Academic literature on the topic 'Modèle de Kelvin-Voigt'
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Dissertations / Theses on the topic "Modèle de Kelvin-Voigt"
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Abdessamad, Zouhair. "Analyse multi-échelle du modèle Kelvin-Voigt de la thermo-viscoélasticité." Saint-Etienne, 2007. http://www.theses.fr/2007STET4005.
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Le travail effectué au cours de cette thèse porte sur l'étude asymptotique d'un modèle mathématique décrivant le processus de formation d'un matériau composite, de structure périodique de période ε. On considère un matériau composite constitué de fibres solides noyées dans une résine qui se solidifie sous l'effet de la chaleur (réaction de réticulation). L'état du milieu déformé décrivant les propriétés thermo-viscoélastiques du matériau est modélisé, au niveau microscopique, par l'équation de la viscoélasticité (modèle de Kelvin-Voigt) avec des coefficients oscillants dépendant de la température, couplée avec un modèle décrivant le processus de solidification de la résine. Ce modèle est décrit mathématiquement par un couplage entre l'équation de la chaleur et une équation cinétique caractérisant la réaction de réticulation. Dans un premier temps, on étudie le modèle de Kelvin-Voigt découplé du problème du transfert thermique où les coefficients sont indépendants de la température. A l'aide de la méthode de Faedo Galerkin, on établit un résultat d'existence et d'unicité. En utilisant un développement asymptotique formel, on détermine la structure du problème homogénéisé et, dans un cas particulier, on obtient une estimation d'erreur d'ordre √ε. Ensuite, on établit une estimation de la différence entre la solution exacte du problème du transfert thermique et celle du problème homogénéisé associé. Le dernier chapitre est consacré au problème complet, prenant en compte les effets thermiques et viscoélastiques. On détermine le problème homogénéisé décrivant le comportement macroscopique du matériau et on obtient une estimation d'erreurWe aim, in this work, the asymptotic study of a mathematical model describing the process of formation of a composite material which has a periodic geometry with a small period ε. We consider a composite material composed of solid fibres included in a resin which becomes solid when it is heated up (reaction of reticulation). The mechanical properties are described by the viscoelastic media equation (Kelvin-Voigt model) with rapidly oscillating periodic coefficients depending on the temperature. The temperature is given by the heat equation coupled with a kinetic equation describing the process of solidification of the resin. First, we study the model of Kevin-Voigt, where the coefficients are independent of the temperature. By using the Faedo Galerkin method, we prove the existence and uniqueness results. By using an asymptotic development, we establish the structure of the homogenized problem and, in a particular case, we obtain an error estimate in order √ε. Second, we interest by the study of the problem modelling the cure process where we obtain an estimate of the difference between the exact solution and the solution of its associated homogenized problem. Finally, we study the complete problem taking account of the thermal and viscoelastic effects. We prove the existence and uniqueness of a solution, we establish the homogenized problem describing the macroscopic behavior of the material components and we obtain an error estimate proving the convergence of the exact solution to the approximate solution as the small parameter ε tends to zero
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Najdi, Nadine. "Étude de la stabilisation exponentielle et polynomiale de certains systèmes d'équations couplées par des contrôles indirects bornés ou non bornés." Thesis, Valenciennes, 2016. http://www.theses.fr/2016VALE0017/document.
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La thèse porte essentiellement sur la stabilisation indirecte de certains systèmes d’équations couplées moyennant un seul contrôle agissant localement à l’intérieur ou sur le bord du domaine. La nature du système ainsi couplé dépend du couplage des équations et du type de l’amortissement, et ceci donne divers résultats de stabilisation (exponentielle ou polynômiale) des systèmes étudiés. D’abord, dans le cas de la stabilisation d’un système de Bresse formé de trois équations d’ondes couplées, un amortissement local de type chaleur est appliqué à une seule équation. Par une méthode fréquentielle combinée avec une méthode de multiplicateurs par morceau la décroissance exponentielle de l’énergie du système est établie sous la condition d’égalité de vitesses de propagation des ondes. Dans le cas contraire, une décroissance polynomiale est assurée. Ensuite, un système de deux équations d’ondes couplées sous l’effet d’un seul amortissement frontière appliqué à une seule équation est considéré. Dans ce cas, la stabilité du système est influencée par la nature algébrique du terme de couplage ainsi que par la nature arithmétique du quotient de vitesses de propagation des ondes. Par conséquence, différents résultats de stabilité exponentielle ou polynomiale sont établis. Une étude spectrale conduit à l’optimalité des résultats obtenus. Finalement, dans le cas de la stabilisation d’un système de deux équations d’ondes couplées, un amortissement localement distribué de type Kelvin-Voight est appliqué à une seule équation. D’abord, d’après un théorème de Hormander, un résultat d’unicité est montré et par conséquent la stabilité forte du système est assurée. Ensuite, une décroissance polynomiale de l’énergie du système est établieRésumé en anglais non disponible
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Sarkis, Bruno. "Étude numérique de la relaxation de capsules confinées par couplage des méthodes Volumes Finis - Éléments Finis via la méthode des frontières immergées IBM : influence de l'inertie et du degré de confinement." Thesis, Sorbonne université, 2018. http://www.theses.fr/2018SORUS184/document.
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Les capsules, formées d’une goutte protégée par une membrane élastique, sont très présentes naturellement et dans diverses applications industrielles, mais peu d’études ont exploré les phénomènes transitoires de leur relaxation. L’objectif est d’étudier l’influence de l’inertie et du confinement sur la relaxation d’une capsule sphérique (1) pré-déformée en ellipsoïde et relâchée dans un canal carré où le fluide est au repos, (2) sous écoulement dans un canal carré à expansion soudaine (‘marche’). La capsule est modélisée comme un fluide Newtonien dans une membrane hyper-élastique sans épaisseur ni viscosité, et simulée en couplant les méthodes Volumes Finis - Eléments Finis - frontières immergées. Sa relaxation dans un fluide au repos comporte 3 phases : amorçage du mouvement du fluide, phases rapide puis lente de rétraction de la membrane. Trois régimes existent selon le rapport de confinement et le rapport des nombres de Reynolds et capillaire : amortissements pur, critique ou oscillant. Un modèle de Kelvin-Voigt inertiel est proposé pour prédire les temps de réponse et aussi appliqué à une capsule en écoulement dans le canal microfluidique avec marche. La comparaison aux simulations 3D montre sa pertinence aux temps courts de la relaxation. Ces travaux ouvrent la voie à l’étude d’écoulements transitoires de capsules confinées dans des systèmes microfluidiques complexesCapsules, made of a drop protected by an elastic membrane, are widly present in nature and in diverse industrial applications, but few studies have explored the transient phenomena governing their relaxation. The objective of the PhD is to study the influence of inertia and confinement on the relaxation of a spherical capsule (1) pre-deformed into an ellipsoid and released in a square channel where the fluid is quiescent, (2) flowing in a square channel with a sudden expansion (‘step’). The capsule is modeled as a Newtonian fluid in a hyperelastic membrane without thickness or viscosity and is simulated coupling the Finite Volume - Finite Element - Immersed Boundary Methods. Its relaxation in a quiescent fluid exhibits three phases: the initiation of the fluid motion, the rapid and then slow retraction phases of the membrane. Three regimes exist depending on the confinement ratio and the Reynolds to capillary number ratio: pure, critical or oscillating damping. A Kelvin-Voigt inertial model is proposed to predict the response time constants and also applied to a capsule flowing in the microfluidic channel with a step. The comparison to 3D simulations shows its relevance at short relaxation times. This work paves the way to the study of transient flows of capsules confined in microfluidic devices
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Scarella, Gilles. "Etude théorique et numérique de la propagation d'ondes en présence de contact unilatéral dans un milieu fissuré." Phd thesis, Université Paris Dauphine - Paris IX, 2004. http://tel.archives-ouvertes.fr/tel-00006272.
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La diffraction d'ondes élastiques par une fissure dans un matériau est un problème majeur en contrôle non destructif. Une modélisation réaliste consiste à prendre en compte une condition de contact unilatéral sur la fissure. Dans cette thèse, on étudie des problèmes dynamiques de contact unilatéral dans des milieux fissurés. Au niveau théorique, on présente un résultat d'existence pour un milieu viscoélastique de Kelvin-Voigt fissuré, pour lequel on considère une condition de contact unilatéral avec frottement non local (régularisé). Ce résultat est obtenu en utilisant une méthode de pénalisation et des propriétés de compacité. L'étude numérique porte sur le problème de l'élastodynamique avec contact unilatéral sans frottement, qui reste un problème ouvert sur le plan mathématique. Pour le résoudre, on utilise la méthode des domaines fictifs. On propose pour cela une formulation du problème en contraintes-déplacements-multiplicateurs de Lagrange. Un élément fini adapté est utilisé pour la discrétisation en espace et permet d'obtenir un schéma explicite en temps, par condensation de masse. Plusieurs schémas de discrétisation en temps sont présentés: un schéma implicite décentré dont on démontre la stabilité, un schéma implicite centré qui apparaît stable au vu des expériences numériques. Des résultats de validation sont présentés ainsi que des résultats concernant des applications plus réalistes.
Book chapters on the topic "Modèle de Kelvin-Voigt"
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Dobrescu, Cornelia-Florentina. "Comparative Analysis of the Voigt–Kelvin and Maxwell Models in the Compaction by Vibration Process." In Springer Proceedings in Physics, 359–66. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-54136-1_36.
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Merveil Anague Tabejieu, Lionel, Blaise Roméo Nana Nbendjo, and Giovanni Filatrella. "Vibrations of an Elastic Beam Subjected by Two Kinds of Moving Loads and Positioned on a Foundation having Fractional Order Viscoelastic Physical Properties." In Advances in Dynamical Systems Theory, Models, Algorithms and Applications. IntechOpen, 2021. http://dx.doi.org/10.5772/intechopen.96878.
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The present chapter investigates both the effects of moving loads and of stochastic wind on the steady-state vibration of a first mode Rayleigh elastic beam. The beam is assumed to lay on foundations (bearings) that are characterized by fractional-order viscoelastic material. The viscoelastic property of the foundation is modeled using the constitutive equation of Kelvin-Voigt type, which contain fractional derivatives of real order. Based to the stochastic averaging method, an analytical explanation on the effects of the viscoelastic physical properties and number of the bearings, additive and parametric wind turbulence on the beam oscillations is provided. In particular, it is found that as the number of bearings increase, the resonant amplitude of the beam decreases and shifts towards larger frequency values. The results also indicate that as the order of the fractional derivative increases, the amplitude response decreases. We are also demonstrated that a moderate increase of the additive and parametric wind turbulence contributes to decrease the chance for the beam to reach the resonance. The remarkable agreement between the analytical and numerical results is also presented in this chapter.
Conference papers on the topic "Modèle de Kelvin-Voigt"
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Butcher, Eric A., and Daniel J. Segalman. "Characterizing Damping and Restitution in Compliant Impacts via Linear Viscoelastic Models." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/vib-8335.
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Abstract Strategies for characterizing damping and restitution in compliant impacts while eliminating the force discontinuities associated with the standard Kelvin-Voigt model are examined within the framework of linear viscoelasticity. A modification of the Kelvin-Voigt model as well as higher-order (Maxwell and standard linear) models are studied in an effort to satisfy the expected force-displacement boundary conditions. The restitution coefficients, energy losses per cycle, and equivalent linear damping ratios are then obtained analytically as functions of the dimensionless viscoelastic parameters which may be easily related to and obtained from experimentally measured restitution coefficients.
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David, N. V., X. L. Gao, J. Q. Zheng, and K. Masters. "Three-Parameter Viscoelasticity Models for Ballistic Fabrics." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-68853.
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Ballistic fabrics are made from high performance polymeric fibers such as Kevlar®, Twaron® and Spectra®. These fibers often behave viscoelastically in high strain rate deformations. The Kelvin-Voigt and Maxwell rheological models have been used to characterize such viscoelastic responses at different strain rates. However, these two-parameter models have been found to be inadequate and inaccurate in some applications. As a result, three-parameter rheological models have been utilized to develop constitutive relations for viscoelastic polymeric fabrics. In this study, a generalized Maxwell (GM) model and a generalized Kelvin-Voigt (GKV) model are proposed to describe the viscoelastic behavior of a ballistic fabric, Twaron® CT716, at the strain rates of 1 s−1 and 495 s−1. The GM model consists of a Maxwell element (including a viscous dashpot and a spring in series) and a second spring in parallel to the Maxwell element, while the GKV model is an assembly of a Kelvin-Voigt (KV) element (containing a viscous dashpot and a spring in parallel) and a second spring in series with the KV element. The predictions by the GM and GKV models are compared with existing experimental data, which shows that the two sets of results are in fairly good agreement. In particular, the comparison reveals that the GKV model gives more accurate results at the low strain rate, whereas the GM model performs better at the high strain rate while still providing accurate predictions for the low strain rate responses.
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Herrmann, Torsten, and Valdas Chaika. "Identification of Viscoelastic Properties of Finite Element Structures With Joints." In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/vib-4246.
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Abstract Identification of the damping and stiffness parameters of the composite joints in finite element structures is analyzed. For the modeling of the viscoelastic properties of the joints the classical Voigt-Kelvin and generalized Maxwell model (three parameter solid) are used. A time domain identification algorithm for classically and non-classically damped dynamic systems is developed. It is based on the application of an extended Kalman filter and least square technique. The algorithm uses complex modal analysis and sparse matrix technology. Both force and base excited systems are considered. Experimental verification of the identification results is carried out on a test structure. The accuracy of the modeling of damping in the joint using the Voigt-Kelvin and generalized Maxwell models is investigated.
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Kaul, Sudhir. "Nonlinear Design of a Passive Vibration Isolator: Influence of Multi-Axial Stiffness." In ASME 2019 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/imece2019-10021.
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Abstract Passive vibration isolators are widely used in multiple engineering applications to reduce resonance peaks or to mitigate transmissibility in the presence of internal or external sources of dynamic excitation. The design of a linear passive isolator involves multiple trade-offs. In the literature, different design configurations with nonlinearities have been investigated to limit some of these trade-offs. These include designs with quasi-zero stiffness (QZS) or high-static-low-dynamic stiffness (HSLDS) characteristics. This study investigates three viscoelastic models that incorporate stiffness nonlinearity along the non-isolating axes in order to exhibit more control over the dynamic response of the isolated system and possibly mitigate some of the design trade-offs. The dynamic response of these three models is compared to an existing HSLDS model in the literature. The three models investigated in this study are as follows: Kelvin-Voigt (or Voigt), Zener, and Generalized Maxwell (or Maxwell Ladder). These three models have been commonly used in the literature for vibration analysis of passive isolators. Two methods have been used for analysis, namely the Harmonic Balance Method (HBM) and explicit numerical integration. Test results from a previous study have been used for model characterization of all the models. It is observed that the modified Kelvin-Voigt model is analogous to the HSLDS model from the literature. For the isolator parameters used in this study, it is observed that the Kelvin-Voigt model with stiffness nonlinearity is able to exhibit characteristics similar to the HSLDS design, this includes the jump phenomenon as well as the hardening behavior. In general, all three models demonstrate that stiffness nonlinearity results in a reduction in peak transmissibility as well as an enhancement of the isolation bandwidth. The findings of this study could be useful in the design of passive isolation systems for products with significantly different multi-axial requirements with various design constraints.
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Bakhtiari-Nejad, Firooz, Ehsan Loghman, and Mostafa Pirasteh. "Nonlinear Vibration Analysis of a Fractional Viscoelastic Euler-Bernoulli Microbeam." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-87061.
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Nonlinear vibration of a simply-supported Euler-Bernoulli microbeam with fractional Kelvin-Voigt viscoelastic model subjected to harmonic excitation is investigated in this paper. For small scale effects the modified strain gradient theory is used. For take into account geometric nonlinearities the Von karman theory is applied. Beam equations are derived from Hamilton principle and the Galerkin method is used to convert fractional partial differential equations into fractional ordinary differential equations. Problem is solved by using the method of multiple scales and amplitude-frequency equations are obtained for primary, super-harmonic and sub-harmonic resonance. Effects of force amplitude, fractional parameters and nonlinearity on the frequency responses for primary, super-harmonic and sub-harmonic resonance are investigated. Finally results are compared with ordinary Kelvin-Voigt viscoelastic model.
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Banks, H. T., and C. A. Smith. "Modeling of Coupled Bending and Torsion in Elastic Structures." In ASME 1993 Design Technical Conferences. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/detc1993-0215.
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Abstract In this presentation we will report on joint efforts with D.J. Inman and his colleagues at MSL, SUNY at Buffalo, to develop viable models for the analysis and control of elastic structures exhibiting coupled torsional and flexural vibrations. A model for coupled torsion and bending is developed which incorporates Kelvin Voigt damping and warping. Approximation techniques are introduced and preliminary numerical results are discussed. Experimental data is presented and used to test our computational results.
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Chakraborty, Nilanjan, Stephen Berard, Srinivas Akella, and Jeff Trinkle. "An Implicit Time-Stepping Method for Quasi-Rigid Multibody Systems With Intermittent Contact." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35526.
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We recently developed a time-stepping method for simulating rigid multi-body systems with intermittent contact that is implicit in the geometric information [1]. In this paper, we extend this formulation to quasi-rigid or locally compliant objects, i.e., objects with a rigid core surrounded by a compliant layer, similar to Song et al. [2]. The difference in our compliance model from existing quasi-rigid models is that, based on physical motivations, we assume the compliant layer has a maximum possible normal deflection beyond which it acts as a rigid body. Therefore, we use an extension of the Kelvin-Voigt (i.e. linear spring-damper) model for obtaining the normal contact forces by incorporating the thickness of the compliant layer explicitly in the contact model. We use the Kelvin-Voigt model for the tangential forces and assume that the contact forces and moment satisfy an ellipsoidal friction law. We model each object as an intersection of convex inequalities and write the contact constraint as a complementarity constraint between the contact force and a distance function dependent on the closest points and the local deformation of the body. The closest points satisfy a system of nonlinear algebraic equations and the resultant continuous model is a Differential Complementarity Problem (DCP). This enables us to formulate a geometrically implicit time-stepping scheme for solving the DCP which is more accurate than a geometrically explicit scheme. The discrete problem to be solved at each time-step is a mixed nonlinear complementarity problem.
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Sorrentino, Silvio, and Luigi Garibaldi. "Frequency Domain Analysis of a Fractional Derivative SDOF System." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84651.
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This paper presents a study of the frequency domain behaviour of a single degree of freedom (SDOF) system with a fractional derivative model, named Fractional Kelvin-Voigt. Frequency response functions (FRFs) as receptance and transmissibility are analytically studied. Then the model is applied to describe the dynamic behaviour of a magneto-mechanic system in the frequency domain, consisting of a body of para or dia-magnetic material vibrating in a field created by a pair of magnets.
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Chen, Tao, and Zhichao Hou. "Summation Resonance of Parametrically Excited Moving Viscoelastic Belts." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-43995.
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The nonlinear dynamic analysis is performed on parametrically excited, viscoelastic moving-belts at summation resonance. The belt material behavior is described by a Voigt-Kelvin model. Closed-form solutions are derived at the first order approximation. Focus is put on the stability of the nontrivial solutions. The explicit expressions on the stability conditions are obtained, and then simplified through numerical simulations. The influences of moving speed and tension fluctuation on the stability of the nontrivial solutions are also demonstrated.
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Amador, Carolina, Matthew W. Urban, Shigao Chen, and James F. Greenleaf. "Acoustic Radiation Force Creep and Shear Wave Propagation Method for Elasticity Imaging." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-87622.
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Elasticity imaging methods have been used to study tissue mechanical properties and have demonstrated that tissue elasticity changes with disease state. Quantitative mechanical properties can be measured in a model independent manner if both shear wave speed and attenuation are known. However, measuring shear wave speed attenuation is challenging in the field of elasticity imaging. Typically, only shear wave speed is measured and rheological models, such as Kelvin-Voigt, Maxwell and Standard Linear Solid, are used to solve for shear viscoelastic complex modulus. Acoustic radiation force has been used to study quasi-static viscoelastic properties of tissue during creep and relaxation conditions, however, as with shear wave propagation methods, a rheological model needs to be fit to the creep or relaxation experimental data to solve for viscoelastic parameters. This paper presents a method to quantify viscoelastic properties in a model-independent way by estimating complex shear elastic modulus over a wide frequency range using time-dependent creep response induced by acoustic radiation force. The acoustic radiation force induced creep (RFIC) method uses a conversion formula that is the analytic solution of the constitutive equation relating time dependent stress and time dependent strain. The RFIC method in combination with shear wave propagation is used to measure the complex shear modulus so that knowledge of the applied radiation force magnitude is not necessary. Numerical simulation of creep strain and compliance using the Kelvin-Voigt model shown that the conversion formula is sensitive to sampling frequency, the first reliable measure in time and the long term viscosity approximation. Experimental data are obtained in homogeneous tissue mimicking phantoms and excised swine kidneys.