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Journal articles on the topic 'Viscoelastic Kelvin-Voigt model'

Author: Grafiati

Published: 28 May 2022

Last updated: 30 July 2025

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1

Makwana, Harsh, Dr Girish P. Deshmukh, and Dr Laxman Kumar Pandey. "STRAIN RATE DEPENDENCY OF NEOHOOKEAN MATERIAL USING KELVIN-VOIGT VISCOELASTIC MODEL." International Journal of Engineering Applied Sciences and Technology 8, no. 1 (2023): 205–12. http://dx.doi.org/10.33564/ijeast.2023.v08i01.032.

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This research paper examines the strain rate dependency of a Neo-Hookean material using the Kelvin-Voigt viscoelastic model. The Neo-Hookean model is widely used to describe the mechanical behavior of rubber-like materials, but it fails to consider the timedependent response observed in many materials. To overcome this limitation, the Kelvin-Voigt viscoelastic model, which incorporates a viscosity term into the NeoHookean model, is employed to capture the strain rate dependency. The paper commences by introducing the Neo-Hookean material model and its assumptions. It then elucidates the ration

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2

Abdessamad, Zouhair, Ilya Kostin, Grigory Panasenko, and Valery P. Smyshlyaev. "Homogenization of thermo-viscoelastic Kelvin–Voigt model." Comptes Rendus Mécanique 335, no. 8 (2007): 423–29. http://dx.doi.org/10.1016/j.crme.2007.05.022.

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3

Stan, Felicia, Adriana-Madalina Turcanu (Constantinescu), and Catalin Fetecau. "Analysis of Viscoelastic Behavior of Polypropylene/Carbon Nanotube Nanocomposites by Instrumented Indentation." Polymers 12, no. 11 (2020): 2535. http://dx.doi.org/10.3390/polym12112535.

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In this work, the viscoelastic behavior of polypropylene (PP)/multi-walled carbon nanotube (MWCNT) nanocomposites was investigated by indentation testing and phenomenological modeling. Firstly, indentation tests including two-cycle indentation were carried out on PP/MWCNT nanocomposite with three MWCNT loadings (1, 3 and 5 wt %). Next, the Maxwell–Voigt–Kelvin model coupled with two-cycle indentation tests was used to predict the shear creep compliance function and the equivalent indentation modulus. The indentation hardness and elastic modulus of the PP/MWCNT nanocomposites extracted based on

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4

Pezzinga, Giuseppe. "On the Characterization of Viscoelastic Parameters of Polymeric Pipes for Transient Flow Analysis." Modelling 4, no. 2 (2023): 283–95. http://dx.doi.org/10.3390/modelling4020016.

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The behaviour of polymeric pipes in transient flows has been proved to be viscoelastic. Generalized Kelvin–Voigt (GKV) models perform very well when simulating the experimental pressure. However, in the literature, no general indications on the evaluation of the model parameters are given. In the present study, the calibration of GKV model parameters is carried out using a micro-genetic algorithm for experimental tests of transient flows in polymeric pipes taken from the literature. The results confirm that the higher the number of Kelvin–Voigt elements, the better the reproduction of experime

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5

Kundu, Sudeep, and Amiya K. Pani. "Stabilization of Kelvin–Voigt viscoelastic fluid flow model." Applicable Analysis 98, no. 12 (2018): 2284–307. http://dx.doi.org/10.1080/00036811.2018.1460810.

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6

Chen, Genmeng. "Comparison of 2-D numerical viscoelastic waveform modeling with ultrasonic physical modeling." GEOPHYSICS 61, no. 3 (1996): 862–71. http://dx.doi.org/10.1190/1.1444011.

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The objective of the study is to test the validity of theoretical models of wave attenuation by comparing their predictions of attenuation against physical model results. The study is confined to a 2-D geometry, and the viscoelastic materials used in physical modeling are those commonly used in the experiment. The physical modeling data of homogeneous media are compared with the numerical results in the frequency domain. The time‐domain comparisons between numerical modeling and physical modeling are also shown by three examples. The theoretical viscoelastic models used in the numerical study

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7

Amosov, Andrey, Ilya Kostin, Grigory Panasenko, and Valery P. Smyshlyaev. "Homogenization of a thermo-chemo-viscoelastic Kelvin-Voigt model." Journal of Mathematical Physics 54, no. 8 (2013): 081501. http://dx.doi.org/10.1063/1.4813106.

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8

Reyes de Luna, Eduardo, Andriy Kryvko, Juan B. Pascual-Francisco, Ignacio Hernández, and Didier Samayoa. "Generalized Kelvin–Voigt Creep Model in Fractal Space–Time." Mathematics 12, no. 19 (2024): 3099. http://dx.doi.org/10.3390/math12193099.

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In this paper, we study the creep phenomena for self-similar models of viscoelastic materials and derive a generalization of the Kelvin–Voigt model in the framework of fractal continuum calculus. Creep compliance for the Kelvin–Voigt model is extended to fractal manifolds through local fractal-continuum differential operators. Generalized fractal creep compliance is obtained, taking into account the intrinsic time τ and the fractal dimension of time-scale β. The model obtained is validated with experimental data obtained for resin samples with the fractal structure of a Sierpinski carpet and e

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9

Gholipour, Alireza, Mergen H. Ghayesh, and Yueqiang Zhang. "A Comparison between Elastic and Viscoelastic Asymmetric Dynamics of Elastically Supported AFG Beams." Vibration 3, no. 1 (2020): 3–17. http://dx.doi.org/10.3390/vibration3010002.

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This investigation compares the dynamic simulation results of perfect, elastically-supported, axially-functionally-graded (AFG) beams between viscoelastic and elastic models. When modeling and simulating the dynamics of AFG beams, the elastic model is commonly assumed so as to simplify calculations. This investigation shows how the dynamics varies if viscosity is present. The nonlinear continuous/discretized, axial/transverse motion derivation procedure is explained briefly based on Hamilton’s principle for energy/energy-loss, Kelvin–Voigt viscosity, elastic foundation assumption, and exponent

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10

Nowfal, Shaymaa Hussein, Ganga Rama Koteswara Rao, V. Velmurugan, Sudhakar Sengan, Ravi Kumar Bommisetti, and Pankaj Dadheech. "Advancing viscoelastic material modeling : Tackling time-dependent behavior with fractional calculus." Journal of Interdisciplinary Mathematics 27, no. 2 (2024): 307–16. http://dx.doi.org/10.47974/jim-1827.

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A combination of inherent unique stress-strain response features, Viscoelastic Materials (VM) provide an integral part in many different fields of engineering. Although practical, these materials’ highly complex time-dependent methods according to non-linear loading scenarios are impossible to model using conventional viscoelastic models such as Maxwell and Kelvin-Voigt. The present study introduces a framework that pushes over traditional Maxwell and Kelvin-Voigt approaches by employing fractional calculus in order to enhance the prediction of VM performance. The mathematical representation m

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11

Nguyen, TuanDung, Jin Li, Lijie Sun, DanhQuang Tran, and Fuzhen Xuan. "Viscoelasticity Modeling of Dielectric Elastomers by Kelvin Voigt-Generalized Maxwell Model." Polymers 13, no. 13 (2021): 2203. http://dx.doi.org/10.3390/polym13132203.

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Dielectric elastomers (DEs) are polymer materials consisting of a network of polymer chains connected by covalent cross-links. This type of structural feature allows DEs to generate large displacement outputs owing to the nonlinear electromechanical coupling and time-dependent viscoelastic behavior. The major challenge is to properly actuate the nonlinear soft materials in applications of robotic manipulations. To characterize the complex time-dependent viscoelasticity of the DEs, a nonlinear rheological model is proposed to describe the time-dependent viscoelastic behaviors of DEs by combinin

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12

Yucra, Hancco Alvaro Julio. "Modeling of a Viscoelastic System with Fractional Derivative." Open Journal of Mathematics and Physics 6 (November 22, 2024): 294. https://doi.org/10.5281/zenodo.14204903.

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We present an application of fractional differential equations in the modeling of viscoelastic systems. We consider a viscoelastic system represented by the fractional Kelvin-Voigt model and use the analytical method of the Laplace transform to solve the fractional differential equation associated with the system. Finally, we present a numerical simulation of the analytical solution obtained.

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13

Jiang, Bing. "MODELING NONLINEAR VISCOELASTIC BEHAVIOR UNDER LARGE DEFORMATIONS." Rubber Chemistry and Technology 88, no. 1 (2015): 28–39. http://dx.doi.org/10.5254/rct.14.86927.

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ABSTRACT A simple model was developed to describe the nonlinear viscoelastic behavior of rubberlike materials under large deformation in which the linear spring in the classical Kelvin-Voigt model is replaced by the Langevin-chain spring. This model has a simple mathematical structure and has only three material parameters. The model can capture the main features of the viscoelastic behaviors of polymers in wide range, from linear to nonlinear.

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14

Ciuncanu, Mihai. "The Dynamic Response of the Elastomeric Isolators Modeled as Voigt-Kelvin to the Action of the Seismic Motion." Applied Mechanics and Materials 801 (October 2015): 154–58. http://dx.doi.org/10.4028/www.scientific.net/amm.801.154.

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The paper presents the model of a seismic mass with viscoelastic linear connections, following the Voigt-Kelvin model, with the fundamental unidirectional harmonic kinematic excitation of an earthquake. The motion is caused by seismic action. Thus, the parameters and the motion laws of the mass, the inertial force and the force transmitted to the fixed base are determined. Also, the relations for the amplitude and the transmissibility of the motion are established in function of the elastic and viscous parameters of the composed model Voigt-Kelvin.Based on the established relations the dissipa

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15

Qin, Yuan, Bokai Wang, Yuhui Wang, Yao Wang, Yong Song, and Xin Shi. "Fractional Order Kelvin-Voigt Constitutive Model and Dynamic Damping Characteristics of Viscoelastic Materials." International Journal of Acoustics and Vibration 29, no. 4 (2024): 457–64. https://doi.org/10.20855/ijav.2024.29.42078.

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Viscoelastic damping materials are often under complex service conditions. To precisely characterize its dynamic damping properties, based on fractional calculus and viscoelastic theory, considering the periodic characteristics of viscoelastic materials, the distributed fractional order Kelvin-Voigt constitutive model (DFKV) was constructed. The model accuracy was validated by quasi-static experiments. The dynamic modulus expressions were derived, and the model parametric feature analysis was carried out. Dynamic Mechanical Analysis (DMA) and Separate Hopkinson Pressure Bar (SHPB) experiments

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16

Barzkar, Ahmad, and Hojatollah Adibi. "On the Propagation of Longitudinal Stress Waves in Solids and Fluids by Unifying the Navier-Lame and Navier-Stokes Equations." Mathematical Problems in Engineering 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/789238.

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Propagation of mechanical waves’ phenomenon is the result of infinitely small displacements of integrated individual particles in the materials. These displacements are governed by Navier-Lame and Navier-Stokes equations in solids and fluids, respectively. In the present work, a generalized Kelvin-Voigt model of viscoelasticity has been proposed with the aim of bridging the gap between solids and fluids leading to a new concept of viscoelasticity which unifies the Navier-Lame and the Navier-Stokes equations. On solving this equation in one dimension, propagation of stress disturbance in the so

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17

Fu, Chao. "Vibration Analysis of Viscoelastic Timoshenko Cracked Beams with Massless Viscoelastic Rotational Spring Models." Journal of Applied Mathematics 2023 (July 31, 2023): 1–11. http://dx.doi.org/10.1155/2023/2341137.

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Based on the equivalent bending stiffness of the viscoelastic cracked beam with open cracks, the corresponding complex frequency characteristic equations of a Timoshenko viscoelastic cracked beam are obtained by using the method of separation of variables and the Laplace transform. The vibration characteristics of a viscoelastic Timoshenko cracked beams with the standard linear solid model and Kelvin-Voigt model are investigated. By numerical examples, the effects of the crack location, crack number, crack depth, and slenderness ratio on the vibration characteristics of the viscoelastic cracke

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18

Emmanuel, A. K., G. E. Roger, and P. Nadjime. "ENERGETIC SOLUTIONS FOR REGULARIZED DAMAGE OF A VISCOELASTIC MATERIAL." Advances in Mathematics: Scientific Journal 13, no. 4 (2024): 491–99. http://dx.doi.org/10.37418/amsj.13.4.3.

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A model for the evolution of damage for viscoelastic material in Kelvin voigt rhoelogie by using Generalized Standard Materials definition is addressed. Small strains and rate-depende evolution includind viscous and inertial effects are assumed. By using the methode of energetic solution develop by Alexander Mielke and Tomáš Roubíček.

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19

Korobko, Evguenia V., Mikalai A. Zhurauski, Buhe Bateer, Zoya A. Novikova, and Vladimir A. Kuzmin. "Modeling of strain kinetics of damping viscoelastic magnetically controlled materials in creep mode." Journal of Intelligent Material Systems and Structures 31, no. 2 (2019): 243–52. http://dx.doi.org/10.1177/1045389x19888785.

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The results of experimental studies of strain kinetics of composite magnetically controlled materials in the creep mode with preliminary exposure and without exposure are described by the Burgers model with two elastic and two viscous parameters, which is a combination of viscoelastic Kelvin–Voigt and Maxwell models connected in series. The dependence of the model parameters on the magnetic field induction is determined. The values of elastic and viscous parameters increase with increasing magnetic field induction in the range up to 500 mT by one or two orders of magnitude. It was determined t

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20

Farokhi, Hamed, and Mergen H. Ghayesh. "Viscoelastic resonant responses of shear deformable imperfect microbeams." Journal of Vibration and Control 24, no. 14 (2017): 3049–62. http://dx.doi.org/10.1177/1077546317699345.

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A viscoelastic model for the nonlinear analysis of the coupled transverse, longitudinal, and rotational oscillations of an imperfect shear deformable microbeam is developed, for the first time, based on the modified couple stress theory. An energy dissipation mechanism is developed via use of the Kelvin–Voigt internal energy dissipation mechanism. For the stress and deviatoric part of the symmetric couple stress tensors, the viscous components along with the corresponding work terms are obtained. The size-dependent elastic energy along with the kinetic energy of the viscoelastic microsystem is

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21

Bartlewska-Urban, Monika, Marek Zombroń, and Tomasz Strzelecki. "Numerical analysis of road pavement thermal deformability, based on Biot viscoelastic model of porous medium." Studia Geotechnica et Mechanica 38, no. 1 (2016): 15–22. http://dx.doi.org/10.1515/sgem-2016-0002.

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Abstract The following study presents numerical calculations for establishing the impact of temperature changes on the process of distortion of bi-phase medium represented using Biot consolidation equations with Kelvin–Voigt rheological skeleton presented, on the example of thermo-consolidation of a pavement of expressway S17. We analyzed the behavior of the expressway under the action of its own weight, dynamic load caused by traffic and temperature gradient. This paper presents the application of the Biot consolidation model with the Kelvin–Voigt skeleton rheological characteristics and the

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22

Sánchez, Alejandro, Karla Y. Guerra, Andrés V. Porta, and Susana Orozco. "Viscoelastic Behavior of Polymeric Optical Fiber." MRS Proceedings 1766 (2015): 131–37. http://dx.doi.org/10.1557/opl.2015.420.

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ABSTRACTIn this work, the viscoelastic behavior of a polymeric step-index optical fiber is studied, and the loss factors η of their complex moduli are calculated. The loss factors of the Young and shear moduli were determined from the measurement of the damping ratio γ of a simple pendulum and a torsion pendulum respectively, using the Kelvin-Voigt model of the viscoelastic theory. The shear and Young complex moduli can be used to study the optic-viscoelastic behavior of a polymeric step-index optical fiber.

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23

Bukenov, M. M., and D. S. Rakisheva. "Some estimates for the viscoelastic incompressible Kelvin-Voigt medium." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 118, no. 2 (2025): 52–59. https://doi.org/10.31489/2025m2/52-59.

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In this paper, we consider the application of the method of fictitious domains to a viscoelastic incompressible medium based on the Kelvin-Voigt model. Application of the method of fictitious domains allows solving the original problem in regions with complex geometric configuration. This makes it easier to automate the construction of a consistent difference mesh, and to solve the problem in areas of standard shape. Estimates for the proximity of the auxiliary problem’s solution are obtained. The auxiliary problem is constructed by the method of fictitious domains. These estimates refer to th

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24

Shao-hua, Guo. "Eigen theory of viscoelastic dynamics based on the Kelvin-Voigt model." Applied Mathematics and Mechanics 25, no. 7 (2004): 792–98. http://dx.doi.org/10.1007/bf02437571.

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25

Dobrescu, Cornelia. "Dynamic Response of the Newton Voigt–Kelvin Modelled Linear Viscoelastic Systems at Harmonic Actions." Symmetry 12, no. 9 (2020): 1571. http://dx.doi.org/10.3390/sym12091571.

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The variety of viscoelastic systems and structures, for the most part, is studied analytically, with significant results. As a result of analytical, numerical and experimental research, which was conducted on a larger variety of linear viscoelastic systems and structures. We analyzed the dynamic behavior for the viscoelastic composite materials, anti-vibration viscous-elastic systems consisting of discrete physical devices, road structures consisting of natural soil structures with mineral aggregates and asphalt mixes, and mixed mechanic systems of insulation of the industrial vibrations consi

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26

Li, Junxia, and Xiaoxu Pang. "Belt Conveyor Dynamic Characteristics and Influential Factors." Shock and Vibration 2018 (2018): 1–13. http://dx.doi.org/10.1155/2018/8106879.

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This paper uses the Kelvin-Voigt viscoelastic model to establish the continuous dynamic equations for tail hammer tension belt conveyors. The viscoelastic continuity equations are solved using the generalized coordinate method. We analyze various factors influencing longitudinal vibration of the belt conveyor by simulation and propose a control strategy to limit the vibration. The proposed approach and control strategy were verified by several experimental researches and cases. The proposed approach provides improved accuracy for dynamic design of belt conveyors.

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27

Pezzinga, Giuseppe. "MOC-Z Model of Transient Cavitating Flow in Viscoelastic Pipe." Water 16, no. 11 (2024): 1610. http://dx.doi.org/10.3390/w16111610.

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In this paper, a unitary method for the solution of transient cavitating flow in viscoelastic pipes is proposed in the framework of the method of characteristics (MOC) and a Z-mirror numerical scheme (MOC-Z model). Assuming a standard form of the continuity equation allows the unified treatment of both viscoelasticity and cavitation. An extension of the MOC-Z is used for Courant numbers less than 1 to overcome a few cases with numerical instabilities. Four viscoelastic models were considered: a Kelvin–Voigt (KV) model without the instantaneous strain, and three generalised Kelvin–Voigt models

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28

Loktev, Aleksey A., Ahmad Barakat, and Jaafar Qbaily. "Seismic behavior of the main girder of a bridge with viscoelastic dampers." Vestnik MGSU, no. 7 (July 2021): 809–18. http://dx.doi.org/10.22227/1997-0935.2021.7.809-818.

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Introduction. The seismic stability of bearing structures is one of the main objectives of design and construction of structures in earthquake areas. The co-authors have analyzed the effect of a damper, located at the intersection of structural elements, on the seismic response of the main girder of a steel-concrete bridge exposed to the seismic impact. The purpose of this study is to select optimal values of viscous and elastic elements to ensure the seismic resistance of the bridge. Materials and methods. The finite element method was used to simulate the geometric characteristics of t

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29

Itou, Hiromichi, Victor A. Kovtunenko, and Kumbakonam R. Rajagopal. "On the states of stress and strain adjacent to a crack in a strain-limiting viscoelastic body." Mathematics and Mechanics of Solids 23, no. 3 (2017): 433–44. http://dx.doi.org/10.1177/1081286517709517.

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The viscoelastic Kelvin–Voigt model is considered within the context of quasi-static deformations and generalized with respect to a nonlinear constitutive response within the framework of limiting small strain. We consider a solid possessing a crack subject to stress-free faces. The corresponding class of problems for strain-limiting nonlinear viscoelastic bodies with cracks is considered within a generalized formulation stated as variational equations and inequalities. Its generalized solution, relying on the space of bounded measures, is proved rigorously with the help of an elliptic regular

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30

Eldred, Lloyd B., William P. Baker, and Anthony N. Palazotto. "Kelvin-Voigt versus fractional derivative model as constitutive relations for viscoelastic materials." AIAA Journal 33, no. 3 (1995): 547–50. http://dx.doi.org/10.2514/3.12471.

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31

Wei, ZHANG, and Nobuyuki SIMIZU. "Damping Properties of the Viscoelastic Material Described by Fractional Kelvin-Voigt Model." JSME International Journal Series C 42, no. 1 (1999): 1–9. http://dx.doi.org/10.1299/jsmec.42.1.

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32

Karner, Timi, Janez Gotlih, Boštjan Razboršek, Tomaž Vuherer, Lucijano Berus, and Karl Gotlih. "Use of single and double fractional Kelvin–Voigt model on viscoelastic elastomer." Smart Materials and Structures 29, no. 1 (2019): 015006. http://dx.doi.org/10.1088/1361-665x/ab5337.

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33

Hosseini Hashemi, Sh, and H. Bakhshi Khaniki. "Dynamic Behavior of Multi-Layered Viscoelastic Nanobeam System Embedded in a Viscoelastic Medium with a Moving Nanoparticle." Journal of Mechanics 33, no. 5 (2016): 559–75. http://dx.doi.org/10.1017/jmech.2016.91.

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AbstractIn this paper, dynamic behavior of multi-layered viscoelastic nanobeams resting on a viscoelastic medium with a moving nanoparticle is studied. Eringens nonlocal theory is used to model the small scale effects. Layers are coupled by Kelvin-Voigt viscoelastic medium model. Hamilton's principle, eigen-function technique and the Laplace transform method are employed to solve the governing differential equations. Analytical solutions for transverse displacements of double-layered is presented for both viscoelastic nanobeams embedded in a viscoelastic medium and without it while numerical s

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34

Wang, Jianfeng, Yuke Liu, Chao Yang, Wenmin Jiang, Yun Li, and Yongqiang Xiong. "Modeling the Viscoelastic Behavior of Quartz and Clay Minerals in Shale by Nanoindentation Creep Tests." Geofluids 2022 (January 13, 2022): 1–16. http://dx.doi.org/10.1155/2022/2860077.

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The viscoelastic behavior of minerals in shales is important in predicting the macroscale creep behavior of heterogeneous bulk shale. In this study, in situ indentation measurements of two major constitutive minerals (i.e., quartz and clay) in Longmaxi Formation shale from the Sichuan Basin, South China, were conducted using a nanoindentation technique and high-resolution optical microscope. Firstly, quartz and clay minerals were identified under an optical microscope based on their morphology, surface features, reflection characteristics, particle shapes, and indentation responses. Three visc

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Shitikova, Marina, and Anastasiya Krusser. "FORCE DRIVEN VIBRATIONS OF NONLINEAR PLATES ON A VISCOELASTIC WINKLER FOUNDATION UNDER THE HARMONIC MOVING LOAD." International Journal for Computational Civil and Structural Engineering 17, no. 4 (2021): 161–80. http://dx.doi.org/10.22337/2587-9618-2021-17-4-161-180.

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In the present paper, the forced driven nonlinear vibrations of an elastic plate in a viscoelastic medium and resting on a viscoelastic Winkler-type foundation are studied. The damping features of the surrounding medium and foundation are described by the Kelvin-Voigt model and standard linear solid model with fractional derivatives, respectively. The dynamic response of the plate is described by the set of nonlinear differential equations with due account for the fact that the plate is being under the conditions of the internal resonance accompanied by the external resonance. The expressions

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36

Koumatos, Konstantinos, Corrado Lattanzio, Stefano Spirito, and Athanasios E. Tzavaras. "Existence and uniqueness for a viscoelastic Kelvin–Voigt model with nonconvex stored energy." Journal of Hyperbolic Differential Equations 20, no. 02 (2023): 433–74. http://dx.doi.org/10.1142/s0219891623500133.

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We consider nonlinear viscoelastic materials of Kelvin–Voigt-type with stored energies satisfying an Andrews–Ball condition, allowing for nonconvexity in a compact set. Existence of weak solutions with deformation gradients in [Formula: see text] is established for energies of any superquadratic growth. In two space dimensions, weak solutions notably turn out to be unique in this class. Conservation of energy for weak solutions in two and three dimensions, as well as global regularity for smooth initial data in two dimensions are established under additional mild restrictions on the growth of

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37

Munoz Rivera, Jaime E., Carlos A. da Costa Baldez, and Sebastiao M. S. Cordeiro. "Signorini's problem for the Bresse beam model with localized Kelvin-Voigt dissipation." Electronic Journal of Differential Equations 2024, no. 01-?? (2024): 17. http://dx.doi.org/10.58997/ejde.2024.17.

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We prove the existence of a global solution to Signorini's problem for the localized viscoelastic Bresse beam model (circular arc) with continuous and discontinuous constitutive laws. We show that when the constitutive law is continuous, the solution decays exponentially to zero, and when the constitutive law is discontinuous the solution decays only polynomially to zero. The method we use for proving our result is different the others already used in Signorini's problem and is based on approximations through a hybrid model. Also, we present some numerical results using discrete approximations

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38

Callejas, Antonio, Antonio Gomez, Inas H. Faris, Juan Melchor, and Guillermo Rus. "Kelvin–Voigt Parameters Reconstruction of Cervical Tissue-Mimicking Phantoms Using Torsional Wave Elastography." Sensors 19, no. 15 (2019): 3281. http://dx.doi.org/10.3390/s19153281.

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The reconstruction of viscous properties of soft tissues, and more specifically, of cervical tissue is a challenging problem. In this paper, a new method is proposed to reconstruct the viscoelastic parameters of cervical tissue-mimicking phantoms by a Torsional Wave Elastography (TWE) technique. The reconstruction method, based on a Probabilistic Inverse Problem (PIP) approach, is presented and experimentally validated against Shear Wave Elastography (SWE). The anatomy of the cervical tissue has been mimicked by means of a two-layer gelatine phantom that simulates the epithelial and connective

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39

Vodička, Roman, and Vladislav Mantič. "Numerical Solution of Frictional Contact Problems for Viscoelastic Solids by SGBEM and Quadratic Programming." Key Engineering Materials 681 (February 2016): 175–84. http://dx.doi.org/10.4028/www.scientific.net/kem.681.175.

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The contact problem with Coulomb friction together with a simple Kelvin-Voigt viscoelastic model is studied. The numerical solution is obtained using a time discretization by a semi-implicit formula, the visco-elastic solids in contact being discretized by Symmetric Galerkin Boundary Element Method (SGBEM). The resulting minimization problem with a nonsmooth cost functional is suitably transformed in several ways. Firstly, a transformation is performed to apply SGBEM without any viscoelastic fundamental solution. Secondly, a transformation of contact quantities leads to a minimimization with a

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Xu, Hong Yu, Bing Bing Xue, and Zhu Mu Fu. "Frequency Equations of Magneto-Thermoviscoelastic Surface Wave." Advanced Materials Research 97-101 (March 2010): 479–83. http://dx.doi.org/10.4028/www.scientific.net/amr.97-101.479.

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The model of the generalized linear micropolar magneto-thermoviscoelastic theory is presented in this paper. It can be applied to the coupled theory as well as to five generalizations, such as L-S theory, G-L theory, H-I theory, G-N theory of type (II) and C-T theory. If some parameters in this model are taken as given values, we can easily deduce the known models of Kelvin-Voigt model and other generalized micropolar/magneto/thermo/viscoelastic theory model. The magneto-thermo- viscoelastic waves at an interface between two micropolar viscoelastic solid mediums are discussed with the model. U

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Ghayesh, Mergen H. "Resonant vibrations of FG viscoelastic imperfect Timoshenko beams." Journal of Vibration and Control 25, no. 12 (2019): 1823–32. http://dx.doi.org/10.1177/1077546318825167.

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An investigation is performed on the viscoelastic nonlinear vibrations of functionally graded imperfect Timoshenko beams. The internal viscosity is incorporated using the Kelvin–Voigt scheme. Beam's centerline stretching is the cause of geometric nonlinearities. Material property distributions follow the Mori–Tanaka model. Shear deformation and rotary inertia are incorporated using the Timoshenko theory. A slight curvature is included to account for a geometric imperfection. The coupled axial/transverse/rotational motion model is developed using Hamilton's energy/work/energy loss. Galerkin's m

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Rusinek, Rafal, Marcin Szymanski, and Robert Zablotni. "Biomechanics of the Human Middle Ear with Viscoelasticity of the Maxwell and the Kelvin–Voigt Type and Relaxation Effect." Materials 13, no. 17 (2020): 3779. http://dx.doi.org/10.3390/ma13173779.

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The middle ear is one of the smallest biomechanical systems in the human body and is responsible for the hearing process. Hearing is modelled in different ways and by various methods. In this paper, three-degree-of-freedom models of the human middle ear with different viscoelastic properties are proposed. Model 1 uses the Maxwell type viscoelasticity, Model 2 is based on the Kelvin–Voigt viscoelasticity, and Model 3 uses the Kelvin–Voigt viscoelasticity with relaxation effect. The primary aim of the study is to compare the models and their dynamic responses to a voice excitation. The novelty o

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Fan, Qianqian, Qiumei Liu, Yiming Chen, Yuhuan Cui, Jingguo Qu, and Lei Wang. "Studying the Dynamics Response of Viscoelastic Orthotropic Plates Based on Fractional-Order Derivatives and Shifted Legendre Polynomials." Mathematics 13, no. 4 (2025): 622. https://doi.org/10.3390/math13040622.

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This paper primarily investigates the dynamics response of viscoelastic orthotropic plates under a fractional-order derivative model, which is efficiently simulated numerically using the FKV (Fractional Kelvin–Voigt) model and the shifted Legendre polynomial algorithm. By establishing the fractional-order governing equation and directly solving it in the time domain using a shifted Legendre polynomial, the approach achieves low error and high accuracy. The analysis shows that the load, plate thickness, and creep time all affect the plate displacement, and the fractional-order model outperforms

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Kostyushko, Iryna, and Hlib Shapovalov. "Study of motion stability of a viscoelastic rod." Mechanics and Advanced Technologies 8, no. 1(100) (2024): 80–86. http://dx.doi.org/10.20535/2521-1943.2024.8.1(100).297514.

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Stability of non-conservatively loaded elastic and inelastic bodies - a classic section of deformable solid mechanics that has been of interest for many years. In this paper, we study the motion stability of a free rod subjected to a constant tracking force on one of its ends. The defining ratio of the rod material is the Kelvin-Voigt model. The solution is presented in the form of an expansion in terms of beam functions. The number of terms of this expansion is substantiated. The values of the critical load in the presence and absence of viscosity are determined. The given analytical results

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Li, Haibo, Xi Wang, Heling Wang, and Jubing Chen. "The nonlocal multi-directional vibration behaviors of buckled viscoelastic nanoribbons." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 234, no. 18 (2020): 3571–83. http://dx.doi.org/10.1177/0954406220916500.

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This paper presents the multi-directional vibration behaviors of buckled viscoelastic nanoribbons based on the nonlocal theory containing scale effect, where the Lagrange’s motion equation is introduced to construct the nonlocal viscoelastic governing equation. The first-order transverse vibration mode and the first-order longitudinal vibration mode are considered to study the influences of the scale characteristics on the natural frequency of two different vibration modes. The Kelvin–Voigt model is used to characterize the material viscoelastic property, and an analytical method is presented

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Michozounnou, Robert, Valery K. Doko, Agapi K. Houanou, Gerard L. Gbaguidi Aisse, Amos E. Foudjet, and Antoine Vianou. "LINEAR VISCOELASTIC MODEL OF BORASSUS WOOD: RHEOLOGICAL PARAMETERS." International Journal of Advanced Research 10, no. 01 (2022): 233–42. http://dx.doi.org/10.21474/ijar01/14037.

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The aim of the presentworkis to study the viscoelastic model of Borassus Aethiopum Mart whichis relevant for the characterisation of a Borassus Pre-stressedConcretebeam. Mechanical tests werecarried out mainly the creep test on typical Borassus Aethiopum Mart specimensfrom the Pahou-Ahozon forestgallery in southern Benin, Africa, subjected to a constant bending stress along the beam. The moisture content of the specimensis set at 12% and isobtained by kilndrying at ATC du Bois. The loadinglevel of the specimensis set at 20% of the failureload. A methodologystartingfrom the determination of the

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Zamani, HA, and MM Aghdam. "Hybrid material and foundation damping of Timoshenko beams." Journal of Vibration and Control 23, no. 18 (2016): 2869–87. http://dx.doi.org/10.1177/1077546315624077.

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In this paper, vibration suppression of shear deformable beams with hybrid material-foundation viscoelastic damping is studied. The precise behavior of viscoelastic polymeric structures is taken into consideration by Boltzmann superposition integral and utilizing dynamic mechanical analysis (DMA) results while foundation viscoelasticity is adapted by Kelvin-Voigt model. The integro-partial differential equations of motion are derived based on the Timoshenko theory via Hamilton principle. Assessment of the solution procedure is carried out by comparison with elastic Timoshenko and viscoelastic

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Barboteu, M., T. V. Hoarau-Mantel, and M. Sofonea. "On the frictionless unilateral contact of two viscoelastic bodies." Journal of Applied Mathematics 2003, no. 11 (2003): 575–603. http://dx.doi.org/10.1155/s1110757x03212043.

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We consider a mathematical model which describes the quasistatic contact between two deformable bodies. The bodies are assumed to have a viscoelastic behavior that we model with Kelvin-Voigt constitutive law. The contact is frictionless and is modeled with the classical Signorini condition with zero-gap function. We derive a variational formulation of the problem and prove the existence of a unique weak solution to the model by using arguments of evolution equations with maximal monotone operators. We also prove that the solution converges to the solution of the corresponding elastic problem,

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Zhou, Yunying, Dongying Liu, Dinggui Hou, Jiahuan Liu, Xiaoliang Li, and Zhijie Yue. "Wave Propagation in the Viscoelastic Functionally Graded Cylindrical Shell Based on the First-Order Shear Deformation Theory." Materials 16, no. 17 (2023): 5914. http://dx.doi.org/10.3390/ma16175914.

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Based on the first-order shear deformation theory (FSDT) and Kelvin–Voigt viscoelastic model, one derives a wave equation of longitudinal guide waves in viscoelastic orthotropic cylindrical shells, which analytically solves the wave equation and explains the intrinsic meaning of the wave propagation. In the numerical examples, the velocity curves of the first few modes for the elastic cylindrical shell are first calculated, and the results of the available literature are compared to verify the derivation and programming. Furthermore, the phase velocity curves and attenuation coefficient curves

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Abuzeid, Osama M., Anas N. Al-Rabadi, and Hashem S. Alkhaldi. "Fractal Geometry-Based Hypergeometric Time Series Solution to the Hereditary Thermal Creep Model for the Contact of Rough Surfaces Using the Kelvin-Voigt Medium." Mathematical Problems in Engineering 2010 (2010): 1–22. http://dx.doi.org/10.1155/2010/652306.

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This paper aims at constructing a continuous hereditary creep model for the thermoviscoelastic contact of a rough punch and a smooth surface of a rigid half-space. The used model considers the rough surface as a function of the applied load and temperatures. The material of the rough punch surface is assumed to behave as Kelvin-Voigt viscoelastic material. Such a model uses elastic springs and viscous dashpots in parallel. The fractal-based punch surface is modelled using a deterministic Cantor structure. An asymptotic power law, deduced using approximate iterative relations, is used to expres

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