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Towards biaxial fatigue experiments of elastomers using square and cruciform geometries in planar tension conditions

Ali Esmaeili, Deepak George Orcid Logo, Lewis Tunnicliffe, Ian Masters Orcid Logo, Mokarram Hossain Orcid Logo

Polymer Testing, Volume: 154, Start page: 109060

Swansea University Authors: Ali Esmaeili, Deepak George Orcid Logo, Ian Masters Orcid Logo, Mokarram Hossain Orcid Logo

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DOI (Published version): 10.1016/j.polymertesting.2025.109060

Abstract

Soft materials such as natural rubber, hydrogels, and biological tissues have anisotropic properties and are subject to cyclic biaxial loading during their service lives. This requires biaxial loading rather than uniaxial; however, no agreed standard protocol exists. Therefore, the aim of this study...

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Published in: Polymer Testing
ISSN: 0142-9418
Published: Elsevier BV 2026
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URI: https://cronfa.swan.ac.uk/Record/cronfa71045
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This requires biaxial loading rather than uniaxial; however, no agreed standard protocol exists. Therefore, the aim of this study is to provide preliminary suggestions for reliable and consistent biaxial fatigue tests so that a good degree of biaxiality and efficiency can be thoroughly achieved. Several biaxial loading tests (equi-biaxial and unequal-biaxial) were conducted on natural rubber and ecoflex using different geometries including cruciform and square configurations. Three criteria were defined to evaluate the equi-biaxiality performance: (i) test function related to homogeneous strain distribution in the field of interest, (ii) degree of efficiency corresponding to the ratio of strain in the field of interest (gauge section located in the middle regions) to the maximum strain far from the middle area, and (iii) strain ratio, used for fatigue test. Results showed that cruciform geometry underperformed in equi-biaxiality criteria, i.e., samples possessed high uniaxial strain in the arm whereas the simple square geometry could reach a higher degree of biaxiality and efficiency. The highest equi-biaxiality performance was obtained for the optimized square geometry in such a way that a maximum equi-biaxial strain of 65 % was achieved in the field of interest while possessing a degree of efficiency of 0.66 and strain ratio of 1.96. A successful unequal-biaxial fatigue test of up to two million cycles was conducted on the optimized square specimen made of ecoflex. Finally, a new square configuration with circular cavity in the middle was suggested for future biaxial characterization and standardization of biaxial tests in which the numerical study yielded a degree of efficiency of 1 and strain ration of 2.12 manifesting a considerable improvement in the biaxiality performance.</abstract><type>Journal Article</type><journal>Polymer Testing</journal><volume>154</volume><journalNumber/><paginationStart>109060</paginationStart><paginationEnd/><publisher>Elsevier BV</publisher><placeOfPublication/><isbnPrint/><isbnElectronic/><issnPrint>0142-9418</issnPrint><issnElectronic/><keywords>Natural rubber; Ecoflex; Biaxial test; Fatige test; Digital Image Correlation (DIC)</keywords><publishedDay>1</publishedDay><publishedMonth>1</publishedMonth><publishedYear>2026</publishedYear><publishedDate>2026-01-01</publishedDate><doi>10.1016/j.polymertesting.2025.109060</doi><url/><notes/><college>COLLEGE NANME</college><department>Aerospace, Civil, Electrical, and Mechanical Engineering</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>ACEM</DepartmentCode><institution>Swansea University</institution><apcterm>External research funder(s) paid the OA fee (includes OA grants disbursed by the Library)</apcterm><funders>This study is funded by the Swansea Bay City Deal and the European Regional Development Fund through the Welsh European Funding Office. 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spelling 2025-12-03T11:14:15.1253601 v2 71045 2025-12-02 Towards biaxial fatigue experiments of elastomers using square and cruciform geometries in planar tension conditions 25f6a899c6e8e4fa6f8c3b85f0a27c4d Ali Esmaeili Ali Esmaeili true false de539e0c330ac6d9f2d412d3f2fc0a8a 0009-0001-4598-9364 Deepak George Deepak George true false 6fa19551092853928cde0e6d5fac48a1 0000-0001-7667-6670 Ian Masters Ian Masters true false 140f4aa5c5ec18ec173c8542a7fddafd 0000-0002-4616-1104 Mokarram Hossain Mokarram Hossain true false 2025-12-02 ACEM Soft materials such as natural rubber, hydrogels, and biological tissues have anisotropic properties and are subject to cyclic biaxial loading during their service lives. This requires biaxial loading rather than uniaxial; however, no agreed standard protocol exists. Therefore, the aim of this study is to provide preliminary suggestions for reliable and consistent biaxial fatigue tests so that a good degree of biaxiality and efficiency can be thoroughly achieved. Several biaxial loading tests (equi-biaxial and unequal-biaxial) were conducted on natural rubber and ecoflex using different geometries including cruciform and square configurations. Three criteria were defined to evaluate the equi-biaxiality performance: (i) test function related to homogeneous strain distribution in the field of interest, (ii) degree of efficiency corresponding to the ratio of strain in the field of interest (gauge section located in the middle regions) to the maximum strain far from the middle area, and (iii) strain ratio, used for fatigue test. Results showed that cruciform geometry underperformed in equi-biaxiality criteria, i.e., samples possessed high uniaxial strain in the arm whereas the simple square geometry could reach a higher degree of biaxiality and efficiency. The highest equi-biaxiality performance was obtained for the optimized square geometry in such a way that a maximum equi-biaxial strain of 65 % was achieved in the field of interest while possessing a degree of efficiency of 0.66 and strain ratio of 1.96. A successful unequal-biaxial fatigue test of up to two million cycles was conducted on the optimized square specimen made of ecoflex. Finally, a new square configuration with circular cavity in the middle was suggested for future biaxial characterization and standardization of biaxial tests in which the numerical study yielded a degree of efficiency of 1 and strain ration of 2.12 manifesting a considerable improvement in the biaxiality performance. Journal Article Polymer Testing 154 109060 Elsevier BV 0142-9418 Natural rubber; Ecoflex; Biaxial test; Fatige test; Digital Image Correlation (DIC) 1 1 2026 2026-01-01 10.1016/j.polymertesting.2025.109060 COLLEGE NANME Aerospace, Civil, Electrical, and Mechanical Engineering COLLEGE CODE ACEM Swansea University External research funder(s) paid the OA fee (includes OA grants disbursed by the Library) This study is funded by the Swansea Bay City Deal and the European Regional Development Fund through the Welsh European Funding Office. This study is also supported by EPSRC through the Supergen ORE Hub (EP/S000747/1), who have awarded funding for the Flexible Fund project Submerged biaxial fatigue analysis for Flexible membrane Wave Energy Converters (FF2021-1036). A. Esameili and M. Hossain acknowledge financial support from Birla Carbon, USA to facilitate parts of this study. We would like to thank the access to characterization equipment to Swansea University Advanced Imaging of Materials (AIM) facility, which was funded in part by the EPSRC (EP/M028267/1) and the European Regional Development Fund through the Welsh Government (80708). M. H. also acknowledges the support from the Engineering and Physical Sciences Research Council (EPSRC) under the grant (EP/Z535710/1). 2025-12-03T11:14:15.1253601 2025-12-02T09:20:40.2051640 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering Ali Esmaeili 1 Deepak George 0009-0001-4598-9364 2 Lewis Tunnicliffe 3 Ian Masters 0000-0001-7667-6670 4 Mokarram Hossain 0000-0002-4616-1104 5 71045__35726__12e2037d1d0546dd9bb77d5a39cf10fe.pdf 71045.pdf 2025-12-02T09:28:02.1527066 Output 26398971 application/pdf Version of Record true © 2025 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license. true eng http://creativecommons.org/licenses/by/4.0/
title Towards biaxial fatigue experiments of elastomers using square and cruciform geometries in planar tension conditions
spellingShingle Towards biaxial fatigue experiments of elastomers using square and cruciform geometries in planar tension conditions
Ali Esmaeili
Deepak George
Ian Masters
Mokarram Hossain
title_short Towards biaxial fatigue experiments of elastomers using square and cruciform geometries in planar tension conditions
title_full Towards biaxial fatigue experiments of elastomers using square and cruciform geometries in planar tension conditions
title_fullStr Towards biaxial fatigue experiments of elastomers using square and cruciform geometries in planar tension conditions
title_full_unstemmed Towards biaxial fatigue experiments of elastomers using square and cruciform geometries in planar tension conditions
title_sort Towards biaxial fatigue experiments of elastomers using square and cruciform geometries in planar tension conditions
author_id_str_mv 25f6a899c6e8e4fa6f8c3b85f0a27c4d
de539e0c330ac6d9f2d412d3f2fc0a8a
6fa19551092853928cde0e6d5fac48a1
140f4aa5c5ec18ec173c8542a7fddafd
author_id_fullname_str_mv 25f6a899c6e8e4fa6f8c3b85f0a27c4d_***_Ali Esmaeili
de539e0c330ac6d9f2d412d3f2fc0a8a_***_Deepak George
6fa19551092853928cde0e6d5fac48a1_***_Ian Masters
140f4aa5c5ec18ec173c8542a7fddafd_***_Mokarram Hossain
author Ali Esmaeili
Deepak George
Ian Masters
Mokarram Hossain
author2 Ali Esmaeili
Deepak George
Lewis Tunnicliffe
Ian Masters
Mokarram Hossain
format Journal article
container_title Polymer Testing
container_volume 154
container_start_page 109060
publishDate 2026
institution Swansea University
issn 0142-9418
doi_str_mv 10.1016/j.polymertesting.2025.109060
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 - Mechanical Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering
document_store_str 1
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description Soft materials such as natural rubber, hydrogels, and biological tissues have anisotropic properties and are subject to cyclic biaxial loading during their service lives. This requires biaxial loading rather than uniaxial; however, no agreed standard protocol exists. Therefore, the aim of this study is to provide preliminary suggestions for reliable and consistent biaxial fatigue tests so that a good degree of biaxiality and efficiency can be thoroughly achieved. Several biaxial loading tests (equi-biaxial and unequal-biaxial) were conducted on natural rubber and ecoflex using different geometries including cruciform and square configurations. Three criteria were defined to evaluate the equi-biaxiality performance: (i) test function related to homogeneous strain distribution in the field of interest, (ii) degree of efficiency corresponding to the ratio of strain in the field of interest (gauge section located in the middle regions) to the maximum strain far from the middle area, and (iii) strain ratio, used for fatigue test. Results showed that cruciform geometry underperformed in equi-biaxiality criteria, i.e., samples possessed high uniaxial strain in the arm whereas the simple square geometry could reach a higher degree of biaxiality and efficiency. The highest equi-biaxiality performance was obtained for the optimized square geometry in such a way that a maximum equi-biaxial strain of 65 % was achieved in the field of interest while possessing a degree of efficiency of 0.66 and strain ratio of 1.96. A successful unequal-biaxial fatigue test of up to two million cycles was conducted on the optimized square specimen made of ecoflex. Finally, a new square configuration with circular cavity in the middle was suggested for future biaxial characterization and standardization of biaxial tests in which the numerical study yielded a degree of efficiency of 1 and strain ration of 2.12 manifesting a considerable improvement in the biaxiality performance.
published_date 2026-01-01T05:32:10Z
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