[Nomogrammes des matériaux viscoélastiques linéaires solides dans les domaines temporel et fréquentiel]
Le comportement mécanique des matériaux viscoélastiques solides isotropes (VEM) peut être décrit à la fois dans les domaines temporel et fréquentiel, en prenant en compte les effets de la température. Ainsi, il est possible d’utiliser des fonctions viscoélastiques telles que les modules de Young et/ou de cisaillement, ainsi que le coefficient de Poisson. Les comportements dynamiques viscoélastiques dans différentes plages de température, de fréquence ou de temps peuvent être regroupés en un seul graphique, appelé nomogramme. Ce travail propose une méthode pour construire des nomogrammes pour les fonctions viscoélastiques, les modules de relaxation de Young et de cisaillement, et le coefficient de Poisson, définis dans le domaine temporel. Il propose également un nomogramme pour le coefficient de Poisson complexe dans le domaine fréquentiel.
The mechanical behavior of isotropic solid viscoelastic material (VEM) can be described both in time or frequency domain considering temperature effects. Thus, one can make use of viscoelastic functions such as Young’s and/or shear moduli and the Poisson’s ratio. The viscoelastic dynamic behaviors in different temperature and frequency or time ranges can be grouped into a single graph, named nomogram. The present work proposes a method for constructing nomograms for viscoelastic functions, Young’s and shear relaxation moduli, and Poisson’s ratio, defined in the time domain. It also proposed a nomogram for the complex Poisson’s ratio in the frequency domain.
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Mots-clés : Comportement viscoélastique, Fonctions viscoélastiques, Coefficient de Poisson complexe, Module de Young complexe, Module de cisaillement complexe
Tiago Lima de Sousa 1, 2 ; Jéderson da Silva 1, 3 ; Jucélio Tomás Pereira 1 ; Carolina Mocelin Gomes Pires 1
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@article{CRMECA_2025__353_G1_309_0, author = {Tiago Lima de Sousa and J\'ederson da Silva and Juc\'elio Tom\'as Pereira and Carolina Mocelin Gomes Pires}, title = {Nomograms of solid linear viscoelastic materials in time and frequency domains}, journal = {Comptes Rendus. M\'ecanique}, pages = {309--320}, publisher = {Acad\'emie des sciences, Paris}, volume = {353}, year = {2025}, doi = {10.5802/crmeca.283}, language = {en}, }
TY - JOUR AU - Tiago Lima de Sousa AU - Jéderson da Silva AU - Jucélio Tomás Pereira AU - Carolina Mocelin Gomes Pires TI - Nomograms of solid linear viscoelastic materials in time and frequency domains JO - Comptes Rendus. Mécanique PY - 2025 SP - 309 EP - 320 VL - 353 PB - Académie des sciences, Paris DO - 10.5802/crmeca.283 LA - en ID - CRMECA_2025__353_G1_309_0 ER -
%0 Journal Article %A Tiago Lima de Sousa %A Jéderson da Silva %A Jucélio Tomás Pereira %A Carolina Mocelin Gomes Pires %T Nomograms of solid linear viscoelastic materials in time and frequency domains %J Comptes Rendus. Mécanique %D 2025 %P 309-320 %V 353 %I Académie des sciences, Paris %R 10.5802/crmeca.283 %G en %F CRMECA_2025__353_G1_309_0
Tiago Lima de Sousa; Jéderson da Silva; Jucélio Tomás Pereira; Carolina Mocelin Gomes Pires. Nomograms of solid linear viscoelastic materials in time and frequency domains. Comptes Rendus. Mécanique, Volume 353 (2025), pp. 309-320. doi : 10.5802/crmeca.283. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.283/
[1] Viscoelastic measurement techniques, Rev. Sci. Instrum., Volume 75 (2004), pp. 797-810 | DOI
[2] Study on dynamic viscoelastic properties and constitutive model of non-water reacted polyurethane grouting materials, Measurement, Volume 176 (2021), 109115 | DOI
[3] Design of optimum systems of viscoelastic vibration absorbers for a given material based on the fractional calculus model, J. Vib. Control, Volume 14 (2006), pp. 1607-1630 | DOI
[4] Property identification of viscoelastic solid materials in nomograms using optimization techniques, J. Theoret. Appl. Mech., Volume 55 (2017), pp. 1285-1297 | DOI
[5] Wide estimation of dynamic properties of viscoelastic materials using bayesian inference, J. Theoret. Appl. Mech., Volume 59 (2021), pp. 369-384 | DOI
[6] Study on dynamic viscoelastic constitutive model of nonwater reacted polyurethane grouting materials based on DMA, Rev. Adv. Mater. Sci., Volume 61 (2022), pp. 238-249 | DOI
[7] Statistical analysis of identification of linear viscoelastic models, Rheol. Acta, Volume 63 (2024), pp. 301-318 | DOI
[8] Fitting Prony-Series viscoelastic models with power-law presmoothing, J. Mater. Civil Eng., Volume 13 (2001), pp. 26-32 | DOI
[9] Re-examination of the approximate methods for interconversion between frequency- and time-dependent material functions, J. Non-Newton. Fluid Mech., Volume 129 (2005), pp. 75-84 | DOI
[10] Characterization of the viscoelasticity of molding compounds in the time domain, J. Electron. Mater., Volume 39 (2010), pp. 419-425 | DOI
[11] The closed form t-T-P shifting (CFS) algorithm, Soc. Rheol., Volume 55 (2010), pp. 1-16 | DOI
[12] Closed-form solution for horizontal and vertical shiftings of viscoelastic material functions in frequency domain, J. Rheol. Acta, Volume 55 (2016), pp. 351-364 | DOI
[13] Experimental characterization and modelization of the relaxation and complex moduli of a flexible adhesive, Mater. Design, Volume 32 (2011), pp. 2783-2796 | DOI
[14] Modeling of viscoelastic behavior of epoxy molding compound during and after curing, Trans. Compon. Packag. Manuf. Technol., Volume 1 (2011), pp. 1755-1760 | DOI
[15] Prediction of viscoelastic material functions from constant stress- or strain-rate experiments, Mech. Time-Dependent Mater., Volume 18 (2014), pp. 349-372 | DOI
[16] Characterization and modeling of the viscoelastic behavior of a self-adhesive rubber using dynamic mechanical analysis tests, J. Aerosp. Technol. Manag., Volume 7 (2015), pp. 200-208 | DOI
[17] Fractional differential constitutive model for linear viscoelasticity of asphalt and asphalt mastic, Constr. Build. Mater., Volume 306 (2021), 124886 | DOI
[18] Stress relaxation of polymer films in bending, Polymer, Volume 36 (1995), pp. 949-954 | DOI
[19] Frequency dependences of complex moduli and complex Poisson’s ratio of real solid materials, J. Sound Vib., Volume 214 (1998), pp. 83-104 | DOI
[20] Measurement methods of complex Poisson’s ratio of viscoelastic materials, Appl. Acoust., Volume 60 (2000), 124886, pp. 279-292 | DOI
[21] The Poisson’s loss factor of solid viscoelastic materials, J. Sound Vib., Volume 306 (2007), 109115, pp. 790-802 | DOI
[22] Interconversions between linear viscoelastic functions by using relaxation-creep duality representation, Math. Mech. Solids, Volume 18 (2012), p. 701-421 | DOI
[23] Interconversions between linear viscoelastic functions with a time-dependent bulk modulus, Math. Mech. Solids, Volume 23 (2018) no. 6, pp. 879-895 | DOI
[24] Indirect Identification of the Complex Poisson’s Ratio in Fractional Viscoelasticity, Lat. Am. J. Solids Struct., Volume 15 (2018) no. 9, pp. 1-21 | DOI
[25] Temperature-frequency dependence of dynamic properties of damping materials, J. Sound Vib., Volume 33 (1974), pp. 451-470 | DOI
[26] A methodology for an optimal design of physical parameters, positions, and viscoelastic materials of simple dynamic absorbers for passive vibration control, J. Vib. Control, Volume 25 (2019), pp. 1133-1147 | DOI
[27] Dynamic response optimization of structures with viscoelastic material using the equivalent static loads method, J. Automob. Eng., Volume 235 (2021), pp. 589-603 | DOI
[28] On the use of viscoelastic materials characterized by Bayesian inference in vibration control, J. Theoret. Appl. Mech., Volume 59 (2021), pp. 385-399 | DOI
[29] Fractional Calculus and Waves in Linear Viscoelasticity — An Introduction to Mathematical Models, Imperial College Press, London, 2010 | DOI
[30] The Phenomenological Theory of Linear Viscoelastic Behavior: An Introduction, Springer, New York, 1989 | DOI
[31] On the fractional calculus model of viscoelastic behavior, J. Rheol., Volume 30 (1986), pp. 133-155 | DOI
[32] Finite element formulation of viscoelastic sandwich beams using fractional derivative operators, Comput. Mech., Volume 33 (2004), pp. 282-291 | DOI
[33] Five-parameter fractional derivative model for polymeric damping materials, J. Sound Vib., Volume 265 (2003), pp. 935-952 | DOI
[34] Identifying mechanical properties of viscoelastic materials in time domain using the fractional Zener model, Lat. Am. J. Solids Struct., Volume 14 (2016), pp. 131-152 | DOI
[35] Viscoelastic Properties of Polymers, John Wiley & Sons, New York, 1980 | DOI
[36] Vibration Damping, John Wiley & Sons, New York, 1985 | DOI
[37] Isothermal viscoelastic properties of PMMA and LDPE over 11 decades of frequency and time: a test of time–temperature superposition, Rheol. Acta, Volume 47 (2008), pp. 777-786 | DOI
[38] The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids, J. Am. Chem. Soc., Volume 14 (1955), pp. 3701-3707 | DOI
[39] Methods of interconversion between linear viscoelastic material functions. Part I - A numerical method based on Prony series, Int. J. Solids Struct., Volume 36 (1999), pp. 1653-1675 | DOI
[40] Creep, relaxation and viscosity properties for basic fractional models in rheology, Eur. Phys. J. Spec. Top., Volume 193 (2011), pp. 133-160 | DOI
[41] Indirect Identification of Viscoelastic Materials Properties in Time and Frequency Domains, Considering Temperature Effects, Doctoral Thesis, Federal University of Paraná, Paraná, Brazil (2018) | DOI
[42] Results of a round-robin test program: complex modulus properties of a polymeric damping material, 1992 (USAF Report WL-TR-92-3104) | DOI
[43] The effect of temperature and pressure on the mechanical properties of thermo–and/or piezorheologically simple polymeric materials in thermodynamic equilibrium - A critical review, Mech. Time-Dependent Mater., Volume 6 (2002), pp. 53-99 | DOI
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