On the influence of the initial ramp for a correct definition of the parameters of fractional viscoelastic materials

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Abstract

Creep and/or Relaxation tests on viscoelastic materials show a power-law trend. Based upon Boltzmann superposition principle the constitutive law with a power-law kernel is ruled by the Caputo’s fractional derivative. Fractional constitutive law posses a long memory and then the parameters obtained by best fitting procedures on experimental data are strongly influenced by the prestress on the specimen. As in fact during the relaxation test the imposed history of deformation is not instantaneously applied, since a unit step function may not be realized by the test machine. Usually an initial ramp is present in the deformation history and the time at which the deformation attains the maximum value is fixed by the operator. Even though the precharge time is small in comparison with the total duration of the observation time, the parameters obtained by the best fitting procedure leads to relevant error especially for small observation time. In the paper the problem is overcome by considering the time load history for both theoretical and experimental point of view. In order to demonstrate experimentally that the initial ramp of deformation strongly influences the stress history during the relaxation test, different tests were performed on samples of a commercial epoxy resin (SP106) at two different rates of deformation (i.e. 0.2 mm/mm and 2 mm/min). Moreover the corrected approach for the best fitting of the data permits to characterize the viscoelastic materials, in term of fractional viscoelastic parameters, in a short time, and this allows to reduce the long duration of the experimental tests.
Lingua originaleEnglish
pagine (da-a)63-70
Numero di pagine8
RivistaMechanics of Materials
Volume69
Stato di pubblicazionePublished - 2014

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ramps
histories
Epoxy Resins
Epoxy resins
Creep
step functions
epoxy resins
Derivatives
Data storage equipment
trends
operators

All Science Journal Classification (ASJC) codes

  • Instrumentation
  • Mechanics of Materials
  • Materials Science(all)

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title = "On the influence of the initial ramp for a correct definition of the parameters of fractional viscoelastic materials",
abstract = "Creep and/or Relaxation tests on viscoelastic materials show a power-law trend. Based upon Boltzmann superposition principle the constitutive law with a power-law kernel is ruled by the Caputo’s fractional derivative. Fractional constitutive law posses a long memory and then the parameters obtained by best fitting procedures on experimental data are strongly influenced by the prestress on the specimen. As in fact during the relaxation test the imposed history of deformation is not instantaneously applied, since a unit step function may not be realized by the test machine. Usually an initial ramp is present in the deformation history and the time at which the deformation attains the maximum value is fixed by the operator. Even though the precharge time is small in comparison with the total duration of the observation time, the parameters obtained by the best fitting procedure leads to relevant error especially for small observation time. In the paper the problem is overcome by considering the time load history for both theoretical and experimental point of view. In order to demonstrate experimentally that the initial ramp of deformation strongly influences the stress history during the relaxation test, different tests were performed on samples of a commercial epoxy resin (SP106) at two different rates of deformation (i.e. 0.2 mm/mm and 2 mm/min). Moreover the corrected approach for the best fitting of the data permits to characterize the viscoelastic materials, in term of fractional viscoelastic parameters, in a short time, and this allows to reduce the long duration of the experimental tests.",
author = "{Di Paola}, Mario and Antonino Valenza and Vincenzo Fiore and Pinnola, {Francesco Paolo}",
year = "2014",
language = "English",
volume = "69",
pages = "63--70",
journal = "Mechanics of Materials",
issn = "0167-6636",
publisher = "Elsevier",

}

TY - JOUR

T1 - On the influence of the initial ramp for a correct definition of the parameters of fractional viscoelastic materials

AU - Di Paola, Mario

AU - Valenza, Antonino

AU - Fiore, Vincenzo

AU - Pinnola, Francesco Paolo

PY - 2014

Y1 - 2014

N2 - Creep and/or Relaxation tests on viscoelastic materials show a power-law trend. Based upon Boltzmann superposition principle the constitutive law with a power-law kernel is ruled by the Caputo’s fractional derivative. Fractional constitutive law posses a long memory and then the parameters obtained by best fitting procedures on experimental data are strongly influenced by the prestress on the specimen. As in fact during the relaxation test the imposed history of deformation is not instantaneously applied, since a unit step function may not be realized by the test machine. Usually an initial ramp is present in the deformation history and the time at which the deformation attains the maximum value is fixed by the operator. Even though the precharge time is small in comparison with the total duration of the observation time, the parameters obtained by the best fitting procedure leads to relevant error especially for small observation time. In the paper the problem is overcome by considering the time load history for both theoretical and experimental point of view. In order to demonstrate experimentally that the initial ramp of deformation strongly influences the stress history during the relaxation test, different tests were performed on samples of a commercial epoxy resin (SP106) at two different rates of deformation (i.e. 0.2 mm/mm and 2 mm/min). Moreover the corrected approach for the best fitting of the data permits to characterize the viscoelastic materials, in term of fractional viscoelastic parameters, in a short time, and this allows to reduce the long duration of the experimental tests.

AB - Creep and/or Relaxation tests on viscoelastic materials show a power-law trend. Based upon Boltzmann superposition principle the constitutive law with a power-law kernel is ruled by the Caputo’s fractional derivative. Fractional constitutive law posses a long memory and then the parameters obtained by best fitting procedures on experimental data are strongly influenced by the prestress on the specimen. As in fact during the relaxation test the imposed history of deformation is not instantaneously applied, since a unit step function may not be realized by the test machine. Usually an initial ramp is present in the deformation history and the time at which the deformation attains the maximum value is fixed by the operator. Even though the precharge time is small in comparison with the total duration of the observation time, the parameters obtained by the best fitting procedure leads to relevant error especially for small observation time. In the paper the problem is overcome by considering the time load history for both theoretical and experimental point of view. In order to demonstrate experimentally that the initial ramp of deformation strongly influences the stress history during the relaxation test, different tests were performed on samples of a commercial epoxy resin (SP106) at two different rates of deformation (i.e. 0.2 mm/mm and 2 mm/min). Moreover the corrected approach for the best fitting of the data permits to characterize the viscoelastic materials, in term of fractional viscoelastic parameters, in a short time, and this allows to reduce the long duration of the experimental tests.

UR - http://hdl.handle.net/10447/100057

M3 - Article

VL - 69

SP - 63

EP - 70

JO - Mechanics of Materials

JF - Mechanics of Materials

SN - 0167-6636

ER -