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Phase field fracture in elasto-plastic solids: Numerical implementation and application to transversely isotropic fiber-reinforced composites

Jiajun Zhang, Jialu Guo, Chencheng Feng, Jing Wang Orcid Logo, Yang Zhang Orcid Logo, Adesola Ademiloye Orcid Logo

Applied Mathematical Modelling, Volume: 156, Start page: 116769

Swansea University Author: Adesola Ademiloye Orcid Logo

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DOI (Published version): 10.1016/j.apm.2026.116769

Abstract

Due to their superior tensile properties, fiber-reinforced composite (FRC) structures have been widely applied in modern industries. This study employs phase field modeling to simulate the process of elastic-plastic fracture in FRC structures. In this study, we first establish a constitutive model f...

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Published in: Applied Mathematical Modelling
ISSN: 0307-904X
Published: Elsevier BV 2026
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URI: https://cronfa.swan.ac.uk/Record/cronfa71267
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In this study, we first establish a constitutive model for elastoplastic solids and a phase field model for fracture in solid materials. By employing the Newton-Raphson iterative method, the displacement field and phase field are solved separately based on an alternating iterative scheme.Subsequently, we presented three numerical examples to demonstrate the robustness and accuracy of the proposed model. First, we simulated the elastoplastic fracture response of isotropic materials and validate the accuracy of the elastoplastic fracture phase field model. Next, we examined the tensile and fracture behaviors of unidirectional fiber reinforced composite plate with a central circular hole and varying fiber angles. Finally, the influence of curved fiber on the unilateral tensile fracture of FRC plates was investigated. Considering the pronounced heterogeneity between fibers and matrix materials,this study assumes that the fibers remain in the linear elastic regime and introduces a yield function to describe the matrix behavior. Our computational results demonstrate that the accuracy and robustness of the proposed model for predicting the elastoplastic fracture response of FRC structures. 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spelling 2026-02-11T10:35:44.5580845 v2 71267 2026-01-19 Phase field fracture in elasto-plastic solids: Numerical implementation and application to transversely isotropic fiber-reinforced composites e37960ed89a7e3eaeba2201762626594 0000-0002-9741-6488 Adesola Ademiloye Adesola Ademiloye true false 2026-01-19 EAAS Due to their superior tensile properties, fiber-reinforced composite (FRC) structures have been widely applied in modern industries. This study employs phase field modeling to simulate the process of elastic-plastic fracture in FRC structures. In this study, we first establish a constitutive model for elastoplastic solids and a phase field model for fracture in solid materials. By employing the Newton-Raphson iterative method, the displacement field and phase field are solved separately based on an alternating iterative scheme.Subsequently, we presented three numerical examples to demonstrate the robustness and accuracy of the proposed model. First, we simulated the elastoplastic fracture response of isotropic materials and validate the accuracy of the elastoplastic fracture phase field model. Next, we examined the tensile and fracture behaviors of unidirectional fiber reinforced composite plate with a central circular hole and varying fiber angles. Finally, the influence of curved fiber on the unilateral tensile fracture of FRC plates was investigated. Considering the pronounced heterogeneity between fibers and matrix materials,this study assumes that the fibers remain in the linear elastic regime and introduces a yield function to describe the matrix behavior. Our computational results demonstrate that the accuracy and robustness of the proposed model for predicting the elastoplastic fracture response of FRC structures. Furthermore, we observed that in comparison to the elastic phase field fracture model, the occurrence of fracture is delayed when an elastoplastic phase model is employed due to the complex interactions between the plastic dissipation energy and the fracture energy. Journal Article Applied Mathematical Modelling 156 116769 Elsevier BV 0307-904X Elastoplastic Fracture, Fiber-Reinforced Composites, Transversely Isotropic, Phase Field Modeling, Crack 1 8 2026 2026-08-01 10.1016/j.apm.2026.116769 COLLEGE NANME Engineering and Applied Sciences School COLLEGE CODE EAAS Swansea University Not Required NSFC, Royal Society - International Exchange Grant 12272182, IES\NSFC\223217 2026-02-11T10:35:44.5580845 2026-01-19T10:22:39.4042177 Faculty of Science and Engineering School of Engineering and Applied Sciences - Biomedical Engineering Jiajun Zhang 1 Jialu Guo 2 Chencheng Feng 3 Jing Wang 0000-0001-9735-6641 4 Yang Zhang 0000-0003-0725-7274 5 Adesola Ademiloye 0000-0002-9741-6488 6 71267__36096__2e955527c618433ea1256fc3ecc7bf6b.pdf AS_Ademiloye_Accepted manuscript_Phase field_2026.pdf 2026-01-25T07:15:27.0470055 Output 8040036 application/pdf Accepted Manuscript true Author accepted manuscript document released under the terms of a Creative Commons CC-BY licence using the Swansea University Research Publications Policy (rights retention). true eng https://creativecommons.org/licenses/by/4.0/deed.en
title Phase field fracture in elasto-plastic solids: Numerical implementation and application to transversely isotropic fiber-reinforced composites
spellingShingle Phase field fracture in elasto-plastic solids: Numerical implementation and application to transversely isotropic fiber-reinforced composites
Adesola Ademiloye
title_short Phase field fracture in elasto-plastic solids: Numerical implementation and application to transversely isotropic fiber-reinforced composites
title_full Phase field fracture in elasto-plastic solids: Numerical implementation and application to transversely isotropic fiber-reinforced composites
title_fullStr Phase field fracture in elasto-plastic solids: Numerical implementation and application to transversely isotropic fiber-reinforced composites
title_full_unstemmed Phase field fracture in elasto-plastic solids: Numerical implementation and application to transversely isotropic fiber-reinforced composites
title_sort Phase field fracture in elasto-plastic solids: Numerical implementation and application to transversely isotropic fiber-reinforced composites
author_id_str_mv e37960ed89a7e3eaeba2201762626594
author_id_fullname_str_mv e37960ed89a7e3eaeba2201762626594_***_Adesola Ademiloye
author Adesola Ademiloye
author2 Jiajun Zhang
Jialu Guo
Chencheng Feng
Jing Wang
Yang Zhang
Adesola Ademiloye
format Journal article
container_title Applied Mathematical Modelling
container_volume 156
container_start_page 116769
publishDate 2026
institution Swansea University
issn 0307-904X
doi_str_mv 10.1016/j.apm.2026.116769
publisher Elsevier BV
college_str Faculty of Science and Engineering
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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 - Biomedical Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Biomedical Engineering
document_store_str 1
active_str 0
description Due to their superior tensile properties, fiber-reinforced composite (FRC) structures have been widely applied in modern industries. This study employs phase field modeling to simulate the process of elastic-plastic fracture in FRC structures. In this study, we first establish a constitutive model for elastoplastic solids and a phase field model for fracture in solid materials. By employing the Newton-Raphson iterative method, the displacement field and phase field are solved separately based on an alternating iterative scheme.Subsequently, we presented three numerical examples to demonstrate the robustness and accuracy of the proposed model. First, we simulated the elastoplastic fracture response of isotropic materials and validate the accuracy of the elastoplastic fracture phase field model. Next, we examined the tensile and fracture behaviors of unidirectional fiber reinforced composite plate with a central circular hole and varying fiber angles. Finally, the influence of curved fiber on the unilateral tensile fracture of FRC plates was investigated. Considering the pronounced heterogeneity between fibers and matrix materials,this study assumes that the fibers remain in the linear elastic regime and introduces a yield function to describe the matrix behavior. Our computational results demonstrate that the accuracy and robustness of the proposed model for predicting the elastoplastic fracture response of FRC structures. Furthermore, we observed that in comparison to the elastic phase field fracture model, the occurrence of fracture is delayed when an elastoplastic phase model is employed due to the complex interactions between the plastic dissipation energy and the fracture energy.
published_date 2026-08-01T05:34:53Z
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