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On the advantages of mixed formulation and higher-order elements for computational morphoelasticity

Chennakesava Kadapa Orcid Logo, Zhanfeng Li, Mokarram Hossain Orcid Logo, Jiong Wang

Journal of the Mechanics and Physics of Solids, Volume: 148, Start page: 104289

Swansea University Authors: Chennakesava Kadapa Orcid Logo, Mokarram Hossain Orcid Logo

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DOI (Published version): 10.1016/j.jmps.2020.104289

Abstract

In this paper, we present a mixed displacement–pressure finite element formulation that can successively model compressible as well as truly incompressible behaviour in growth-induced deformations significantly observed in soft materials. Inf–sup stable elements of various shapes based on quadratic...

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Published in: Journal of the Mechanics and Physics of Solids
ISSN: 0022-5096
Published: Elsevier BV 2021
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URI: https://cronfa.swan.ac.uk/Record/cronfa55967
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spelling 2021-02-03T13:04:19.0858984 v2 55967 2021-01-05 On the advantages of mixed formulation and higher-order elements for computational morphoelasticity de01927f8c2c4ad9dcc034c327ac8de1 0000-0001-6092-9047 Chennakesava Kadapa Chennakesava Kadapa true false 140f4aa5c5ec18ec173c8542a7fddafd 0000-0002-4616-1104 Mokarram Hossain Mokarram Hossain true false 2021-01-05 SCS In this paper, we present a mixed displacement–pressure finite element formulation that can successively model compressible as well as truly incompressible behaviour in growth-induced deformations significantly observed in soft materials. Inf–sup stable elements of various shapes based on quadratic Bézier elements are employed for spatial discretisation. At first, the capability of the proposed framework to accurately model finite-strain growth-induced deformations is illustrated using several examples of plate models in which numerical results are directly compared with analytical solutions. The framework is also compared with the classical Q1/P0 finite element that has been used extensively for simulating the deformation behaviour of soft materials using the quasi-incompressibility assumption. The comparisons clearly demonstrate the superior capabilities of the proposed framework. Later, the effect of hyperelastic constitute models and compressibility on the growth-induced deformation is also studied using the example of a bilayered strip in three dimensions. Finally, the potential of the proposed finite element framework to simulate growth-induced deformations in complex three-dimensional problems is illustrated using the models of flower petals, morphoelastic rods, and thin cylindrical tubes. Journal Article Journal of the Mechanics and Physics of Solids 148 104289 Elsevier BV 0022-5096 Growth-induced deformations, Finite element analysis, Mixed formulation, Hyperelasticity, Morphoelasticity 1 3 2021 2021-03-01 10.1016/j.jmps.2020.104289 COLLEGE NANME Computer Science COLLEGE CODE SCS Swansea University 2021-02-03T13:04:19.0858984 2021-01-05T15:54:26.0456802 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Chennakesava Kadapa 0000-0001-6092-9047 1 Zhanfeng Li 2 Mokarram Hossain 0000-0002-4616-1104 3 Jiong Wang 4 55967__18976__89f3bfb378e74d768a04d921adc8915e.pdf 55967.pdf 2021-01-05T15:58:34.3250427 Output 3917106 application/pdf Accepted Manuscript true 2021-12-29T00:00:00.0000000 ©2020 All rights reserved. All article content, except where otherwise noted, is licensed under a Creative Commons Attribution Non-Commercial No Derivatives License (CC-BY-NC-ND) true eng http://creativecommons.org/licenses/by-nc-nd/4.0/
title On the advantages of mixed formulation and higher-order elements for computational morphoelasticity
spellingShingle On the advantages of mixed formulation and higher-order elements for computational morphoelasticity
Chennakesava Kadapa
Mokarram Hossain
title_short On the advantages of mixed formulation and higher-order elements for computational morphoelasticity
title_full On the advantages of mixed formulation and higher-order elements for computational morphoelasticity
title_fullStr On the advantages of mixed formulation and higher-order elements for computational morphoelasticity
title_full_unstemmed On the advantages of mixed formulation and higher-order elements for computational morphoelasticity
title_sort On the advantages of mixed formulation and higher-order elements for computational morphoelasticity
author_id_str_mv de01927f8c2c4ad9dcc034c327ac8de1
140f4aa5c5ec18ec173c8542a7fddafd
author_id_fullname_str_mv de01927f8c2c4ad9dcc034c327ac8de1_***_Chennakesava Kadapa
140f4aa5c5ec18ec173c8542a7fddafd_***_Mokarram Hossain
author Chennakesava Kadapa
Mokarram Hossain
author2 Chennakesava Kadapa
Zhanfeng Li
Mokarram Hossain
Jiong Wang
format Journal article
container_title Journal of the Mechanics and Physics of Solids
container_volume 148
container_start_page 104289
publishDate 2021
institution Swansea University
issn 0022-5096
doi_str_mv 10.1016/j.jmps.2020.104289
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 Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
document_store_str 1
active_str 0
description In this paper, we present a mixed displacement–pressure finite element formulation that can successively model compressible as well as truly incompressible behaviour in growth-induced deformations significantly observed in soft materials. Inf–sup stable elements of various shapes based on quadratic Bézier elements are employed for spatial discretisation. At first, the capability of the proposed framework to accurately model finite-strain growth-induced deformations is illustrated using several examples of plate models in which numerical results are directly compared with analytical solutions. The framework is also compared with the classical Q1/P0 finite element that has been used extensively for simulating the deformation behaviour of soft materials using the quasi-incompressibility assumption. The comparisons clearly demonstrate the superior capabilities of the proposed framework. Later, the effect of hyperelastic constitute models and compressibility on the growth-induced deformation is also studied using the example of a bilayered strip in three dimensions. Finally, the potential of the proposed finite element framework to simulate growth-induced deformations in complex three-dimensional problems is illustrated using the models of flower petals, morphoelastic rods, and thin cylindrical tubes.
published_date 2021-03-01T04:10:34Z
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score 11.012678

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