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High-performance unsymmetric 8-node hexahedral element in modeling nearly-incompressible soft tissues

Yu-Fei Wang, Song Cen, Chenfeng Li Orcid Logo, Qun Zhang

International Journal of Mechanical Sciences, Volume: 260, Start page: 108647

Swansea University Author: Chenfeng Li Orcid Logo

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DOI (Published version): 10.1016/j.ijmecsci.2023.108647

Abstract

In biomechanics problems, the biological soft tissues are usually treated as anisotropic nearly incompressible hyperelastic materials, but such complicated nonlinear material models often cause challenging problems of severe volumetric locking and instabilities in numerical simulations. In this pape...

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Published in: International Journal of Mechanical Sciences
ISSN: 0020-7403 1879-2162
Published: Elsevier BV 2023
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URI: https://cronfa.swan.ac.uk/Record/cronfa64064
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spelling v2 64064 2023-08-09 High-performance unsymmetric 8-node hexahedral element in modeling nearly-incompressible soft tissues 82fe170d5ae2c840e538a36209e5a3ac 0000-0003-0441-211X Chenfeng Li Chenfeng Li true false 2023-08-09 ACEM In biomechanics problems, the biological soft tissues are usually treated as anisotropic nearly incompressible hyperelastic materials, but such complicated nonlinear material models often cause challenging problems of severe volumetric locking and instabilities in numerical simulations. In this paper, the recent unsymmetric 8-node, 24-DOF hexahedral solid element US-ATFH8 with different test and analytical trial functions (ATFs) is modified for the analysis of the anisotropic nearly-incompressible hyperelastic soft tissues. Unlike the original formulation, the linear analytical general solutions for anisotropic elasticity and the consistent tangent modulus are firstly employed for formulating the trial functions, and are used to construct the incremental displacement fields that result in the incremental deformation gradient. The total deformation gradient is obtained by multiplying the incremental deformation gradient by the deformation gradient, after which the Cauchy stresses can be directly calculated from a total-form constitutive equation relating to the deformation gradient. Numerical tests, including commonly used benchmarks and cardiac examples, demonstrate attractive properties of the proposed finite element formulation in modeling nearly-incompressible anisotropic hyperelastic materials. It is free of various locking and quite insensitive to mesh distortions, and provides high accuracy with faster convergence rates when compared with other existing models. Journal Article International Journal of Mechanical Sciences 260 108647 Elsevier BV 0020-7403 1879-2162 Unsymmetric finite element, Hyperelastic soft tissues, Nearly-incompressible, Finite deformation, Analytical trial functions, Hexahedral element 15 12 2023 2023-12-15 10.1016/j.ijmecsci.2023.108647 http://dx.doi.org/10.1016/j.ijmecsci.2023.108647 COLLEGE NANME Aerospace, Civil, Electrical, and Mechanical Engineering COLLEGE CODE ACEM Swansea University The financial support from the National Natural Science Foundation of China (11872229) is greatly appreciated. 2024-09-04T16:51:57.2199308 2023-08-09T09:54:21.0325856 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Yu-Fei Wang 1 Song Cen 2 Chenfeng Li 0000-0003-0441-211X 3 Qun Zhang 4 64064__28374__1c607d47129342c8aa39b985ccd2a3bd.pdf 64064.pdf 2023-08-24T14:59:10.3173060 Output 1801489 application/pdf Accepted Manuscript true 2024-07-26T00:00:00.0000000 Distributed under the terms of a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). true eng https://creativecommons.org/licenses/by-nc-nd/4.0/
title High-performance unsymmetric 8-node hexahedral element in modeling nearly-incompressible soft tissues
spellingShingle High-performance unsymmetric 8-node hexahedral element in modeling nearly-incompressible soft tissues
Chenfeng Li
title_short High-performance unsymmetric 8-node hexahedral element in modeling nearly-incompressible soft tissues
title_full High-performance unsymmetric 8-node hexahedral element in modeling nearly-incompressible soft tissues
title_fullStr High-performance unsymmetric 8-node hexahedral element in modeling nearly-incompressible soft tissues
title_full_unstemmed High-performance unsymmetric 8-node hexahedral element in modeling nearly-incompressible soft tissues
title_sort High-performance unsymmetric 8-node hexahedral element in modeling nearly-incompressible soft tissues
author_id_str_mv 82fe170d5ae2c840e538a36209e5a3ac
author_id_fullname_str_mv 82fe170d5ae2c840e538a36209e5a3ac_***_Chenfeng Li
author Chenfeng Li
author2 Yu-Fei Wang
Song Cen
Chenfeng Li
Qun Zhang
format Journal article
container_title International Journal of Mechanical Sciences
container_volume 260
container_start_page 108647
publishDate 2023
institution Swansea University
issn 0020-7403
1879-2162
doi_str_mv 10.1016/j.ijmecsci.2023.108647
publisher Elsevier BV
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 - Civil Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering
url http://dx.doi.org/10.1016/j.ijmecsci.2023.108647
document_store_str 1
active_str 0
description In biomechanics problems, the biological soft tissues are usually treated as anisotropic nearly incompressible hyperelastic materials, but such complicated nonlinear material models often cause challenging problems of severe volumetric locking and instabilities in numerical simulations. In this paper, the recent unsymmetric 8-node, 24-DOF hexahedral solid element US-ATFH8 with different test and analytical trial functions (ATFs) is modified for the analysis of the anisotropic nearly-incompressible hyperelastic soft tissues. Unlike the original formulation, the linear analytical general solutions for anisotropic elasticity and the consistent tangent modulus are firstly employed for formulating the trial functions, and are used to construct the incremental displacement fields that result in the incremental deformation gradient. The total deformation gradient is obtained by multiplying the incremental deformation gradient by the deformation gradient, after which the Cauchy stresses can be directly calculated from a total-form constitutive equation relating to the deformation gradient. Numerical tests, including commonly used benchmarks and cardiac examples, demonstrate attractive properties of the proposed finite element formulation in modeling nearly-incompressible anisotropic hyperelastic materials. It is free of various locking and quite insensitive to mesh distortions, and provides high accuracy with faster convergence rates when compared with other existing models.
published_date 2023-12-15T16:51:55Z
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