strain energy density (SED). A dynamic increase factor (DIF) formula was developed based on experimental data, and a nonlinear viscoelastic constitutive model was proposed to predict compressive behavior across various strain rates. Results indicate that while the addition of 10% CR slightly reduces the quasi-static compressive and flexural strength, it significantly enhances tensile ductility. Under high strain rates, CR-modified UHP-ECC shows no substantial effect on peak compressive stress but a marked increase in peak compressive strain. The SED also increased by 20.2%, outperforming other high-performance materials such as UHPC and normal ECC. These findings demonstrate that incorporating 10% CR into UHP-ECC offers considerable advantages, particularly in enhancing structural resilience under dynamic loading conditions. The proposed nonlinear viscoelastic model accurately predicts the compressive behavior of CR-modified UHP-ECC, presenting significant implications for practical engineering applications where high strain rate performance is crucial.

Mitigation Techniques for Volumetric Locking in the Implicit Material Point Method (MPM)

ABSTRACTThe material point method (MPM) aims to avoid mesh distortion problems occurring in the commonly used finite element method (FEM). To achieve this, the continuum is discretized as a set of material points, while the solution of the weak form of the underlying partial differential equations is conducted on an Eulerian background mesh. As this process works similar to FEM, the MPM also displays volumetric locking for near‐incompressible materials. However, this also means that mitigation techniques developed for FEM can be adapted to the MPM. The main difficulty for this process lies in the higher‐continuity basis functions, which are required in MPM to achieve reasonable results. This study first reviews the applicability of different locking mitigation techniques in MPM. Then, a framework for a locking‐free implicit MPM is presented and validated using common tests investigating the locking behavior and stress oscillations. Finally, the presented methods are applied to a viscoelastic material model representing unvulcanized rubber to show the potential of MPM for tire molding simulations.

Rheology-dependent surface wave characteristics in an advanced geomaterial flexoelectric plate with viscoelastic coating

Abstract This study investigates the transmission of seismic surface waves in a composite framework comprising a viscoelastic layer overlying a flexoelectric material. The study focuses on understanding the impact of different viscoelastic models (Maxwell, Newtonian, and Kelvin-Voigt) and interface conditions (smooth and welded contact) on the damping and dispersion characteristics of these waves.To achieve this, the study employs a variable-separable technique and appropriate boundary conditions to derive complex frequency relations for electrically open and short circuits scenarios. These relations are subsequently divided into real and imaginary parts to examine the dispersion and dampening properties, respectively. Numerical simulations are conducted to analyze the response of flexoelectric coefficient, viscoelastic layer thickness, and bonding parameter on phase velocity and dampening coefficient.The research findings indicate that the attenuation properties of the Maxwell and Newtonian models are lower compared to the Kelvin-Voigt model. Graphical comparisons highlight the influence of viscoelastic models and interface characteristics on wave propagation.This research can help in the development of sensors, energy harvesters, and wave manipulation devices that employ flexoelectric materials with viscoelastic coatings. Knowledge of surface wave dynamics in these structures is vital for their optimal performance.

Modeling and Simulation of Curing Kinetics and Stress of a Bonded Mirror with a Room-Temperature Curable Adhesive

Adhesive bonding widely appears in optomechanical products. Nevertheless, the occurrence of curing stress often leads to structure deformation, which significantly compromises the performance of optomechanical systems. This work focuses on the formation and evolution of curing stress and its influence on a multi-point face-bonded mirror. The adhesive’s degree of cure (DOC) was measured using the differential scanning calorimetry (DSC) technique. The functional relationship between DOC and glass-transition temperature ([Formula: see text]) was determined utilizing DiBenedetto’s equation. The time–DOC shift factor of the adhesive was obtained by stress relaxation tests on specimens with different DOCs. Subsequently, a viscoelastic constitutive model concerning the curing process and an accurate finite-element (FE) model of the bonded mirror were developed to simulate the surface-figure error (SFE) evolution. The predicted surface figure was compared with experiments, and the model was verified and validated. Further, simulation analyses were conducted on the performance of the multi-point face-bonded mirror, and the influences of adhesive thickness, bonding area, and spot number on the SFE of the mirror were examined.

Velocity field measurements under Very Large Floating Structures interacting with surface waves

Increasing utilization of ocean space and a global push for renewable energy solutions has spurred interest in wave behavior around Very Large Floating Structures, like floating photovoltaic (PV) systems. Flexible PV modules may be more suitable for the varying wave conditions found in offshore environments. However, while viscoelastic models are commonly used for wave prediction, they show notable discrepancies with experiments, likely due to untested assumptions of inviscid flow. This experimental study aims to fill that gap by investigating both the wave characteristics and velocity fields underneath flexible and rigid structures using simultaneous Particle Image Velocimetry (PIV) and wave elevation measurements. Wave attenuation is observed for short wavelengths over the flexible structure length. The 2nd order Stokes wave theory provides a good approximation of the wave-induced horizontal velocity profiles under the flexible structure but underestimates the velocities under the rigid one which further lacks the typical exponential decay with water depth. The presence of a wave boundary layer is showcased and compared to an adaptation of the Stokes 2nd problem.

Impact of structural adhesive creep on the performance of CFRP-strengthened steel beams

This paper examines the viscoelastic creep response of the structural strengthening epoxy adhesive and develops a viscoelastic constitutive model for numerical analyses to assess its impact on the long-term performance of carbon fibre reinforced polymer (CFRP)-strengthened steel beams. The numerical studies explore the behaviour of CFRP-strengthened steel beams subjected to both three-point and four-point bending over a one-year period, with temperatures ranging from −20 to 60 °C. The results revealed that the stiffeners could reduce the deflection and peak stress in the steel under four-point bending, yet they had the opposite effect under three-point bending. Furthermore, whilst the larger CFRP plates could reduce the slip at the plate ends, they provided only a limited enhancement in the strengthening effectiveness. The impact of viscoelastic creep in the adhesive is more marked and apparent, particularly at higher temperatures. Over time, the increased slip leads to a rise in maximum stress and deflection of the steel beams, thereby diminishing the effectiveness of the strengthening. A low-temperature environment can mitigate these negative impacts, whereas elevated temperatures can significantly exacerbate them. Notably, at a moderate temperature of 30 °C, the maximum CFRP stress can already be reduced by 32.25 %, which corresponds to an increase in steel stress by 4.15 %. Therefore, in practical applications at warm service temperatures, the creep of CFRP-strengthened steel beams should be carefully considered to ensure their long-term safety.

Stress boundary layers for the Phan-Thien–Tanner fluid at the static contact line in extrudate swell

The method of matched asymptotic expansions is used to examine the behaviour of the Phan-Thien–Tanner (PTT) fluid in the neighbourhood of the contact line singularity in extrudate swell. The solution structure for this shear-thinning viscoelastic fluid model has solvent stresses that dominate the polymer stresses, but requires stress boundary layers to fully resolve the solution at the die wall and free surface. The sizes and mechanism of the boundary layers at the two surfaces are different. We derive and present a similarity solution for the boundary layer at the die wall and an exact solution for the boundary layer at the free surface. An expression for the local behaviour of the free surface is also derived. The results for the boundary layers completes the preliminary asymptotic results for the PTT model presented in previous work.

Response Analysis and Vibration Suppression of Fractional Viscoelastic Shape Memory Alloy Spring Oscillator Under Harmonic Excitation

This study investigates the dynamic behavior and vibration mitigation of a fractional single-degree-of-freedom (SDOF) viscoelastic shape memory alloy spring oscillator system subjected to harmonic external forces. A fractional derivative approach is employed to characterize the viscoelastic properties of shape memory alloy materials, leading to the development of a novel fractional viscoelastic model. The model is then theoretically examined using the averaging method, with its effectiveness being confirmed through numerical simulations. Furthermore, the impact of various parameters on the system’s low- and high-amplitude vibrations is explored through a visual response analysis. These findings offer valuable insights for applying fractional sliding mode control (SMC) theory to address the system’s vibration control challenges. Despite the high-amplitude vibrations induced by the fractional order, SMC effectively suppresses these vibrations in the shape memory alloy spring system, thereby minimizing the risk of catastrophic events.

Viscoelastic plastic creep constitutive model based on energy conservation law and strain energy theory

On the basis of the law of conservation of energy, the three stages of rock creep are analyzed. The reasons for the difficulty in studying the accelerated creep stage of rocks using the traditional creep model are expounded. The triaxial creep deformation law and critical point parameter values of rocks are obtained by carrying out rock creep tests under different confining pressures. Based on strain energy theory, the law of conservation of energy, and Perzyna viscoplastic theory, a creep constitutive model, which can describe the whole process of primary creep, steady-state creep, and accelerated creep, is established. Results show that the model can well reflect the creep characteristics of rocks, especially when the load of rocks is greater than the long-term strength. It has an obvious effect on highlighting the accelerated creep stage of rocks. The fitting degree of the creep model curve and test curve is considerably greater than that of the Nishihara model curve and test curve. The model not only describes the whole process of rock primary creep, steady-state creep, and accelerated creep thoroughly but also compensates for the shortcomings of traditional models in describing accelerated creep. This model can provide a theoretical basis for further revealing the objective law of rock creep.

Damage mechanism and energy evolution of frozen soil under coupled compression–shear impact loading

In cold region engineering, the impact of coupled compression–shear loading on frozen soil foundations is a critical issue that urgently needs to be addressed, as it often significantly reduces bearing capacity and can cause structural failures. Accurately characterizing the mechanical behavior of frozen soil under dynamic coupled compression–shear loading is essential for enhancing the safety and stability of cold region engineering projects. This study prepared four frozen-soil specimens with varying tilting angles to investigate failure mechanisms and energy evolution under coupled compression–shear impact loading. The impact-compression experiments were conducted on the specimens under different loading strain rates and temperature conditions using a split Hopkinson pressure bar. The results indicated that the strength of frozen soil was effectively enhanced by higher strain rates and lower temperatures, while it was reduced by increased tilting angle. The fracturing morphology of frozen soil was analyzed from both microscopic and macroscopic perspectives to reveal its failure mechanisms. To quantify the strength characteristics of the frozen soil under various loading conditions, damage variables were defined from an energy-based perspective and incorporated into the Zhu–Wang–Tang viscoelastic constitutive model. Hence, a dynamic constitutive model for frozen soil under coupled compression–shear loading was developed. The model's predictive capability was validated through comparisons with the experimental data, which revealed a high level of agreement. The results of this study provide practical insights into the failure mechanisms and construction design of frozen soil foundations under coupled compression–shear impact loading in cold region engineering.

Effect of Part Size, Displacement Rate, and Aging on Compressive Properties of Elastomeric Parts of Different Unit Cell Topologies Formed by Vat Photopolymerization Additive Manufacturing.

Due to its ability to achieve geometric complexity at high resolution and low length scales, additive manufacturing (AM) has increasingly been used for fabricating cellular structures (e.g., foams and lattices) for a variety of applications. Specifically, elastomeric cellular structures offer tunability of compliance as well as energy absorption and dissipation characteristics. However, there are limited data available on compression properties for printed elastomeric cellular structures of different designs and testing parameters. In this work, the authors evaluate how unit cell topology, part size, the rate of compression, and aging affect the compressive response of polyurethane-based simple cubic, body-centered, and gyroid structures formed by vat photopolymerization AM. Finite element simulations incorporating hyperelastic and viscoelastic models were used to describe the data, and the simulated results compared well with the experimental data. Of the designs tested, only the parts with the body-centered unit cell exhibited differences in stress-strain responses at different part sizes. Of the compression rates tested, the highest displacement rate (1000 mm/min) often caused stiffer compressive behavior, indicating deviation from the quasi-static assumption and approaching the intermediate rate response. The cellular structures did not change in compression properties across five weeks of aging time, which is desirable for cushioning applications. This work advances knowledge on the structure-property relationships of printed elastomeric cellular materials, which will enable more predictable compressive properties that can be traced to specific unit cell designs.

The comparative role of physical system processes in Hudson Strait ice stream cycling: a comprehensive model-based test of Heinrich event hypotheses

Abstract. Despite their recognized significance on global climate and extensive research efforts, the mechanism(s) driving Heinrich events remain(s) a subject of debate. Here, we use the 3D thermomechanically coupled glacial systems model (GSM) to examine the Hudson Strait ice stream surge cycling and the role of three factors previously hypothesized to play a critical role in Heinrich events: ice shelves, glacial isostatic adjustment, and sub-surface ocean temperature forcings. In contrast to all previous modeling studies examining HEs, the GSM uses a transient last glacial cycle climate forcing, global viscoelastic glacial isostatic adjustment model, and sub-glacial hydrology model. The results presented here are based on a high-variance sub-ensemble retrieved from North American history matching for the last glacial cycle. Over our comparatively wide sampling of the potential parameter space (52 ensemble parameters for climate forcing and process uncertainties), we find two modes of Hudson Strait ice streaming: classic binge–purge versus near-continuous ice streaming with occasional shutdowns and subsequent surge onset overshoot. Our model results indicate that large ice shelves covering the Labrador Sea during the last glacial cycle only occur when extreme calving restrictions are applied. The otherwise minor ice shelves provide insignificant buttressing for the Hudson Strait ice stream. While sub-surface ocean temperature forcing leads to minor differences regarding surge characteristics, glacial isostatic adjustment does have a significant impact. Given input uncertainties, the strongest controls on ice stream surge cycling are the poorly constrained deep geothermal heat flux under Hudson Bay and Hudson Strait and the basal drag law. Decreasing the geothermal heat flux within available constraints and/or using a Coulomb sliding law instead of a Weertman-type power law leads to a shift from the near-continuous streaming mode to the binge–purge mode.

Research on mechanical behavior of particle/matrix interface in composite solid propellant

In the mesostructure of composite solid propellant, the interface formed between solid particle and matrix is a region with very special physical and chemical properties, and the mechanical behavior of the interface will directly affect the mechanical properties of the propellant. This article derived a viscoelastic cohesive constitutive model to describe the mechanical behavior of the interface. subsequently a particle/matrix interface specimen was design to measure the interface mechanical properties under different conditions. To this end, the parameters of the constitutive model were solved through a combination of experimental data fitting and inversion. It was found that the interface behavior exhibits strong rate and temperature correlations, and the cohesive constitutive model can effectively describe this characteristic.

Tensile properties and constitutive modeling of Kevlar29 fibers: From filaments to bundles

This paper experimentally investigates the tensile properties of Kevlar29 filaments and fiber bundles, revealing the size and strain rate effects on the mechanical properties of fiber bundles. The fracture modes and mechanisms of the fibers were analyzed, and viscoelastic constitutive models at the fiber bundle scale and constitutive models for filaments-bundles based on the Weibull distribution were established. The results show that Kevlar29 fiber bundles exhibit significant strain rate effects: as the strain rate increases, tensile strength and modulus increase, while fracture strain and toughness decrease. Under quasi-static loading, the fracture modes of the fibers are mainly fibrillation or shear flow, but as the strain rate increases, the failure modes shift towards brittle fracture. Both constitutive models can accurately predict the tensile properties of fiber bundles at different strain rates. The accuracy and applicability of the filament-to-bundle constitutive model were verified through numerical simulations, demonstrating that the model better describes the size effect of fibers and quantifies the damage to the fiber bundles.

Three-Dimensional Micromechanical Simulation and Evaluation of High-Toughness Ultra-Thin Friction Course with X-Ray Computed Tomography

As a novel pavement wear layer material, the micromechanical mechanisms of High-toughness Ultra-thin Friction Course (HUFC) have not been fully elucidated. This paper presents a new method for the three-dimensional micromechanical simulation of high-toughness asphalt mixtures based on a viscoelastic parameter calibration model. X-ray Computerized Tomography (CT) was employed to scan samples of high-toughness asphalt mixtures to obtain detailed information on the internal structure (aggregate, fine aggregate matrix FAM and voids), and a three-dimensional micromechanical model was constructed based on the real-scale distribution of these components. Aggregates in the high-toughness asphalt mixture were modeled as elastic bodies, while FAM was treated as a viscoelastic material characterized by the Burgers model. Using the Boltzmann linear superposition principle and Laplace transform theory, the viscoelastic properties of FAM were converted into Prony parameters recognizable by finite element software, and the viscoelastic parameters were calibrated. Micromechanical simulations were conducted for three different gradings of high-toughness asphalt mixtures, and the results show that the predicted deformation closely matched the measured deformation. This method accurately reflects the deformation characteristics of different gradings of high-toughness asphalt mixtures, overcoming the limitations of traditional numerical simulations based on homogeneous material models. It represents an advancement and refinement of micromechanical simulation methods for high-toughness asphalt mixtures.

Atomic Force Microscopy Analysis of Velocity Dependent Adhesive Viscoelastic Contact.

Adhesive contact phenomena play a crucial role in various scientific and engineering fields. However, considering viscoelasticity, which is essential for understanding practical applications involving soft materials like polymers, makes analysis challenging. Traditional elastic contact models such as the Johnson-Kendall-Roberts and Maugis-Dugdale models often fail to account for viscoelastic behavior. In this study, rate-dependent viscoelastic adhesive contacts were analyzed using atomic force microscopy force-distance curve measurements, comparing the elastic models with the viscoelastic model proposed by Barthel. The force curve analysis, conducted with the Barthel model for the first time, reveals that viscoelastic behaviors inside the contact area and the interaction zone both affect the contact state. These viscoelastic behaviors result in phenomena specific to viscoelastic contact, such as the "stick region" and the apparent work of adhesion. The Barthel model successfully captures the rate dependence of the contact situation, promoting a comprehensive understanding of viscoelastic adhesive contact phenomena.

Nonlinear electro-thermo-mechanical dynamic behavior of complexly curved GPL-reinforced panels with auxetic core

This research aims to study the nonlinear electro-thermo-mechanical dynamic responses of cylindrical, sine, and parabolic graphene platelets reinforced panels with auxetic cores and piezoelectric layers. By applying the higher-order shear deformation theory, viscoelastic foundation model, approximate technique for stress function, Rayleigh dissipation function, and energy method, the governing formulations are established. The natural frequency is determined explicitly, and the Runge-Kutta method is used to acquire the time amplitude responses of panels numerically. The noticeable effects of piezoelectrical layers, auxetic core, and GPL parameters on the mechanical and thermal dynamic buckling and vibration responses are recognized from the numerical investigations.

Rapid Prediction and Parameter Evaluation of Process-Induced Deformation in L-Shape Structures Based on Feature Selection and Artificial Neural Networks

The process-induced deformation (PID) during the manufacturing of thermosetting composite materials can significantly compromise manufacturing precision. This paper introduces an innovative method that combines a finite element analysis (FEA), feature classification algorithms, and an Artificial Neural Network (ANN) framework to rapidly predict the PID of a typical L-shaped structure. Initially, a comprehensive range of parameters that influence PID are compiled in this research, followed by the generation of a dataset through FEA considering viscoelastic constitutive models, validated by experimental results. Influential parameters are classified using Random Forest and LASSO regression methods, with each parameter rated according to its impact on PID, delineating their varying degrees of importance. Subsequently, through a hyperparameter analysis, an ANN framework is developed to rapidly predict the PID, while also refining the assessment of the parameters’ significance. This innovative approach achieves a computational time reduction of 98% with less than a 5% loss in accuracy, and highlights that under limited computational conditions, considering only a subset or all of the parameters—the peak temperature, corner angle, coefficient of chemical shrinkage, coefficient of thermal expansion, curing pressure, and E1—minimizes accuracy loss. The study demonstrates that machine learning algorithms can effectively address the challenge of predicting composite material PID, providing valuable insights for practical manufacturing applications.

A globally divergence-free weak Galerkin finite element method with IMEX-SAV scheme for the Kelvin–Voigt viscoelastic fluid flow model with high Reynolds number

In this manuscript, we present a globally divergence-free weak Galerkin finite element method with the IMEX-SAV scheme for solving the Kelvin–Voigt viscoelastic fluid flow model. Firstly, the weak Galerkin finite element method is used to analyze the spatial discretization, this method can yield globally divergence-free velocity solutions. Secondly, the IMEX-SAV difference scheme is adopted in the temporal discretization for the fully discrete scheme, and we can obtain the unconditional stability result for the velocity. In addition, combined with the stabilization idea, the method can not only reduce the spurious numerical oscillation at the high Reynolds number but also yield the uniform results that the constants in the error estimates do not explicitly depend on the inverse power of the physical parameters of the Kelvin–Voigt viscoelastic fluid flow model. Finally, several numerical experiments are performed to verify the theoretical results.