Fractional-order poromechanics for a fully saturated biological tissue: Biomechanics of meniscus

Fabiana Amiri; Emanuela Bologna; Gianmarco Nuzzo; Lorenzo Moroni; Massimiliano Zingales

doi:10.1002/cnm.3732

Fractional-order poromechanics for a fully saturated biological tissue: Biomechanics of meniscus

Fabiana Amiri
, Emanuela Bologna^*
, Gianmarco Nuzzo
, Lorenzo Moroni
, Massimiliano Zingales

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

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Abstract

Biomechanics of biological fibrous tissues as the meniscus are strongly influenced by past histories of strains involving the so-called material hereditariness. In this paper, a three-axial model of linear hereditariness that makes use of fractional-order calculus is used to describe the constitutive behavior of the tissue. Fluid flow across meniscus' pores is modeled in this paper with Darcy relation yielding a novel model of fractional-order poromechanics, describing the evolution of the diffusion phenomenon in the meniscus. A numerical application involving an 1D confined compression test is reported to show the effect of the material hereditariness on the pressure drop evolution.

Original language	English
Article number	e3732
Number of pages	20
Journal	International Journal for Numerical Methods in Biomedical Engineering
Volume	39
Issue number	11
Early online date	1 May 2023
DOIs	https://doi.org/10.1002/cnm.3732
Publication status	Published - Nov 2023

Keywords

fractional calculus
fractional-order hereditariness
meniscus
pore pressure
poromechanics
CALCULUS
LAW
HEREDITARINESS
RELAXATION
DIFFUSION
MODELS

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10.1002/cnm.3732

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title = "Fractional-order poromechanics for a fully saturated biological tissue: Biomechanics of meniscus",

abstract = "Biomechanics of biological fibrous tissues as the meniscus are strongly influenced by past histories of strains involving the so-called material hereditariness. In this paper, a three-axial model of linear hereditariness that makes use of fractional-order calculus is used to describe the constitutive behavior of the tissue. Fluid flow across meniscus' pores is modeled in this paper with Darcy relation yielding a novel model of fractional-order poromechanics, describing the evolution of the diffusion phenomenon in the meniscus. A numerical application involving an 1D confined compression test is reported to show the effect of the material hereditariness on the pressure drop evolution.",

keywords = "fractional calculus, fractional-order hereditariness, meniscus, pore pressure, poromechanics, CALCULUS, LAW, HEREDITARINESS, RELAXATION, DIFFUSION, MODELS",

author = "Fabiana Amiri and Emanuela Bologna and Gianmarco Nuzzo and Lorenzo Moroni and Massimiliano Zingales",

year = "2023",

month = nov,

doi = "10.1002/cnm.3732",

language = "English",

volume = "39",

journal = "International Journal for Numerical Methods in Biomedical Engineering",

issn = "2040-7939",

publisher = "Wiley-Blackwell",

number = "11",

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T1 - Fractional-order poromechanics for a fully saturated biological tissue: Biomechanics of meniscus

AU - Amiri, Fabiana

AU - Bologna, Emanuela

AU - Nuzzo, Gianmarco

AU - Moroni, Lorenzo

AU - Zingales, Massimiliano

PY - 2023/11

Y1 - 2023/11

N2 - Biomechanics of biological fibrous tissues as the meniscus are strongly influenced by past histories of strains involving the so-called material hereditariness. In this paper, a three-axial model of linear hereditariness that makes use of fractional-order calculus is used to describe the constitutive behavior of the tissue. Fluid flow across meniscus' pores is modeled in this paper with Darcy relation yielding a novel model of fractional-order poromechanics, describing the evolution of the diffusion phenomenon in the meniscus. A numerical application involving an 1D confined compression test is reported to show the effect of the material hereditariness on the pressure drop evolution.

AB - Biomechanics of biological fibrous tissues as the meniscus are strongly influenced by past histories of strains involving the so-called material hereditariness. In this paper, a three-axial model of linear hereditariness that makes use of fractional-order calculus is used to describe the constitutive behavior of the tissue. Fluid flow across meniscus' pores is modeled in this paper with Darcy relation yielding a novel model of fractional-order poromechanics, describing the evolution of the diffusion phenomenon in the meniscus. A numerical application involving an 1D confined compression test is reported to show the effect of the material hereditariness on the pressure drop evolution.

KW - fractional calculus

KW - fractional-order hereditariness

KW - meniscus

KW - pore pressure

KW - poromechanics

KW - CALCULUS

KW - LAW

KW - HEREDITARINESS

KW - RELAXATION

KW - DIFFUSION

KW - MODELS

U2 - 10.1002/cnm.3732

DO - 10.1002/cnm.3732

M3 - Article

C2 - 37203427

SN - 2040-7939

VL - 39

JO - International Journal for Numerical Methods in Biomedical Engineering

JF - International Journal for Numerical Methods in Biomedical Engineering

IS - 11

M1 - e3732

ER -

Fractional-order poromechanics for a fully saturated biological tissue: Biomechanics of meniscus

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