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The Use of Contravariant Tensors to Model Anisotropic Soft Tissues

Arthesh Basak, Amirtham Rajagopal, Umesh Basappa, Mokarram Hossain Orcid Logo

International Journal of Applied Mechanics, Volume: 13, Issue: 3, Start page: 2150039

Swansea University Author: Mokarram Hossain Orcid Logo

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DOI (Published version): 10.1142/s1758825121500393

Abstract

Biological tissues have been shown to behave isotropically at lower strain values, while at higher strains the fibers embedded in the tissue straighten and tend to take up the load. Thus, the anisotropy induced at higher loads can be mathematically modeled by incorporating the strains experienced by...

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Published in: International Journal of Applied Mechanics
ISSN: 1758-8251 1758-826X
Published: World Scientific Pub Co Pte Lt 2021
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URI: https://cronfa.swan.ac.uk/Record/cronfa56784
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first_indexed 2021-05-04T12:10:48Z
last_indexed 2021-08-13T03:23:58Z
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spelling 2021-08-12T12:18:22.6668011 v2 56784 2021-05-04 The Use of Contravariant Tensors to Model Anisotropic Soft Tissues 140f4aa5c5ec18ec173c8542a7fddafd 0000-0002-4616-1104 Mokarram Hossain Mokarram Hossain true false 2021-05-04 GENG Biological tissues have been shown to behave isotropically at lower strain values, while at higher strains the fibers embedded in the tissue straighten and tend to take up the load. Thus, the anisotropy induced at higher loads can be mathematically modeled by incorporating the strains experienced by the fibers. From histological studies on soft tissues it is evident that for a wide range of tissues the fibers have an oblique mean orientation about the physiological loading directions. Thus, we require a mathematical framework of tensors defined in nonorthogonal basis to capture the direction-dependent response of fibers under high induced loads. In this work, we propose a novel approach to determine the fiber strains with the aid of the contravariant tensors defined in an oblique coordinate system. To determine the fiber strains, we introduce a fourth-order contravariant fiber orientation transformation tensor. The approach helps us successfully in determining the fiber strains, for a family of symmetrically and asymmetrically oriented fibers, with the aid of a single anisotropic invariant. The proposed model was fitted with the experimental data from literature to determine the corresponding material parameters. Journal Article International Journal of Applied Mechanics 13 3 2150039 World Scientific Pub Co Pte Lt 1758-8251 1758-826X Oblique coordinate system, reciprocal basis, anisotropic hyperelasticity 30 4 2021 2021-04-30 10.1142/s1758825121500393 COLLEGE NANME General Engineering COLLEGE CODE GENG Swansea University Not Required 2021-08-12T12:18:22.6668011 2021-05-04T13:06:55.1341520 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - General Engineering Arthesh Basak 1 Amirtham Rajagopal 2 Umesh Basappa 3 Mokarram Hossain 0000-0002-4616-1104 4 56784__20050__1fa24976cf99429e880993e86548207e.pdf paperIJAM.56784.AAM.pdf 2021-06-02T16:16:54.1186430 Output 646236 application/pdf Accepted Manuscript true 2022-04-30T00:00:00.0000000 © [copyright World Scientific Publishing Company] true eng
title The Use of Contravariant Tensors to Model Anisotropic Soft Tissues
spellingShingle The Use of Contravariant Tensors to Model Anisotropic Soft Tissues
Mokarram Hossain
title_short The Use of Contravariant Tensors to Model Anisotropic Soft Tissues
title_full The Use of Contravariant Tensors to Model Anisotropic Soft Tissues
title_fullStr The Use of Contravariant Tensors to Model Anisotropic Soft Tissues
title_full_unstemmed The Use of Contravariant Tensors to Model Anisotropic Soft Tissues
title_sort The Use of Contravariant Tensors to Model Anisotropic Soft Tissues
author_id_str_mv 140f4aa5c5ec18ec173c8542a7fddafd
author_id_fullname_str_mv 140f4aa5c5ec18ec173c8542a7fddafd_***_Mokarram Hossain
author Mokarram Hossain
author2 Arthesh Basak
Amirtham Rajagopal
Umesh Basappa
Mokarram Hossain
format Journal article
container_title International Journal of Applied Mechanics
container_volume 13
container_issue 3
container_start_page 2150039
publishDate 2021
institution Swansea University
issn 1758-8251
1758-826X
doi_str_mv 10.1142/s1758825121500393
publisher World Scientific Pub Co Pte Lt
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - General Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - General Engineering
document_store_str 1
active_str 0
description Biological tissues have been shown to behave isotropically at lower strain values, while at higher strains the fibers embedded in the tissue straighten and tend to take up the load. Thus, the anisotropy induced at higher loads can be mathematically modeled by incorporating the strains experienced by the fibers. From histological studies on soft tissues it is evident that for a wide range of tissues the fibers have an oblique mean orientation about the physiological loading directions. Thus, we require a mathematical framework of tensors defined in nonorthogonal basis to capture the direction-dependent response of fibers under high induced loads. In this work, we propose a novel approach to determine the fiber strains with the aid of the contravariant tensors defined in an oblique coordinate system. To determine the fiber strains, we introduce a fourth-order contravariant fiber orientation transformation tensor. The approach helps us successfully in determining the fiber strains, for a family of symmetrically and asymmetrically oriented fibers, with the aid of a single anisotropic invariant. The proposed model was fitted with the experimental data from literature to determine the corresponding material parameters.
published_date 2021-04-30T04:12:00Z
_version_ 1763753821613326336
score 10.9992285

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