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Hyperelastic finite deformation analysis with the unsymmetric finite element method containing homogeneous solutions of linear elasticity

Zhi Li, Song Cen, Junbin Huang, Chenfeng Li Orcid Logo

International Journal for Numerical Methods in Engineering, Volume: 121, Issue: 16

Swansea University Author: Chenfeng Li Orcid Logo

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DOI (Published version): 10.1002/nme.6378

Abstract

A recent unsymmetric 4‐node, 8‐DOF plane finite element US‐ATFQ4 is generalized to hyperelastic finite deformation analysis. Since the trial functions of US‐ATFQ4 contain the homogenous closed analytical solutions of governing equations for linear elasticity, the key of the proposed strategy is how...

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Published in: International Journal for Numerical Methods in Engineering
ISSN: 0029-5981 1097-0207
Published: Wiley 2020
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URI: https://cronfa.swan.ac.uk/Record/cronfa54435
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spelling 2022-12-07T16:37:43.6657684 v2 54435 2020-06-11 Hyperelastic finite deformation analysis with the unsymmetric finite element method containing homogeneous solutions of linear elasticity 82fe170d5ae2c840e538a36209e5a3ac 0000-0003-0441-211X Chenfeng Li Chenfeng Li true false 2020-06-11 CIVL A recent unsymmetric 4‐node, 8‐DOF plane finite element US‐ATFQ4 is generalized to hyperelastic finite deformation analysis. Since the trial functions of US‐ATFQ4 contain the homogenous closed analytical solutions of governing equations for linear elasticity, the key of the proposed strategy is how to deal with these linear analytical trial functions (ATFs) during the hyperelastic finite deformation analysis. Assuming that the ATFs can properly work in each increment, an algorithm for updating the deformation gradient interpolated by ATFs is designed. Furthermore, the update of the corresponding ATFs referred to current configuration is discussed with regard to the hyperelastic material model, and a specified model, neo‐Hookean model, is employed to verify the present formulation of US‐ATFQ4 for hyperelastic finite deformation analysis. Various examples show that the present formulation not only remain the high accuracy and mesh distortion tolerance in the geometrically nonlinear problems, but also possess excellent performance in the compressible or quasi‐incompressible hyperelastic finite deformation problems where the strain is large. Journal Article International Journal for Numerical Methods in Engineering 121 16 Wiley 0029-5981 1097-0207 24 5 2020 2020-05-24 10.1002/nme.6378 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2022-12-07T16:37:43.6657684 2020-06-11T10:40:03.4157744 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Zhi Li 1 Song Cen 2 Junbin Huang 3 Chenfeng Li 0000-0003-0441-211X 4 54435__17471__03b4f7adbdd34c27b2a6966dc8601288.pdf 54435.pdf 2020-06-11T11:31:40.2154587 Output 465702 application/pdf Accepted Manuscript true 2021-05-15T00:00:00.0000000 © 2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ true
title Hyperelastic finite deformation analysis with the unsymmetric finite element method containing homogeneous solutions of linear elasticity
spellingShingle Hyperelastic finite deformation analysis with the unsymmetric finite element method containing homogeneous solutions of linear elasticity
Chenfeng Li
title_short Hyperelastic finite deformation analysis with the unsymmetric finite element method containing homogeneous solutions of linear elasticity
title_full Hyperelastic finite deformation analysis with the unsymmetric finite element method containing homogeneous solutions of linear elasticity
title_fullStr Hyperelastic finite deformation analysis with the unsymmetric finite element method containing homogeneous solutions of linear elasticity
title_full_unstemmed Hyperelastic finite deformation analysis with the unsymmetric finite element method containing homogeneous solutions of linear elasticity
title_sort Hyperelastic finite deformation analysis with the unsymmetric finite element method containing homogeneous solutions of linear elasticity
author_id_str_mv 82fe170d5ae2c840e538a36209e5a3ac
author_id_fullname_str_mv 82fe170d5ae2c840e538a36209e5a3ac_***_Chenfeng Li
author Chenfeng Li
author2 Zhi Li
Song Cen
Junbin Huang
Chenfeng Li
format Journal article
container_title International Journal for Numerical Methods in Engineering
container_volume 121
container_issue 16
publishDate 2020
institution Swansea University
issn 0029-5981
1097-0207
doi_str_mv 10.1002/nme.6378
publisher Wiley
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
document_store_str 1
active_str 0
description A recent unsymmetric 4‐node, 8‐DOF plane finite element US‐ATFQ4 is generalized to hyperelastic finite deformation analysis. Since the trial functions of US‐ATFQ4 contain the homogenous closed analytical solutions of governing equations for linear elasticity, the key of the proposed strategy is how to deal with these linear analytical trial functions (ATFs) during the hyperelastic finite deformation analysis. Assuming that the ATFs can properly work in each increment, an algorithm for updating the deformation gradient interpolated by ATFs is designed. Furthermore, the update of the corresponding ATFs referred to current configuration is discussed with regard to the hyperelastic material model, and a specified model, neo‐Hookean model, is employed to verify the present formulation of US‐ATFQ4 for hyperelastic finite deformation analysis. Various examples show that the present formulation not only remain the high accuracy and mesh distortion tolerance in the geometrically nonlinear problems, but also possess excellent performance in the compressible or quasi‐incompressible hyperelastic finite deformation problems where the strain is large.
published_date 2020-05-24T04:07:58Z
_version_ 1763753568574111744
score 11.013082

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