A new identification method of viscoelastic behavior: Application to the generalized Maxwell model

Renaud, François; Dion, Jean-Luc; Chevallier, Gaël; Tawfiq, Imad; Lemaire, R.

doi:10.1016/j.ymssp.2010.09.002

Cited by 124 publications

(81 citation statements)

References 12 publications

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“…The enclosing curve technique (Vinh, 1967;Renaud et al, 2011), a graphical technique based on the Pole-Zero formulation of the generalized Maxwell model, is used for that purpose. Twelve Maxwell components are found to lead to a good fit of the frequency-dependent shear modulus of the SR, as shown in Fig.…”

Section: Viscoelastic Models Generalized Maxwell Modelmentioning

confidence: 99%

Characterization and Modeling of the Viscoelastic Behavior of a Self-Adhesive Rubber Using Dynamic Mechanical Analysis Tests

Rouleau

Pirk²,

Pluymers³

et al. 2015

J.Aerosp. Technol. Manag.

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ABSTRACT:The goal of this study is twofold. The first one is to assess the applicability of approaches based on dynamicmechanical analysis to investigate the viscoelastic properties of a self-adhesive synthetic rubber. The second goal is to identify the parameters of a viscoelastic model which accurately represents the frequency-dependent mechanical properties. For that purpose, the time-temperature superposition principle is successfully applied to build the master curves of the material up to 1 MHz. The thickness of the samples and the thermal expansion effects are found to have a negligible influence on the mechanical properties measured by dynamic-mechanical analysis. The parameters of a generalized Maxwell model and a fractional derivative model are identified from the obtained master curves and lead to an accurate representation of the frequency-dependent mechanical properties of the rubber.

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Section: Viscoelastic Models Generalized Maxwell Modelmentioning

confidence: 99%

Characterization and Modeling of the Viscoelastic Behavior of a Self-Adhesive Rubber Using Dynamic Mechanical Analysis Tests

Rouleau

Pirk²,

Pluymers³

et al. 2015

J.Aerosp. Technol. Manag.

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“…For example, in widely-used commercial finite element software (Simulia, 2010), the Prony series presentation of viscoelasticity corresponding to the classical generalized Maxwell model is typically used within the context of small strains (Park and Schapery, 1999;Park and Kim, 2001). In recent years, the fractional calculus versions of different viscoelastic models have also been of high interest, see, for example (Bagley and Torvik, 1986;Renaud et al, 2011). In this work, the viscoelastic material is a solid amorphous polymer which we model using the generalized Maxwell model shown in Fig.…”

Section: Mechanical Model Of Viscoelastic Behaviormentioning

confidence: 99%

Identification of the viscoelastic parameters of a polymer model by the aid of a MCMC method

Haario

Hertzen

Karttunen

et al. 2014

Mechanics Research Communications

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A procedure to identify the viscoelastic material parameters of a solid amorphous polymer and to estimate their values is presented. Stress-strain material data is obtained for the polymer by a compression experiment. The material behavior of the polymer is modeled according to the generalized Maxwell model, which is fitted to the experimental data by the method of least squares to obtain a first approximation for the model parameters. The identification of the model parameters is completed by a Markov chain Monte Carlo (MCMC) method, which generates the probability distributions of the relevant parameters of the material. The utilized MCMC method enables us to determine a suitable complexity (i.e., the number of Maxwell elements) for the generalized Maxwell model, so that the model best fits the data and, simultaneously, leads to an identifiable set of parameters. The numerical results imply that the uniqueness of the solution is lost when the number of model parameters becomes redundant.

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“…On the other hand, time-domain formalism appears to be more natural 25 when dealing with structures excited by impulses as it naturally takes transient aspects of simulated response into account, or in presence of nonlinear vibrations. In this framework, the literature is plentiful of models initially developed in the framework of linear viscoelasticity [13].…”

Section: Introductionmentioning

confidence: 99%

“…From Equations (9b) and (13a), this may be enforced by the following condition acting on the coefficients of H k : tions (6), (16) and (18) in order to guarantee the well-posedness of the corresponding discrete-time model. From a general point of view, finding an efficient method to correctly identify a material law from data given in the complex plane is still a tricky task, though it has been recently addressed in some original way when identifying rheological behaviors, using mathematical results from 155 complex analysis [22] or graphical methods stemming from the field of system automation [25].…”

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confidence: 99%

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Time-domain damping models in structural acoustics using digital filtering

Parret-Fréaud¹,

Cotté²,

Chaigne³

2016

Mechanical Systems and Signal Processing

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This paper describes a new approach in order to formulate well-posed timedomain damping models able to represent various frequency domain profiles of damping properties. The novelty of this approach is to represent the behavior law of a given material directly in a discrete-time framework as a digital filter, which is synthesized for each material from a discrete set of frequency-domain data such as complex modulus through an optimization process. A key point is the addition of specific constraints to this process in order to guarantee stability, causality and verification of thermodynamics second law when transposing the resulting discrete-time behavior law into the time domain. Thus, this method offers a framework which is particularly suitable for time-domain simulations in structural dynamics and acoustics for a wide range of materials (polymers, wood, foam...), allowing to control and even reduce the distortion effects induced by time-discretization schemes on the frequency response of continuous-time behavior laws.

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A new identification method of viscoelastic behavior: Application to the generalized Maxwell model

Cited by 124 publications

References 12 publications

Characterization and Modeling of the Viscoelastic Behavior of a Self-Adhesive Rubber Using Dynamic Mechanical Analysis Tests

Characterization and Modeling of the Viscoelastic Behavior of a Self-Adhesive Rubber Using Dynamic Mechanical Analysis Tests

Identification of the viscoelastic parameters of a polymer model by the aid of a MCMC method

Time-domain damping models in structural acoustics using digital filtering

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