On a fractional derivative type of a viscoelastic body

Atanacković, Milica; Novakovic, N Branislava

doi:10.2298/tam0229027a

Cited by 2 publications

(2 citation statements)

References 8 publications

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“…This simple 5 element model has proved to be reliable and robust describing real materials [5], [8], [9], [16]. As analyzed by Bagley and Torvik [7], the constraint α=β predicts positive energy dissipation for all frequencies.…”

Section: A Modellingmentioning

confidence: 89%

“…These classical derivatives can be extended including fractional derivatives. This generalization to any real-order derivative was applied to many fields and eventually in rheological cases including molecular theories [5]- [10]. Some important advantages must be emphasized i) They proved to describe accurately complex model with less number of parameters (model order) ii) They improved the curve fitting, principally with power-law frequency responses iii) They allowed a physical justification in rheological and tissue cases.…”

Section: Introductionmentioning

confidence: 99%

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Arterial viscoelasticity: a fractional derivative model

Craiem¹,

Armentano²

2006

2006 International Conference of the IEEE Engineering in Medicine and Biology Society

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Arteries are viscoelastic materials. Viscoelastic laws are fully characterized by measuring a complex modulus. Arterial mechanics can be described using stress-strain dynamic measurements applied to the particular cylindrical geometry. Most materials show an energy loss per cycle that increases steadily with frequency. By contrast, the frequency modulus response in arteries presents a frequency independence describing a plateau above a corner frequency near 4Hz. Traditional methods to fit this response include several spring and dashpot elements to model integer order differential equations in time domain. Recently, fractional derivative models proved to be efficient to describe rheological tissues, reducing the number of parameters and showing a natural power-law response. In this work a fractional derivative model with 4-parameter was selected to describe the arterial wall mechanics in-vivo. Strain and stress were measured simultaneously in an anaesthetized sheep. A fractional model was applied. The order resulted α=0.12, confirming the manifest elastic response of the aorta. The fractional derivative model proved to naturally mimic the elastic modulus spectrum with only 4 parameters and a reasonable small computational effort.

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Section: A Modellingmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Arterial viscoelasticity: a fractional derivative model

Craiem¹,

Armentano²

2006

2006 International Conference of the IEEE Engineering in Medicine and Biology Society

View full text Add to dashboard Cite

show abstract

Arterial viscoelasticity: a fractional derivative model

Craiem

Armentano²

2006

2006 International Conference of the IEEE Engineering in Medicine and Biology Society

View full text Add to dashboard Cite

Arteries are viscoelastic materials. Viscoelastic laws are fully characterized by measuring a complex modulus. Arterial mechanics can be described using stress-strain dynamic measurements applied to the particular cylindrical geometry. Most materials show an energy loss per cycle that increases steadily with frequency. By contrast, the frequency modulus response in arteries presents a frequency independence describing a plateau above a corner frequency near 4Hz. Traditional methods to fit this response include several spring and dashpot elements to model integer order differential equations in time domain. Recently, fractional derivative models proved to be efficient to describe rheological tissues, reducing the number of parameters and showing a natural power-law response. In this work a fractional derivative model with 4-parameter was selected to describe the arterial wall mechanics in-vivo. Strain and stress were measured simultaneously in an anaesthetized sheep. A fractional model was applied. The order resulted alpha=0.12, confirming the manifest elastic response of the aorta. The fractional derivative model proved to naturally mimic the elastic modulus spectrum with only 4 parameters and a reasonable small computational effort.

show abstract

On a fractional derivative type of a viscoelastic body

Cited by 2 publications

References 8 publications

Arterial viscoelasticity: a fractional derivative model

Arterial viscoelasticity: a fractional derivative model

Arterial viscoelasticity: a fractional derivative model

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