A primer on experimental and computational rheology with fractional viscoelastic constitutive models

Luís Lima Ferrás; Neville John Ford; Maria Luísa Morgado; Magda Rebelo; Gareth Huw McKinley; João Miguel Nóbrega

doi:10.1063/1.4982977

A primer on experimental and computational rheology with fractional viscoelastic constitutive models

Luís Lima Ferrás, Neville John Ford, Maria Luísa Morgado, Magda Rebelo, Gareth Huw McKinley, João Miguel Nóbrega

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

10 Citations (Scopus)

Abstract

This work presents a brief introduction to fractional calculus and its application to some problems in rheology. We present two different viscoelastic models based on fractional derivatives (the Fractional Maxwell Model - FMM and the Fractional Viscoelastic Fluid - FVF) and discuss their reduction to the classical Newtonian and Maxwell fluids. A third model is also studied (an extension of the FMM to an invariant form), being given by a combination of the K-BKZ integral model with a fractional memory function which we denote the Fractional K-BKZ model. We discuss and illustrate the ability of these models to fit experimental data, and present numerical results for simple stress relaxation following step strain and steady shearing.

Original language	English
Title of host publication	Novel Trends in Rheology VII
Publisher	American Institute of Physics
Volume	1843
ISBN (Electronic)	9780735415133
DOIs	https://doi.org/10.1063/1.4982977
Publication status	Published - 2017
Event	7th International Conference on Novel Trends in Rheology 2017 - Zlin, Czech Republic Duration: 26 Jul 2017 → 27 Jul 2017

Conference

Conference	7th International Conference on Novel Trends in Rheology 2017
Country/Territory	Czech Republic
City	Zlin
Period	26/07/17 → 27/07/17

Keywords

NONLINEAR RHEOLOGY
RELAXATION
EQUATIONS
DERIVATIVES
CALCULUS
FLOW
MELT

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title = "A primer on experimental and computational rheology with fractional viscoelastic constitutive models",

abstract = "This work presents a brief introduction to fractional calculus and its application to some problems in rheology. We present two different viscoelastic models based on fractional derivatives (the Fractional Maxwell Model - FMM and the Fractional Viscoelastic Fluid - FVF) and discuss their reduction to the classical Newtonian and Maxwell fluids. A third model is also studied (an extension of the FMM to an invariant form), being given by a combination of the K-BKZ integral model with a fractional memory function which we denote the Fractional K-BKZ model. We discuss and illustrate the ability of these models to fit experimental data, and present numerical results for simple stress relaxation following step strain and steady shearing.",

keywords = "NONLINEAR RHEOLOGY, RELAXATION, EQUATIONS, DERIVATIVES, CALCULUS, FLOW, MELT",

author = "Ferr{\'a}s, {Lu{\'i}s Lima} and Ford, {Neville John} and Morgado, {Maria Lu{\'i}sa} and Magda Rebelo and McKinley, {Gareth Huw} and N{\'o}brega, {Jo{\~a}o Miguel}",

note = "Sem PDF. FEDER through the COMPETE Programme National Funds through FCT - Portuguese Foundation for Science and Technology (UID/CTM/50025/2013) FCT (SFRH/BPD/100353/2014; UID/MAT/00013/2013; UID/MAT/00297/2013) ; 7th International Conference on Novel Trends in Rheology 2017 ; Conference date: 26-07-2017 Through 27-07-2017",

year = "2017",

doi = "10.1063/1.4982977",

language = "English",

volume = "1843",

booktitle = "Novel Trends in Rheology VII",

publisher = "American Institute of Physics",

address = "United States",

}

Ferrás, LL, Ford, NJ, Morgado, ML, Rebelo, M, McKinley, GH & Nóbrega, JM 2017, A primer on experimental and computational rheology with fractional viscoelastic constitutive models. in Novel Trends in Rheology VII. vol. 1843, 020002, American Institute of Physics, 7th International Conference on Novel Trends in Rheology 2017, Zlin, Czech Republic, 26/07/17. https://doi.org/10.1063/1.4982977

TY - GEN

T1 - A primer on experimental and computational rheology with fractional viscoelastic constitutive models

AU - Ferrás, Luís Lima

AU - Ford, Neville John

AU - Morgado, Maria Luísa

AU - Rebelo, Magda

AU - McKinley, Gareth Huw

AU - Nóbrega, João Miguel

N1 - Sem PDF. FEDER through the COMPETE Programme National Funds through FCT - Portuguese Foundation for Science and Technology (UID/CTM/50025/2013) FCT (SFRH/BPD/100353/2014; UID/MAT/00013/2013; UID/MAT/00297/2013)

PY - 2017

Y1 - 2017

N2 - This work presents a brief introduction to fractional calculus and its application to some problems in rheology. We present two different viscoelastic models based on fractional derivatives (the Fractional Maxwell Model - FMM and the Fractional Viscoelastic Fluid - FVF) and discuss their reduction to the classical Newtonian and Maxwell fluids. A third model is also studied (an extension of the FMM to an invariant form), being given by a combination of the K-BKZ integral model with a fractional memory function which we denote the Fractional K-BKZ model. We discuss and illustrate the ability of these models to fit experimental data, and present numerical results for simple stress relaxation following step strain and steady shearing.

AB - This work presents a brief introduction to fractional calculus and its application to some problems in rheology. We present two different viscoelastic models based on fractional derivatives (the Fractional Maxwell Model - FMM and the Fractional Viscoelastic Fluid - FVF) and discuss their reduction to the classical Newtonian and Maxwell fluids. A third model is also studied (an extension of the FMM to an invariant form), being given by a combination of the K-BKZ integral model with a fractional memory function which we denote the Fractional K-BKZ model. We discuss and illustrate the ability of these models to fit experimental data, and present numerical results for simple stress relaxation following step strain and steady shearing.

KW - NONLINEAR RHEOLOGY

KW - RELAXATION

KW - EQUATIONS

KW - DERIVATIVES

KW - CALCULUS

KW - FLOW

KW - MELT

UR - http://www.scopus.com/inward/record.url?scp=85019766416&partnerID=8YFLogxK

U2 - 10.1063/1.4982977

DO - 10.1063/1.4982977

M3 - Conference contribution

AN - SCOPUS:85019766416

VL - 1843

BT - Novel Trends in Rheology VII

PB - American Institute of Physics

T2 - 7th International Conference on Novel Trends in Rheology 2017

Y2 - 26 July 2017 through 27 July 2017

ER -

A primer on experimental and computational rheology with fractional viscoelastic constitutive models

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