How non-integer order derivatives can be useful to rheology

L. L. Ferras; Neville J. Ford; Maria Lusa Morgado; Magda Rebelo; Gareth H. McKinley; Joao M. Nobrega

How non-integer order derivatives can be useful to rheology

L. L. Ferras, Neville J. Ford, Maria Lusa Morgado, Magda Rebelo, Gareth H. McKinley, Joao M. Nobrega

Research output: Contribution to conference › Paper › peer-review

Abstract

In this work we extend a numerical method developed by the group for the solution of fractional differential equations governing the flow of complex fluids. The method is robust and can now deal with graded meshes in time. The grading can be performed in a semi-automatic way, taking into account the evolution in time of the gradient of stress. We also explore the ability of fractional viscoleastic models to fit rheological data obtained from small-amplitude oscillatory shear experiments with blood.

Original language	English
Pages	406-421
Number of pages	16
Publication status	Published - 1 Jan 2017
Event	3rd International Conference on Numerical and Symbolic Computation: Developments and Applications, SYMCOMP 2017 - Guimaraes, Portugal Duration: 6 Apr 2017 → 7 Apr 2017

Conference

Conference	3rd International Conference on Numerical and Symbolic Computation: Developments and Applications, SYMCOMP 2017
Country/Territory	Portugal
City	Guimaraes
Period	6/04/17 → 7/04/17

Keywords

Caputo Fractional Derivative
Fractional Viscoelastic Models
Graded Meshes
Numerical Solution
Relaxation Tests
Rheology

Cite this

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title = "How non-integer order derivatives can be useful to rheology",

abstract = "In this work we extend a numerical method developed by the group for the solution of fractional differential equations governing the flow of complex fluids. The method is robust and can now deal with graded meshes in time. The grading can be performed in a semi-automatic way, taking into account the evolution in time of the gradient of stress. We also explore the ability of fractional viscoleastic models to fit rheological data obtained from small-amplitude oscillatory shear experiments with blood.",

keywords = "Caputo Fractional Derivative, Fractional Viscoelastic Models, Graded Meshes, Numerical Solution, Relaxation Tests, Rheology",

author = "Ferras, {L. L.} and Ford, {Neville J.} and Morgado, {Maria Lusa} and Magda Rebelo and McKinley, {Gareth H.} and Nobrega, {Joao M.}",

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T1 - How non-integer order derivatives can be useful to rheology

AU - Ferras, L. L.

AU - Ford, Neville J.

AU - Morgado, Maria Lusa

AU - Rebelo, Magda

AU - McKinley, Gareth H.

AU - Nobrega, Joao M.

N1 - Sem PDF.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - In this work we extend a numerical method developed by the group for the solution of fractional differential equations governing the flow of complex fluids. The method is robust and can now deal with graded meshes in time. The grading can be performed in a semi-automatic way, taking into account the evolution in time of the gradient of stress. We also explore the ability of fractional viscoleastic models to fit rheological data obtained from small-amplitude oscillatory shear experiments with blood.

AB - In this work we extend a numerical method developed by the group for the solution of fractional differential equations governing the flow of complex fluids. The method is robust and can now deal with graded meshes in time. The grading can be performed in a semi-automatic way, taking into account the evolution in time of the gradient of stress. We also explore the ability of fractional viscoleastic models to fit rheological data obtained from small-amplitude oscillatory shear experiments with blood.

KW - Caputo Fractional Derivative

KW - Fractional Viscoelastic Models

KW - Graded Meshes

KW - Numerical Solution

KW - Relaxation Tests

KW - Rheology

UR - http://www.scopus.com/inward/record.url?scp=85040729824&partnerID=8YFLogxK

M3 - Paper

AN - SCOPUS:85040729824

SP - 406

EP - 421

T2 - 3rd International Conference on Numerical and Symbolic Computation: Developments and Applications, SYMCOMP 2017

Y2 - 6 April 2017 through 7 April 2017

ER -

How non-integer order derivatives can be useful to rheology

Abstract

Conference

Keywords

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