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On improving the numerical convergence of highly nonlinear elasticity problems

Yue Mei, Daniel E. Hurtado, Sanjay Pant Orcid Logo, Ankush Aggarwal Orcid Logo

Computer Methods in Applied Mechanics and Engineering, Volume: 337, Pages: 110 - 127

Swansea University Authors: Sanjay Pant Orcid Logo, Ankush Aggarwal Orcid Logo

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DOI (Published version): 10.1016/j.cma.2018.03.033

Abstract

Finite elasticity problems commonly include material and geometric nonlinearities and are solved using various numerical methods. However, for highly nonlinear problems, achieving convergence is relatively difficult and requires small load step sizes. In this work, we present a new method to transfo...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 0045-7825
Published: 2018
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa39195
first_indexed 2018-03-26T13:31:38Z
last_indexed 2023-02-15T03:48:15Z
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spelling 2023-02-14T15:23:40.3177306 v2 39195 2018-03-26 On improving the numerical convergence of highly nonlinear elasticity problems 43b388e955511a9d1b86b863c2018a9f 0000-0002-2081-308X Sanjay Pant Sanjay Pant true false 33985d0c2586398180c197dc170d7d19 0000-0002-1755-8807 Ankush Aggarwal Ankush Aggarwal true false 2018-03-26 ACEM Finite elasticity problems commonly include material and geometric nonlinearities and are solved using various numerical methods. However, for highly nonlinear problems, achieving convergence is relatively difficult and requires small load step sizes. In this work, we present a new method to transform the discretized governing equations so that the transformed problem has significantly reduced nonlinearity and, therefore, Newton solvers exhibit improved convergence properties. We study exponential-type nonlinearity in soft tissues and geometric nonlinearity in compression, and propose novel formulations for the two problems. We test the new formulations in several numerical examples and show significant reduction in iterations required for convergence, especially at large load steps. Notably, the proposed formulation is capable of yielding convergent solution even when 10–100 times larger load steps are applied. The proposed framework is generic and can be applied to other types of nonlinearities as well. Journal Article Computer Methods in Applied Mechanics and Engineering 337 110 127 0045-7825 Nonlinear elasticity, Newton’s method, Nonlinear preconditioning, Compression, Soft tissues, Solver convergence 1 8 2018 2018-08-01 10.1016/j.cma.2018.03.033 http://dx.doi.org/10.1016/j.cma.2018.03.033 COLLEGE NANME Aerospace, Civil, Electrical, and Mechanical Engineering COLLEGE CODE ACEM Swansea University 2023-02-14T15:23:40.3177306 2018-03-26T09:02:22.8045999 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering Yue Mei 1 Daniel E. Hurtado 2 Sanjay Pant 0000-0002-2081-308X 3 Ankush Aggarwal 0000-0002-1755-8807 4 0039195-26032018090450.pdf mei2018.pdf 2018-03-26T09:04:50.7100000 Output 4524829 application/pdf Accepted Manuscript true 2019-03-30T00:00:00.0000000 Distributed under the terms of a Creative Commons CC-BY-NC-ND licence. true eng
title On improving the numerical convergence of highly nonlinear elasticity problems
spellingShingle On improving the numerical convergence of highly nonlinear elasticity problems
Sanjay Pant
Ankush Aggarwal
title_short On improving the numerical convergence of highly nonlinear elasticity problems
title_full On improving the numerical convergence of highly nonlinear elasticity problems
title_fullStr On improving the numerical convergence of highly nonlinear elasticity problems
title_full_unstemmed On improving the numerical convergence of highly nonlinear elasticity problems
title_sort On improving the numerical convergence of highly nonlinear elasticity problems
author_id_str_mv 43b388e955511a9d1b86b863c2018a9f
33985d0c2586398180c197dc170d7d19
author_id_fullname_str_mv 43b388e955511a9d1b86b863c2018a9f_***_Sanjay Pant
33985d0c2586398180c197dc170d7d19_***_Ankush Aggarwal
author Sanjay Pant
Ankush Aggarwal
author2 Yue Mei
Daniel E. Hurtado
Sanjay Pant
Ankush Aggarwal
format Journal article
container_title Computer Methods in Applied Mechanics and Engineering
container_volume 337
container_start_page 110
publishDate 2018
institution Swansea University
issn 0045-7825
doi_str_mv 10.1016/j.cma.2018.03.033
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 - Mechanical Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering
url http://dx.doi.org/10.1016/j.cma.2018.03.033
document_store_str 1
active_str 0
description Finite elasticity problems commonly include material and geometric nonlinearities and are solved using various numerical methods. However, for highly nonlinear problems, achieving convergence is relatively difficult and requires small load step sizes. In this work, we present a new method to transform the discretized governing equations so that the transformed problem has significantly reduced nonlinearity and, therefore, Newton solvers exhibit improved convergence properties. We study exponential-type nonlinearity in soft tissues and geometric nonlinearity in compression, and propose novel formulations for the two problems. We test the new formulations in several numerical examples and show significant reduction in iterations required for convergence, especially at large load steps. Notably, the proposed formulation is capable of yielding convergent solution even when 10–100 times larger load steps are applied. The proposed framework is generic and can be applied to other types of nonlinearities as well.
published_date 2018-08-01T08:33:36Z
_version_ 1830268454205128704
score 11.060683

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