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Mathematics
Volume 13
Issue 11
10.3390/math13111742
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Efficient Phase-Field Modeling of Quasi-Static and Dynamic Crack Propagation Under Mechanical and Thermal Loadings

by
Lotfi Ben Said
1,*,
Hamdi Hentati
2,3,
Mohamed Turki
4,
Alaa Chabir
4,
Sattam Alharbi
1 and
Mohamed Haddar
2
1
Department of Mechanical Engineering, College of Engineering, University of Ha’il, Ha’il City 81451, Saudi Arabia
2
Laboratory of Mechanics Modeling and Production, National Engineering School of Sfax, University of Sfax, Sfax 3038, Tunisia
3
Higher School of Sciences and Technologies of Hammam Sousse, University of Sousse, Soussse 4023, Tunisia
4
College of Computer Science and Engineering, University of Ha’il, Ha’il City 81451, Saudi Arabia
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(11), 1742; https://doi.org/10.3390/math13111742 (registering DOI)
Submission received: 28 April 2025 / Revised: 18 May 2025 / Accepted: 22 May 2025 / Published: 24 May 2025
(This article belongs to the Special Issue Scientific Computing for Phase-Field Models)
Versions Notes

Abstract

The main objective of this work was to model the failure mechanisms of brittle materials subjected to thermal and mechanical loads. A diffusive representation of the crack topology provides the basis for the regularized kinematic framework used. With a smooth transition from the undamaged to the fully damaged state, the fracture surface was roughly represented as a diffusive field. By integrating a staggered scheme and spectral decomposition, the variational formulation was used after being mathematically written and developed. Its effectiveness was analyzed using extensive benchmark tests, demonstrating the effectiveness of the phase-field model in modeling the behavior of brittle materials. This proposed approach was experimentally tested through the examination of crack propagation paths in brittle materials that were subjected to variable mechanical and thermal loads. This work focused on the integration of a spectral decomposition-based phase-field model with thermo-mechanical coupling for dynamic fracture, supported by benchmark validation and the comparative assessment of energy decomposition strategies. The results highlight the accuracy and robustness of numerical and experimental methodologies proposed to model fracture mechanics in brittle materials subjected to complex loading conditions.
Keywords: phase-field; dynamic; quasi-static; failure; crack; thermal loading phase-field; dynamic; quasi-static; failure; crack; thermal loading

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MDPI and ACS Style

Ben Said, L.; Hentati, H.; Turki, M.; Chabir, A.; Alharbi, S.; Haddar, M. Efficient Phase-Field Modeling of Quasi-Static and Dynamic Crack Propagation Under Mechanical and Thermal Loadings. Mathematics 2025, 13, 1742. https://doi.org/10.3390/math13111742

AMA Style

Ben Said L, Hentati H, Turki M, Chabir A, Alharbi S, Haddar M. Efficient Phase-Field Modeling of Quasi-Static and Dynamic Crack Propagation Under Mechanical and Thermal Loadings. Mathematics. 2025; 13(11):1742. https://doi.org/10.3390/math13111742

Chicago/Turabian Style

Ben Said, Lotfi, Hamdi Hentati, Mohamed Turki, Alaa Chabir, Sattam Alharbi, and Mohamed Haddar. 2025. "Efficient Phase-Field Modeling of Quasi-Static and Dynamic Crack Propagation Under Mechanical and Thermal Loadings" Mathematics 13, no. 11: 1742. https://doi.org/10.3390/math13111742

APA Style

Ben Said, L., Hentati, H., Turki, M., Chabir, A., Alharbi, S., & Haddar, M. (2025). Efficient Phase-Field Modeling of Quasi-Static and Dynamic Crack Propagation Under Mechanical and Thermal Loadings. Mathematics, 13(11), 1742. https://doi.org/10.3390/math13111742

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