Exact analytical representation of fiber stress tensor based on angular integration (AI) through cellular level probabilistic equations

Gürsan Çoban; M. Serdar Çelebi

doi:10.1063/1.4912568

Exact analytical representation of fiber stress tensor based on angular integration (AI) through cellular level probabilistic equations

Gürsan Çoban, M. Serdar Çelebi

Informatics Institute

Istanbul Technical University

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

1 Citation (Scopus)

Abstract

An analytical representation of the structural stress tensor which describes the fiber dispersion in soft biological tissue has been represented. The mathematical form is computationally efficient compared to the angular integration schemes and it interelates the cellular scale fiber rotation concept with macroscopic deformation of the tissue. It has been shown that, based on well known cellular rotation concepts, the steady state second Piola-Kirschoff stress tensor can be described by a set of structural and remodeling variables, and the current strain tensor.

Original language	English
Title of host publication	Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014
Editors	Theodore E. Simos, Theodore E. Simos, Theodore E. Simos, Charalambos Tsitouras
Publisher	American Institute of Physics Inc.
ISBN (Electronic)	9780735412873
DOIs	https://doi.org/10.1063/1.4912568
Publication status	Published - 10 Mar 2015
Event	International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014 - Rhodes, Greece Duration: 22 Sept 2014 → 28 Sept 2014

Publication series

Name	AIP Conference Proceedings
Volume	1648
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014
Country/Territory	Greece
City	Rhodes
Period	22/09/14 → 28/09/14

Bibliographical note

Publisher Copyright:
© 2015 AIP Publishing LLC.

Keywords

Angular Integration
Fiber Dispersion
Remodeling
Soft Tissue
Strutural Tensor

Access to Document

10.1063/1.4912568

Cite this

Çoban, G., & Çelebi, M. S. (2015). Exact analytical representation of fiber stress tensor based on angular integration (AI) through cellular level probabilistic equations. In T. E. Simos, T. E. Simos, T. E. Simos, & C. Tsitouras (Eds.), Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014 Article 320002 (AIP Conference Proceedings; Vol. 1648). American Institute of Physics Inc.. https://doi.org/10.1063/1.4912568

Çoban, Gürsan ; Çelebi, M. Serdar. / Exact analytical representation of fiber stress tensor based on angular integration (AI) through cellular level probabilistic equations. Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014. editor / Theodore E. Simos ; Theodore E. Simos ; Theodore E. Simos ; Charalambos Tsitouras. American Institute of Physics Inc., 2015. (AIP Conference Proceedings).

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title = "Exact analytical representation of fiber stress tensor based on angular integration (AI) through cellular level probabilistic equations",

abstract = "An analytical representation of the structural stress tensor which describes the fiber dispersion in soft biological tissue has been represented. The mathematical form is computationally efficient compared to the angular integration schemes and it interelates the cellular scale fiber rotation concept with macroscopic deformation of the tissue. It has been shown that, based on well known cellular rotation concepts, the steady state second Piola-Kirschoff stress tensor can be described by a set of structural and remodeling variables, and the current strain tensor.",

keywords = "Angular Integration, Fiber Dispersion, Remodeling, Soft Tissue, Strutural Tensor",

author = "G{\"u}rsan {\c C}oban and {\c C}elebi, {M. Serdar}",

note = "Publisher Copyright: {\textcopyright} 2015 AIP Publishing LLC.; International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014 ; Conference date: 22-09-2014 Through 28-09-2014",

year = "2015",

month = mar,

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doi = "10.1063/1.4912568",

language = "English",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics Inc.",

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Çoban, G & Çelebi, MS 2015, Exact analytical representation of fiber stress tensor based on angular integration (AI) through cellular level probabilistic equations. in TE Simos, TE Simos, TE Simos & C Tsitouras (eds), Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014., 320002, AIP Conference Proceedings, vol. 1648, American Institute of Physics Inc., International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014, Rhodes, Greece, 22/09/14. https://doi.org/10.1063/1.4912568

Exact analytical representation of fiber stress tensor based on angular integration (AI) through cellular level probabilistic equations. / Çoban, Gürsan; Çelebi, M. Serdar.
Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014. ed. / Theodore E. Simos; Theodore E. Simos; Theodore E. Simos; Charalambos Tsitouras. American Institute of Physics Inc., 2015. 320002 (AIP Conference Proceedings; Vol. 1648).

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

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AU - Çelebi, M. Serdar

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N2 - An analytical representation of the structural stress tensor which describes the fiber dispersion in soft biological tissue has been represented. The mathematical form is computationally efficient compared to the angular integration schemes and it interelates the cellular scale fiber rotation concept with macroscopic deformation of the tissue. It has been shown that, based on well known cellular rotation concepts, the steady state second Piola-Kirschoff stress tensor can be described by a set of structural and remodeling variables, and the current strain tensor.

AB - An analytical representation of the structural stress tensor which describes the fiber dispersion in soft biological tissue has been represented. The mathematical form is computationally efficient compared to the angular integration schemes and it interelates the cellular scale fiber rotation concept with macroscopic deformation of the tissue. It has been shown that, based on well known cellular rotation concepts, the steady state second Piola-Kirschoff stress tensor can be described by a set of structural and remodeling variables, and the current strain tensor.

KW - Angular Integration

KW - Fiber Dispersion

KW - Remodeling

KW - Soft Tissue

KW - Strutural Tensor

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DO - 10.1063/1.4912568

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BT - Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014

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Çoban G, Çelebi MS. Exact analytical representation of fiber stress tensor based on angular integration (AI) through cellular level probabilistic equations. In Simos TE, Simos TE, Simos TE, Tsitouras C, editors, Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014, ICNAAM 2014. American Institute of Physics Inc. 2015. 320002. (AIP Conference Proceedings). doi: 10.1063/1.4912568

Exact analytical representation of fiber stress tensor based on angular integration (AI) through cellular level probabilistic equations

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