Asymptotic Models of Anisotropic Heterogeneous Elastic Walls of Blood Vessels

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Asymptotic Models of Anisotropic Heterogeneous Elastic Walls of Blood Vessels. / Kozlov, V. A.; Nazarov, S. A.

In: Journal of Mathematical Sciences (United States), Vol. 213, No. 4, 01.03.2016, p. 561-581.

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

Author

Kozlov, V. A. ; Nazarov, S. A. / Asymptotic Models of Anisotropic Heterogeneous Elastic Walls of Blood Vessels. In: Journal of Mathematical Sciences (United States). 2016 ; Vol. 213, No. 4. pp. 561-581.

BibTeX

@article{0ad4240d954a47b5b48eb8ac737119cb,

title = "Asymptotic Models of Anisotropic Heterogeneous Elastic Walls of Blood Vessels",

abstract = "Using the dimension reduction procedure for a three-dimensional elasticity system, we derive a two-dimensional model for elastic laminate walls of a blood vessel. In the case of a sufficiently small wall thickness, we derive a system of limit equations coupled with the Navier–Stokes equations through the stress and velocity, i.e., dynamic and kinematic conditions on the interior surface of the wall. We deduce explicit formulas for the effective rigidity tensor of the wall in two natural cases. We show that if the blood flow remains laminar, then the cross-section of the orthotropic homogeneous blood vessel becomes circular.",

keywords = "Blood Vessel Wall, Stokes System, Rigidity Matrix, Elastic Wall, Periodic Family",

author = "Kozlov, {V. A.} and Nazarov, {S. A.}",

note = "Kozlov, V.A., Nazarov, S.A. Asymptotic Models of Anisotropic Heterogeneous Elastic Walls of Blood Vessels. J Math Sci 213, 561–581 (2016). https://doi.org/10.1007/s10958-016-2725-1",

year = "2016",

month = mar,

day = "1",

doi = "10.1007/s10958-016-2725-1",

language = "English",

volume = "213",

pages = "561--581",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "4",

}

RIS

TY - JOUR

T1 - Asymptotic Models of Anisotropic Heterogeneous Elastic Walls of Blood Vessels

AU - Kozlov, V. A.

AU - Nazarov, S. A.

N1 - Kozlov, V.A., Nazarov, S.A. Asymptotic Models of Anisotropic Heterogeneous Elastic Walls of Blood Vessels. J Math Sci 213, 561–581 (2016). https://doi.org/10.1007/s10958-016-2725-1

PY - 2016/3/1

Y1 - 2016/3/1

N2 - Using the dimension reduction procedure for a three-dimensional elasticity system, we derive a two-dimensional model for elastic laminate walls of a blood vessel. In the case of a sufficiently small wall thickness, we derive a system of limit equations coupled with the Navier–Stokes equations through the stress and velocity, i.e., dynamic and kinematic conditions on the interior surface of the wall. We deduce explicit formulas for the effective rigidity tensor of the wall in two natural cases. We show that if the blood flow remains laminar, then the cross-section of the orthotropic homogeneous blood vessel becomes circular.

AB - Using the dimension reduction procedure for a three-dimensional elasticity system, we derive a two-dimensional model for elastic laminate walls of a blood vessel. In the case of a sufficiently small wall thickness, we derive a system of limit equations coupled with the Navier–Stokes equations through the stress and velocity, i.e., dynamic and kinematic conditions on the interior surface of the wall. We deduce explicit formulas for the effective rigidity tensor of the wall in two natural cases. We show that if the blood flow remains laminar, then the cross-section of the orthotropic homogeneous blood vessel becomes circular.

KW - Blood Vessel Wall

KW - Stokes System

KW - Rigidity Matrix

KW - Elastic Wall

KW - Periodic Family

UR - http://www.scopus.com/inward/record.url?scp=84962291551&partnerID=8YFLogxK

U2 - 10.1007/s10958-016-2725-1

DO - 10.1007/s10958-016-2725-1

M3 - Article

AN - SCOPUS:84962291551

VL - 213

SP - 561

EP - 581

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 4

ER -

ID: 40974350