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Journal articles on the topic 'Phase field modeling of brittle fracture'

Author: Grafiati

Published: 1 June 2024

Last updated: 31 July 2025

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1

Li, Haifeng, Wei Wang, Yajun Cao, and Shifan Liu. "Phase-Field Modeling Fracture in Anisotropic Materials." Advances in Civil Engineering 2021 (July 30, 2021): 1–13. http://dx.doi.org/10.1155/2021/4313755.

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The phase-field method is a widely used technique to simulate crack initiation, propagation, and coalescence without the need to trace the fracture surface. In the phase-field theory, the energy to create a fracture surface per unit area is equal to the critical energy release rate. Therefore, the precise definition of the crack-driving part is the key to simulate crack propagation. In this work, we propose a modified phase-field model to capture the complex crack propagation, in which the elastic strain energy is decomposed into volumetric-deviatoric energy parts. Because of the volumetric-de

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2

Ulmer, Heike, Martina Hofacker, and Christian Miehe. "Phase Field Modeling of Brittle and Ductile Fracture." PAMM 13, no. 1 (2013): 533–36. http://dx.doi.org/10.1002/pamm.201310258.

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3

Seleš, Karlo, Tomislav Lesičar, Zdenko Tonković, and Jurica Sorić. "A Phase Field Staggered Algorithm for Fracture Modeling in Heterogeneous Microstructure." Key Engineering Materials 774 (August 2018): 632–37. http://dx.doi.org/10.4028/www.scientific.net/kem.774.632.

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The phase field approach to fracture modelling is based on a variational principle of the energy minimization as an extension of the Griffith’s brittle fracture theory. It introduces a scalar damage field, to differentiate between the fractured and intact material state. That way, it regularizes the sharp crack discontinuities and eliminates the need for the explicit tracking of the fracture surfaces. Moreover, the numerical implementation complexity is thus vastly reduced. In this contribution, the staggered phase field algorithm for the modelling of brittle fracture is implemented within the

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4

Ulloa, Jacinto, Patricio Rodríguez, Cristóbal Samaniego, and Esteban Samaniego. "Phase-field modeling of fracture for quasi-brittle materials." Underground Space 4, no. 1 (2019): 10–21. http://dx.doi.org/10.1016/j.undsp.2018.08.002.

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5

Teichtmeister, S., D. Kienle, F. Aldakheel, and M. A. Keip. "Phase field modeling of fracture in anisotropic brittle solids." International Journal of Non-Linear Mechanics 97 (December 2017): 1–21. http://dx.doi.org/10.1016/j.ijnonlinmec.2017.06.018.

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6

Hou, Yue, Fengyan Sun, Wenjuan Sun, Meng Guo, Chao Xing, and Jiangfeng Wu. "Quasi-Brittle Fracture Modeling of Preflawed Bitumen Using a Diffuse Interface Model." Advances in Materials Science and Engineering 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/8751646.

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Fundamental understandings on the bitumen fracture mechanism are vital to improve the mixture design of asphalt concrete. In this paper, a diffuse interface model, namely, phase-field method is used for modeling the quasi-brittle fracture in bitumen. This method describes the microstructure using a phase-field variable which assumes one in the intact solid and negative one in the crack region. Only the elastic energy will directly contribute to cracking. To account for the growth of cracks, a nonconserved Allen-Cahn equation is adopted to evolve the phase-field variable. Numerical simulations

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7

Santillan Sanchez, David, Hichem Mazighi, and Mustapha Kamel Mihoubi. "Hybrid phase-field modeling of multi-level concrete gravity dam notched cracks." Frattura ed Integrità Strutturale 16, no. 61 (2022): 154–75. http://dx.doi.org/10.3221/igf-esis.61.11.

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Phase-field models have become a powerful tool to simulate crack propagation. They regularize the fracture discontinuity and smooth the transition between the intact and the damaged regions. Based on the thermodynamic function and a diffusive field, they regularize the variational approach to fracture that generalizes Grifﬁth’s theory for brittle fracture. Phase-field models are capable to simulate complex fracture patterns efficiently and straightforwardly. In this paper, we introduce a hybrid phase-ﬁeld approach to simulate the crack propagation in laboratory-scale and life-scale structures.

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8

Wu, Chi, Jianguang Fang, Zhongpu Zhang, et al. "Fracture modeling of brittle biomaterials by the phase-field method." Engineering Fracture Mechanics 224 (February 2020): 106752. http://dx.doi.org/10.1016/j.engfracmech.2019.106752.

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9

Nagaraja, Sindhu, Ulrich Römer, Hermann G. Matthies, and Laura De Lorenzis. "Deterministic and stochastic phase-field modeling of anisotropic brittle fracture." Computer Methods in Applied Mechanics and Engineering 408 (April 2023): 115960. http://dx.doi.org/10.1016/j.cma.2023.115960.

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10

Dinh, Huy, Dimitrios Giannakis, Joanna Slawinska, and Georg Stadler. "Phase-field models of floe fracture in sea ice." Cryosphere 17, no. 9 (2023): 3883–93. http://dx.doi.org/10.5194/tc-17-3883-2023.

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Abstract. We develop a phase-field model of brittle fracture to model fracture in sea ice floes. Phase fields allow for a variational formulation of fracture by using an energy functional that combines a linear elastic energy with a term modeling the energetic cost of fracture. We study the fracture strength of ice floes with stochastic thickness variations under boundary forcings or displacements. Our approach models refrozen cracks or other linear ice impurities with stochastic models for thickness profiles. We find that the orientation of thickness variations is an important factor for the

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11

Singh, N., C. V. Verhoosel, R. de Borst, and E. H. van Brummelen. "A fracture-controlled path-following technique for phase-field modeling of brittle fracture." Finite Elements in Analysis and Design 113 (June 2016): 14–29. http://dx.doi.org/10.1016/j.finel.2015.12.005.

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12

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

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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, de

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13

Patil, Sandeep P., Yousef Heider, Carlos Alberto Hernandez Padilla, Eduardo R. Cruz-Chú, and Bernd Markert. "A comparative molecular dynamics-phase-field modeling approach to brittle fracture." Computer Methods in Applied Mechanics and Engineering 312 (December 2016): 117–29. http://dx.doi.org/10.1016/j.cma.2016.04.005.

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14

Bleyer, Jeremy, and Roberto Alessi. "Phase-field modeling of anisotropic brittle fracture including several damage mechanisms." Computer Methods in Applied Mechanics and Engineering 336 (July 2018): 213–36. http://dx.doi.org/10.1016/j.cma.2018.03.012.

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15

Chen, Yang, Dmytro Vasiukov, Lionel Gélébart, and Chung Hae Park. "A FFT solver for variational phase-field modeling of brittle fracture." Computer Methods in Applied Mechanics and Engineering 349 (June 2019): 167–90. http://dx.doi.org/10.1016/j.cma.2019.02.017.

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16

Wu, Jian-Ying, Jing-Ru Yao, and Jia-Liang Le. "Phase-field modeling of stochastic fracture in heterogeneous quasi-brittle solids." Computer Methods in Applied Mechanics and Engineering 416 (November 2023): 116332. http://dx.doi.org/10.1016/j.cma.2023.116332.

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17

Tan, Yu, Fan Peng, Chang Liu, Daiming Peng, and Xiangyu Li. "Fourth-order phase-field modeling for brittle fracture in piezoelectric materials." Applied Mathematics and Mechanics 45, no. 5 (2024): 837–56. http://dx.doi.org/10.1007/s10483-024-3118-9.

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18

Tomić, Zoran, Krešimir Jukić, Tomislav Jarak, Tamara Aleksandrov Fabijanić, and Zdenko Tonković. "Phase-Field Modeling of Fused Silica Cone-Crack Vickers Indentation." Nanomaterials 12, no. 14 (2022): 2356. http://dx.doi.org/10.3390/nano12142356.

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In this paper, a 3D phase-field model for brittle fracture is applied for analyzing the complex fracture patterns appearing during the Vickers indentation of fused silica. Although recent phase-field models for the fracture caused by the indentation loading have been verified by some simpler academic axis-symmetric examples, a proper validation of such models is still missing. In addition, heavy computational costs, and a complicated compression stress field under the indenter, which demands different energy decompositions, have been identified as the most important impediments for the success

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19

Schreiber, Christoph, Charlotte Kuhn, Ralf Müller, and Tarek Zohdi. "A phase field modeling approach of cyclic fatigue crack growth." International Journal of Fracture 225, no. 1 (2020): 89–100. http://dx.doi.org/10.1007/s10704-020-00468-w.

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AbstractPhase field modeling of fracture has been in the focus of research for over a decade now. The field has gained attention properly due to its benefiting features for the numerical simulations even for complex crack problems. The framework was so far applied to quasi static and dynamic fracture for brittle as well as for ductile materials with isotropic and also with anisotropic fracture resistance. However, fracture due to cyclic mechanical fatigue, which is a very important phenomenon regarding a safe, durable and also economical design of structures, is considered only recently in ter

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20

Rahimi, Mohammad Naqib, and Georgios Moutsanidis. "A smoothed particle hydrodynamics approach for phase field modeling of brittle fracture." Computer Methods in Applied Mechanics and Engineering 398 (August 2022): 115191. http://dx.doi.org/10.1016/j.cma.2022.115191.

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21

Kamensky, David, Georgios Moutsanidis, and Yuri Bazilevs. "Hyperbolic phase field modeling of brittle fracture: Part I—Theory and simulations." Journal of the Mechanics and Physics of Solids 121 (December 2018): 81–98. http://dx.doi.org/10.1016/j.jmps.2018.07.010.

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22

Ambati, Marreddy, Josef Kiendl, and Laura De Lorenzis. "Isogeometric phase-field modeling of brittle and ductile fracture in shell structures." Journal of Physics: Conference Series 734 (August 2016): 032006. http://dx.doi.org/10.1088/1742-6596/734/3/032006.

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23

Aldakheel, Fadi, Blaž Hudobivnik, Ali Hussein, and Peter Wriggers. "Phase-field modeling of brittle fracture using an efficient virtual element scheme." Computer Methods in Applied Mechanics and Engineering 341 (November 2018): 443–66. http://dx.doi.org/10.1016/j.cma.2018.07.008.

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24

Huang, Chuanshi, and Xiaosheng Gao. "Development of a phase field method for modeling brittle and ductile fracture." Computational Materials Science 169 (November 2019): 109089. http://dx.doi.org/10.1016/j.commatsci.2019.109089.

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25

Nagaraja, Sindhu, Pietro Carrara, and Laura De Lorenzis. "Experimental characterization and phase-field modeling of anisotropic brittle fracture in silicon." Engineering Fracture Mechanics 293 (December 2023): 109684. http://dx.doi.org/10.1016/j.engfracmech.2023.109684.

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26

Bhowmick, Sauradeep, and Gui-Rong Liu. "Three Dimensional CS-FEM Phase-Field Modeling Technique for Brittle Fracture in Elastic Solids." Applied Sciences 8, no. 12 (2018): 2488. http://dx.doi.org/10.3390/app8122488.

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The cell based smoothed finite element method (CS-FEM) was integrated with the phase-field technique to model brittle fracture in 3D elastic solids. The CS-FEM was used to model the mechanics behavior and the phase-field method was used for diffuse fracture modeling technique where the damage in a system was quantified by a scalar variable. The integrated CS-FEM phase-field approach provides an efficient technique to model complex crack topologies in three dimensions. The detailed formulation of our combined method is provided. It was implemented in the commercial software ABAQUS using its use

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27

Gupta, Abhinav, U. Meenu Krishnan, Rajib Chowdhury, and Anupam Chakrabarti. "An auto-adaptive sub-stepping algorithm for phase-field modeling of brittle fracture." Theoretical and Applied Fracture Mechanics 108 (August 2020): 102622. http://dx.doi.org/10.1016/j.tafmec.2020.102622.

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28

Noii, Nima, Fadi Aldakheel, Thomas Wick, and Peter Wriggers. "An adaptive global–local approach for phase-field modeling of anisotropic brittle fracture." Computer Methods in Applied Mechanics and Engineering 361 (April 2020): 112744. http://dx.doi.org/10.1016/j.cma.2019.112744.

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29

Rodriguez, P., J. Ulloa, C. Samaniego, and E. Samaniego. "A variational approach to the phase field modeling of brittle and ductile fracture." International Journal of Mechanical Sciences 144 (August 2018): 502–17. http://dx.doi.org/10.1016/j.ijmecsci.2018.05.009.

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30

Liu, Tong-Rui, Fadi Aldakheel, and M. H. Aliabadi. "Numerical recipes of virtual element method for phase field modeling of brittle fracture." Procedia Structural Integrity 52 (2024): 740–51. http://dx.doi.org/10.1016/j.prostr.2023.12.074.

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31

Bleyer, Jeremy, and Jean-François Molinari. "Microbranching instability in phase-field modelling of dynamic brittle fracture." Applied Physics Letters 110, no. 15 (2017): 151903. http://dx.doi.org/10.1063/1.4980064.

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32

Ren, H. L., X. Y. Zhuang, C. Anitescu, and T. Rabczuk. "An explicit phase field method for brittle dynamic fracture." Computers & Structures 217 (June 2019): 45–56. http://dx.doi.org/10.1016/j.compstruc.2019.03.005.

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33

Tsakmakis, Aris, and Michael Vormwald. "Discussion of hardening effects on phase field models for fracture." MATEC Web of Conferences 349 (2021): 02001. http://dx.doi.org/10.1051/matecconf/202134902001.

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Phase field models have been successfully applied in recent years to a variety of fracture mechanics problems, such as quasi-brittle materials, dynamic fracture mechanics, fatigue cracks in brittle materials, as well as ductile materials. The basic idea of the method is to introduce an additional term in the energy functional describing the state of material bodies. A new state variable is included in this term, the so-called phase field, and enables to determine the surface energy of the crack. This approach allows to model phenomena such as crack initiation, crack branching and buckling of c

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34

Hai, Lu, and Jie Li. "Modeling tensile damage and fracture of quasi-brittle materials using stochastic phase-field model." Theoretical and Applied Fracture Mechanics 118 (April 2022): 103283. http://dx.doi.org/10.1016/j.tafmec.2022.103283.

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35

Nguyen-Thanh, Nhon, Hung Nguyen-Xuan, and Weidong Li. "Phase-field modeling of anisotropic brittle fracture in rock-like materials and polycrystalline materials." Computers & Structures 296 (June 2024): 107325. http://dx.doi.org/10.1016/j.compstruc.2024.107325.

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36

Seleš, Karlo, Tomislav Lesičar, Zdenko Tonković, and Jurica Sorić. "A residual control staggered solution scheme for the phase-field modeling of brittle fracture." Engineering Fracture Mechanics 205 (January 2019): 370–86. http://dx.doi.org/10.1016/j.engfracmech.2018.09.027.

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37

Hirshikesh, A. L. N. Pramod, R. K. Annabattula, E. T. Ooi, C. Song, and S. Natarajan. "Adaptive phase-field modeling of brittle fracture using the scaled boundary finite element method." Computer Methods in Applied Mechanics and Engineering 355 (October 2019): 284–307. http://dx.doi.org/10.1016/j.cma.2019.06.002.

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38

Kasirajan, P., S. Bhattacharya, A. Rajagopal, and J. N. Reddy. "Phase field modeling of fracture in Quasi-Brittle materials using natural neighbor Galerkin method." Computer Methods in Applied Mechanics and Engineering 366 (July 2020): 113019. http://dx.doi.org/10.1016/j.cma.2020.113019.

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39

Gerasimov, Tymofiy, Ulrich Römer, Jaroslav Vondřejc, Hermann G. Matthies, and Laura De Lorenzis. "Stochastic phase-field modeling of brittle fracture: Computing multiple crack patterns and their probabilities." Computer Methods in Applied Mechanics and Engineering 372 (December 2020): 113353. http://dx.doi.org/10.1016/j.cma.2020.113353.

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40

Nguyen-Thanh, Nhon, Weidong Li, Jiazhao Huang, and Kun Zhou. "Adaptive higher-order phase-field modeling of anisotropic brittle fracture in 3D polycrystalline materials." Computer Methods in Applied Mechanics and Engineering 372 (December 2020): 113434. http://dx.doi.org/10.1016/j.cma.2020.113434.

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41

Yu, Tao, Yuntian Zhao, and Jidong Zhao. "Full-process GPU-parallelized finite volume framework for phase field modeling of brittle fracture." Computers and Geotechnics 187 (November 2025): 107481. https://doi.org/10.1016/j.compgeo.2025.107481.

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42

Clayton, John D. "Modeling Deformation and Fracture of Boron-Based Ceramics with Nonuniform Grain and Phase Boundaries and Thermal-Residual Stress." Solids 3, no. 4 (2022): 643–64. http://dx.doi.org/10.3390/solids3040040.

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A phase field framework of elasticity, inelasticity, and fracture mechanics is invoked to study the behavior of ceramic materials. Mechanisms addressed by phase field theory include deformation twinning, dislocation slip, amorphization, and anisotropic cleavage fracture. Failure along grain and phase boundaries is resolved explicitly, whereWeibull statistics are used to characterize the surface energies of such boundaries. Residual stress incurred by mismatching coefficients of thermal expansion among phases is included. Polycrystalline materials of interest are the ultra-hard ceramics boron c

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43

Reinoso, José, Percy Durand, Pattabhi Budarapu, and Marco Paggi. "Crack Patterns in Heterogenous Rocks Using a Combined Phase Field-Cohesive Interface Modeling Approach: A Numerical Study." Energies 12, no. 6 (2019): 965. http://dx.doi.org/10.3390/en12060965.

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Rock fracture in geo-materials is a complex phenomenon due to its intrinsic characteristics and the potential external loading conditions. As a result, these materials can experience intricate fracture patterns endowing various cracking phenomena such as: branching, coalescence, shielding, and amplification, among many others. In this article, we present a numerical investigation concerning the applicability of an original bulk-interface fracture simulation technique to trigger such phenomena within the context of the phase field approach for fracture. In particular, the prediction of failure

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44

Si, Zhanfei, Tiantang Yu, Hirshikesh, and Sundararajan Natarajan. "An adaptive multi-patch isogeometric phase-field model for dynamic brittle fracture." Computers & Mathematics with Applications 153 (January 2024): 1–19. http://dx.doi.org/10.1016/j.camwa.2023.11.004.

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45

Nguyen, Ngoc-Hien, Vinh Phu Nguyen, Jian-Ying Wu, Thi-Hong-Hieu Le, and Yan Ding. "Mesh-Based and Meshfree Reduced Order Phase-Field Models for Brittle Fracture: One Dimensional Problems." Materials 12, no. 11 (2019): 1858. http://dx.doi.org/10.3390/ma12111858.

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Modelling brittle fracture by a phase-field fracture formulation has now been widely accepted. However, the full-order phase-field fracture model implemented using finite elements results in a nonlinear coupled system for which simulations are very computationally demanding, particularly for parametrized problems when the randomness and uncertainty of material properties are considered. To tackle this issue, we present two reduced-order phase-field models for parametrized brittle fracture problems in this work. The first one is a mesh-based Proper Orthogonal Decomposition (POD) method. Both th

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46

Aldakheel, Fadi, Ramish Satari, and Peter Wriggers. "Feed-Forward Neural Networks for Failure Mechanics Problems." Applied Sciences 11, no. 14 (2021): 6483. http://dx.doi.org/10.3390/app11146483.

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This work addresses an efficient neural network (NN) representation for the phase-field modeling of isotropic brittle fracture. In recent years, data-driven approaches, such as neural networks, have become an active research field in mechanics. In this contribution, deep neural networks—in particular, the feed-forward neural network (FFNN)—are utilized directly for the development of the failure model. The verification and generalization of the trained models for elasticity as well as fracture behavior are investigated by several representative numerical examples under different loading condit

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47

Zhao, Han, Xiangguo Zeng, Jingbo Wu, Huayan Chen, Wei Li, and Xin Yang. "Phase-field modeling of interactions between double cracks on brittle fracture of Zircaloy-4 cladding." Computational Materials Science 197 (September 2021): 110565. http://dx.doi.org/10.1016/j.commatsci.2021.110565.

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48

Kiran, Raj, Krishana Choudhary, and Nhon Nguyen-Thanh. "Phase-field modeling of brittle anisotropic fracture in polycrystalline materials under combined thermo-mechanical loadings." Computers & Structures 308 (February 2025): 107651. https://doi.org/10.1016/j.compstruc.2025.107651.

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49

Choo, Jinhyun, and WaiChing Sun. "Coupled phase-field and plasticity modeling of geological materials: From brittle fracture to ductile flow." Computer Methods in Applied Mechanics and Engineering 330 (March 2018): 1–32. http://dx.doi.org/10.1016/j.cma.2017.10.009.

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50

Li, Bin, Christian Peco, Daniel Millán, Irene Arias, and Marino Arroyo. "Phase-field modeling and simulation of fracture in brittle materials with strongly anisotropic surface energy." International Journal for Numerical Methods in Engineering 102, no. 3-4 (2014): 711–27. http://dx.doi.org/10.1002/nme.4726.

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