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A phase field formulation for modelling fracture of nearly incompressible hyperelastic materials

DEEPAK GEORGE, Shabnam Konica, Ian Masters Orcid Logo, Mokarram Hossain Orcid Logo

Computer Methods in Applied Mechanics and Engineering, Volume: 436, Start page: 117696

Swansea University Authors: DEEPAK GEORGE, Ian Masters Orcid Logo, Mokarram Hossain Orcid Logo

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DOI (Published version): 10.1016/j.cma.2024.117696

Abstract

Flexible materials are integral to modern applications due to their unique properties, particularly their ability to stretch and resilience to fracture. However, predicting the fracture behaviour of these materials through simulations remains challenging, primarily due to the lack of numerical robus...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 0045-7825 1879-2138
Published: Elsevier BV 2025
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However, predicting the fracture behaviour of these materials through simulations remains challenging, primarily due to the lack of numerical robustness. This study proposes a rate-independent phase field model to predict finite strain fracture in nearly incompressible hyperelastic materials. A Griffith-type criterion is used to predict the fracture behaviour, with a relaxation of the incompressibility constraint in damaged elements, thus allowing crack propagation without affecting the intact material. A novel mixed formulation is developed using a quadratic dissipation function originally proposed by Ambrosio and Tortorelli (AT2) for the phase field method, incorporating two history fields to prevent crack healing. Spatial discretisation is achieved using linear approximations for the displacement and damage fields, whereas the pressure field is treated as discontinuous across the element boundaries (Q1Q0Q1 elements). The numerical algorithm is implemented within a finite element framework using a user-defined element (UEL) subroutine in ABAQUS, with a monolithic solver based on the Broyden&#x2013;Fletcher&#x2013;Goldfarb&#x2013;Shanno (BFGS) technique to solve the global problem. Numerical trials confirmed that this is a robust algorithm that avoids excessive distortion of damaged elements, eliminating the need for adaptive meshing and distorted mesh deletion techniques. The algorithm is tested using three examples and is compared with experimental data. Reproduction of load&#x2013;displacement behaviour and crack paths confirm the effectiveness of the method. The results indicate that the approach effectively predicts the fracture behaviour of nearly incompressible materials under large stretch conditions while maintaining numerical robustness. Additionally, the method successfully predicts multiple crack initiations, propagation paths, and their merging, consistent with various experimental observations. 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spelling 2025-01-08T13:44:37.5416686 v2 68653 2025-01-06 A phase field formulation for modelling fracture of nearly incompressible hyperelastic materials 6170d801808f720f6e3a16eab4fc2ea7 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 2025-01-06 Flexible materials are integral to modern applications due to their unique properties, particularly their ability to stretch and resilience to fracture. However, predicting the fracture behaviour of these materials through simulations remains challenging, primarily due to the lack of numerical robustness. This study proposes a rate-independent phase field model to predict finite strain fracture in nearly incompressible hyperelastic materials. A Griffith-type criterion is used to predict the fracture behaviour, with a relaxation of the incompressibility constraint in damaged elements, thus allowing crack propagation without affecting the intact material. A novel mixed formulation is developed using a quadratic dissipation function originally proposed by Ambrosio and Tortorelli (AT2) for the phase field method, incorporating two history fields to prevent crack healing. Spatial discretisation is achieved using linear approximations for the displacement and damage fields, whereas the pressure field is treated as discontinuous across the element boundaries (Q1Q0Q1 elements). The numerical algorithm is implemented within a finite element framework using a user-defined element (UEL) subroutine in ABAQUS, with a monolithic solver based on the Broyden–Fletcher–Goldfarb–Shanno (BFGS) technique to solve the global problem. Numerical trials confirmed that this is a robust algorithm that avoids excessive distortion of damaged elements, eliminating the need for adaptive meshing and distorted mesh deletion techniques. The algorithm is tested using three examples and is compared with experimental data. Reproduction of load–displacement behaviour and crack paths confirm the effectiveness of the method. The results indicate that the approach effectively predicts the fracture behaviour of nearly incompressible materials under large stretch conditions while maintaining numerical robustness. Additionally, the method successfully predicts multiple crack initiations, propagation paths, and their merging, consistent with various experimental observations. Consequently, this robust numerical scheme, involving 3D finite elements, can be readily applied to simulate various devices made of rubber-like materials, facilitating faster optimal design development and offers a promising alternative to multiple experiments and prototype testings resulting in a significant cost reduction. Journal Article Computer Methods in Applied Mechanics and Engineering 436 117696 Elsevier BV 0045-7825 1879-2138 Phase field modelling; Mixed formulation; Finite strain fracture; Hyperelastic material; Incompressibility 1 3 2025 2025-03-01 10.1016/j.cma.2024.117696 COLLEGE NANME COLLEGE CODE Swansea University SU Library paid the OA fee (TA Institutional Deal) This work was supported by the MEECE project funded by the European Regional Development Fund and the UK & Welsh governments through the Swansea Bay City Deal. 2025-01-08T13:44:37.5416686 2025-01-06T09:36:46.9962039 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering DEEPAK GEORGE 1 Shabnam Konica 2 Ian Masters 0000-0001-7667-6670 3 Mokarram Hossain 0000-0002-4616-1104 4 68653__33246__4372f484a0564a61941a80f5beb933dc.pdf 68653.VOR.pdf 2025-01-06T09:43:52.8135136 Output 4337448 application/pdf Version of Record true © 2024 The Authors. This is an open access article distributed under the terms of the Creative Commons CC-BY license. true eng http://creativecommons.org/licenses/by/4.0/
title A phase field formulation for modelling fracture of nearly incompressible hyperelastic materials
spellingShingle A phase field formulation for modelling fracture of nearly incompressible hyperelastic materials
DEEPAK GEORGE
Ian Masters
Mokarram Hossain
title_short A phase field formulation for modelling fracture of nearly incompressible hyperelastic materials
title_full A phase field formulation for modelling fracture of nearly incompressible hyperelastic materials
title_fullStr A phase field formulation for modelling fracture of nearly incompressible hyperelastic materials
title_full_unstemmed A phase field formulation for modelling fracture of nearly incompressible hyperelastic materials
title_sort A phase field formulation for modelling fracture of nearly incompressible hyperelastic materials
author_id_str_mv 6170d801808f720f6e3a16eab4fc2ea7
6fa19551092853928cde0e6d5fac48a1
140f4aa5c5ec18ec173c8542a7fddafd
author_id_fullname_str_mv 6170d801808f720f6e3a16eab4fc2ea7_***_DEEPAK GEORGE
6fa19551092853928cde0e6d5fac48a1_***_Ian Masters
140f4aa5c5ec18ec173c8542a7fddafd_***_Mokarram Hossain
author DEEPAK GEORGE
Ian Masters
Mokarram Hossain
author2 DEEPAK GEORGE
Shabnam Konica
Ian Masters
Mokarram Hossain
format Journal article
container_title Computer Methods in Applied Mechanics and Engineering
container_volume 436
container_start_page 117696
publishDate 2025
institution Swansea University
issn 0045-7825
1879-2138
doi_str_mv 10.1016/j.cma.2024.117696
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 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 Flexible materials are integral to modern applications due to their unique properties, particularly their ability to stretch and resilience to fracture. However, predicting the fracture behaviour of these materials through simulations remains challenging, primarily due to the lack of numerical robustness. This study proposes a rate-independent phase field model to predict finite strain fracture in nearly incompressible hyperelastic materials. A Griffith-type criterion is used to predict the fracture behaviour, with a relaxation of the incompressibility constraint in damaged elements, thus allowing crack propagation without affecting the intact material. A novel mixed formulation is developed using a quadratic dissipation function originally proposed by Ambrosio and Tortorelli (AT2) for the phase field method, incorporating two history fields to prevent crack healing. Spatial discretisation is achieved using linear approximations for the displacement and damage fields, whereas the pressure field is treated as discontinuous across the element boundaries (Q1Q0Q1 elements). The numerical algorithm is implemented within a finite element framework using a user-defined element (UEL) subroutine in ABAQUS, with a monolithic solver based on the Broyden–Fletcher–Goldfarb–Shanno (BFGS) technique to solve the global problem. Numerical trials confirmed that this is a robust algorithm that avoids excessive distortion of damaged elements, eliminating the need for adaptive meshing and distorted mesh deletion techniques. The algorithm is tested using three examples and is compared with experimental data. Reproduction of load–displacement behaviour and crack paths confirm the effectiveness of the method. The results indicate that the approach effectively predicts the fracture behaviour of nearly incompressible materials under large stretch conditions while maintaining numerical robustness. Additionally, the method successfully predicts multiple crack initiations, propagation paths, and their merging, consistent with various experimental observations. Consequently, this robust numerical scheme, involving 3D finite elements, can be readily applied to simulate various devices made of rubber-like materials, facilitating faster optimal design development and offers a promising alternative to multiple experiments and prototype testings resulting in a significant cost reduction.
published_date 2025-03-01T08:18:31Z
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