Visco-elastic behavior through fractional calculus: an easier method for best fitting experimental results

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Abstract

In capturing visco-elastic behavior, experimental tests play a fundamental rule, since theyallow to build up theoretical constitutive laws very useful for simulating their own behavior.The main challenge is representing the visco-elastic materials through simple models,in order to spread their use. However, the wide used models for capturing both relaxationand creep tests are combinations of simple models as Maxwell and/or Kelvin, that dependon several parameters for fitting both creep and relaxation tests. This paper, following Nuttingand Gemant idea of fitting experimental data through a power law function, aims atstressing the validity of fractional model. In fact, as soon as relaxation test is well fittedby power law decay then the fractional constitutive law involving Caputo’s derivativedirectly appears. It will be shown that fractional model is proper for studying visco-elasticbehavior, since it may capture both relaxation and creep tests, requiring the identificationof two parameters only. This consideration is assessed by the good agreement betweenexperimental tests on creep and relaxation and the fractional model proposed. Experimentaltests, here reported are performed on two polymers having different chemical physicalproperties such that the fractional model may cover a wide range of visco-elastic behavior.
Lingua originaleEnglish
pagine (da-a)799-806
Numero di pagine8
RivistaMechanics of Materials
Volume43
Stato di pubblicazionePublished - 2011

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calculus
creep tests
Creep
Polymers
polymers
decay

All Science Journal Classification (ASJC) codes

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

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title = "Visco-elastic behavior through fractional calculus: an easier method for best fitting experimental results",
abstract = "In capturing visco-elastic behavior, experimental tests play a fundamental rule, since theyallow to build up theoretical constitutive laws very useful for simulating their own behavior.The main challenge is representing the visco-elastic materials through simple models,in order to spread their use. However, the wide used models for capturing both relaxationand creep tests are combinations of simple models as Maxwell and/or Kelvin, that dependon several parameters for fitting both creep and relaxation tests. This paper, following Nuttingand Gemant idea of fitting experimental data through a power law function, aims atstressing the validity of fractional model. In fact, as soon as relaxation test is well fittedby power law decay then the fractional constitutive law involving Caputo’s derivativedirectly appears. It will be shown that fractional model is proper for studying visco-elasticbehavior, since it may capture both relaxation and creep tests, requiring the identificationof two parameters only. This consideration is assessed by the good agreement betweenexperimental tests on creep and relaxation and the fractional model proposed. Experimentaltests, here reported are performed on two polymers having different chemical physicalproperties such that the fractional model may cover a wide range of visco-elastic behavior.",
keywords = "Fractional calculus Visco-elastic Relaxation function Creep function Power law",
author = "Antonina Pirrotta and Antonino Valenza and {Di Paola}, Mario",
year = "2011",
language = "English",
volume = "43",
pages = "799--806",
journal = "Mechanics of Materials",
issn = "0167-6636",
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TY - JOUR

T1 - Visco-elastic behavior through fractional calculus: an easier method for best fitting experimental results

AU - Pirrotta, Antonina

AU - Valenza, Antonino

AU - Di Paola, Mario

PY - 2011

Y1 - 2011

N2 - In capturing visco-elastic behavior, experimental tests play a fundamental rule, since theyallow to build up theoretical constitutive laws very useful for simulating their own behavior.The main challenge is representing the visco-elastic materials through simple models,in order to spread their use. However, the wide used models for capturing both relaxationand creep tests are combinations of simple models as Maxwell and/or Kelvin, that dependon several parameters for fitting both creep and relaxation tests. This paper, following Nuttingand Gemant idea of fitting experimental data through a power law function, aims atstressing the validity of fractional model. In fact, as soon as relaxation test is well fittedby power law decay then the fractional constitutive law involving Caputo’s derivativedirectly appears. It will be shown that fractional model is proper for studying visco-elasticbehavior, since it may capture both relaxation and creep tests, requiring the identificationof two parameters only. This consideration is assessed by the good agreement betweenexperimental tests on creep and relaxation and the fractional model proposed. Experimentaltests, here reported are performed on two polymers having different chemical physicalproperties such that the fractional model may cover a wide range of visco-elastic behavior.

AB - In capturing visco-elastic behavior, experimental tests play a fundamental rule, since theyallow to build up theoretical constitutive laws very useful for simulating their own behavior.The main challenge is representing the visco-elastic materials through simple models,in order to spread their use. However, the wide used models for capturing both relaxationand creep tests are combinations of simple models as Maxwell and/or Kelvin, that dependon several parameters for fitting both creep and relaxation tests. This paper, following Nuttingand Gemant idea of fitting experimental data through a power law function, aims atstressing the validity of fractional model. In fact, as soon as relaxation test is well fittedby power law decay then the fractional constitutive law involving Caputo’s derivativedirectly appears. It will be shown that fractional model is proper for studying visco-elasticbehavior, since it may capture both relaxation and creep tests, requiring the identificationof two parameters only. This consideration is assessed by the good agreement betweenexperimental tests on creep and relaxation and the fractional model proposed. Experimentaltests, here reported are performed on two polymers having different chemical physicalproperties such that the fractional model may cover a wide range of visco-elastic behavior.

KW - Fractional calculus Visco-elastic Relaxation function Creep function Power law

UR - http://hdl.handle.net/10447/63658

M3 - Article

VL - 43

SP - 799

EP - 806

JO - Mechanics of Materials

JF - Mechanics of Materials

SN - 0167-6636

ER -