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Zeitschriftenartikel zum Thema „Phase field modeling of brittle fracture“

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Veröffentlicht am 1. Juni 2024

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1

Li, Haifeng, Wei Wang, Yajun Cao und Shifan Liu. „Phase-Field Modeling Fracture in Anisotropic Materials“. Advances in Civil Engineering 2021 (30.07.2021): 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-deviatoric energy split, we introduce a novel form of the crack-driving energy to simulate mixed-mode fracture. Furthermore, a new degradation function is proposed to simulate crack processes in brittle materials with different degradation rates. The proposed model is implemented by a staggered algorithm and to validate the performance of the phase-field modelling, and several numerical examples are constructed under plane strain condition. All the presented examples demonstrate the capability of the proposed approach in solving problems of brittle fracture propagation.

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2

Ulmer, Heike, Martina Hofacker und Christian Miehe. „Phase Field Modeling of Brittle and Ductile Fracture“. PAMM 13, Nr. 1 (29.11.2013): 533–36. http://dx.doi.org/10.1002/pamm.201310258.

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3

Ulloa, Jacinto, Patricio Rodríguez, Cristóbal Samaniego und Esteban Samaniego. „Phase-field modeling of fracture for quasi-brittle materials“. Underground Space 4, Nr. 1 (März 2019): 10–21. http://dx.doi.org/10.1016/j.undsp.2018.08.002.

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4

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

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5

Seleš, Karlo, Tomislav Lesičar, Zdenko Tonković und 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 finite element program Abaqus. A common issue of the existing Abaqus implementations of the staggered phase field schemes is the computationally demanding fine incrementation of the loading applied, required to obtain an accurate solution. The computational time is reduced by imposing an appropriate convergence control paired with the Abaqus automatic time incrementation. Therefore, by taking advantage of the Abaqus computational efficiency, an accurate solution can be obtained for a moderate time step. The proposed model is verified on the symmetrically double notched tensile benchmark test. Compared to the existing implementations, it demonstrates an improvement in accuracy and the computational performance. Furthermore, a heterogeneous steel microstructure is analyzed displaying the model’s ability to solve crack nucleation and curvilinear crack paths.

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6

Hou, Yue, Fengyan Sun, Wenjuan Sun, Meng Guo, Chao Xing und 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 of fracture are performed in bituminous materials with the consideration of quasi-brittle properties. It is found that the simulation results agree well with classic fracture mechanics.

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7

Wu, Chi, Jianguang Fang, Zhongpu Zhang, Ali Entezari, Guangyong Sun, Michael V. Swain und Qing Li. „Fracture modeling of brittle biomaterials by the phase-field method“. Engineering Fracture Mechanics 224 (Februar 2020): 106752. http://dx.doi.org/10.1016/j.engfracmech.2019.106752.

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8

Nagaraja, Sindhu, Ulrich Römer, Hermann G. Matthies und 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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9

Santillan Sanchez, David, Hichem Mazighi und Mustapha Kamel Mihoubi. „Hybrid phase-field modeling of multi-level concrete gravity dam notched cracks“. Frattura ed Integrità Strutturale 16, Nr. 61 (19.06.2022): 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. First, we apply our methodology to the three-point bending test on notched laboratory beams. Second, we simulate the fracture propagation in a life-size structure: the Koyna gravity dam. We account for the pressure load inside the fracture, and we study the effect of the position and number of initial fractures in the upstream face and the value of the Grifﬁth critical energy release, on the fracture propagation under a flood event. The position of the fracture plays an important role in the final fracture pattern and crest displacements, whereas the value of the Grifﬁth critical energy release alters the onset of the fracture propagation. We conclude that phase-ﬁeld models are a promising computational tool that may be applied to real engineering problems.

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10

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

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11

Dinh, Huy, Dimitrios Giannakis, Joanna Slawinska und Georg Stadler. „Phase-field models of floe fracture in sea ice“. Cryosphere 17, Nr. 9 (07.09.2023): 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 strength of ice floes, and we study the distribution of critical stresses leading to fracture. Potential applications to discrete element method (DEM) simulations and field data from the ICEX 2018 campaign are discussed.

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12

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

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13

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

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14

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

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15

Wu, Jian-Ying, Jing-Ru Yao und 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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16

Tan, Yu, Fan Peng, Chang Liu, Daiming Peng und Xiangyu Li. „Fourth-order phase-field modeling for brittle fracture in piezoelectric materials“. Applied Mathematics and Mechanics 45, Nr. 5 (29.04.2024): 837–56. http://dx.doi.org/10.1007/s10483-024-3118-9.

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17

Tomić, Zoran, Krešimir Jukić, Tomislav Jarak, Tamara Aleksandrov Fabijanić und Zdenko Tonković. „Phase-Field Modeling of Fused Silica Cone-Crack Vickers Indentation“. Nanomaterials 12, Nr. 14 (09.07.2022): 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 successful application of the phase-field method for such problems. An adaptive strategy is utilized for reducing the computational costs, and some modifications are introduced, which enable an accurate simulation of the Vickers indentation fracture. Here, the fracture initiation ring outside the contact zone is detected by using different energy decompositions, and the dominant cone-crack formation under the Vickers indenter is observed. Different contact conditions are investigated. The proposed model is validated by experimental measurements, and a quantitative and qualitative comparison between experimental and numerical results is conducted.

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18

Rahimi, Mohammad Naqib, und 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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19

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

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20

Ambati, Marreddy, Josef Kiendl und 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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21

Aldakheel, Fadi, Blaž Hudobivnik, Ali Hussein und 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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22

Huang, Chuanshi, und 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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23

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

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24

Schreiber, Christoph, Charlotte Kuhn, Ralf Müller und Tarek Zohdi. „A phase field modeling approach of cyclic fatigue crack growth“. International Journal of Fracture 225, Nr. 1 (17.07.2020): 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 terms of phase field modeling. While in first phase field models the material’s fracture toughness becomes degraded to simulate fatigue crack growth, we present an alternative method within this work, where the driving force for the fatigue mechanism increases due to cyclic loading. This new contribution is governed by the evolution of fatigue damage, which can be approximated by a linear law, namely the Miner’s rule, for damage accumulation. The proposed model is able to predict nucleation as well as growth of a fatigue crack. Furthermore, by an assessment of crack growth rates obtained from several numerical simulations by a conventional approach for the description of fatigue crack growth, it is shown that the presented model is able to predict realistic behavior.

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25

Gupta, Abhinav, U. Meenu Krishnan, Rajib Chowdhury und 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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26

Noii, Nima, Fadi Aldakheel, Thomas Wick und 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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27

Rodriguez, P., J. Ulloa, C. Samaniego und 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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28

Liu, Tong-Rui, Fadi Aldakheel und 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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29

Bleyer, Jeremy, und Jean-François Molinari. „Microbranching instability in phase-field modelling of dynamic brittle fracture“. Applied Physics Letters 110, Nr. 15 (10.04.2017): 151903. http://dx.doi.org/10.1063/1.4980064.

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30

Bhowmick, Sauradeep, und Gui-Rong Liu. „Three Dimensional CS-FEM Phase-Field Modeling Technique for Brittle Fracture in Elastic Solids“. Applied Sciences 8, Nr. 12 (04.12.2018): 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 user-element (UEL) and user-material (UMAT) subroutines. The coupled system of equations were solved in a staggered fashion using the in-built non-linear Newton–Raphson solver in ABAQUS. Eight node hexahedral (H8) elements with eight smoothing domains were coded in CS-FEM. Several representative numerical examples are presented to demonstrate the capability of the method. We also discuss some of its limitations.

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31

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

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32

Tsakmakis, Aris, und 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 cracks, as well as the modelling of the crack front in three-dimensional geometries, without further assumptions. There is yet no systematic investigation of the influence of strain hardening on crack development within the phase field method. Thus, the aim of the paper is to provide an analysis of the effect of kinematic and isotropic hardening on the evolution of the phase field variable.

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33

Hai, Lu, und 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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34

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

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35

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

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36

Kasirajan, P., S. Bhattacharya, A. Rajagopal und 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 (Juli 2020): 113019. http://dx.doi.org/10.1016/j.cma.2020.113019.

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37

Gerasimov, Tymofiy, Ulrich Römer, Jaroslav Vondřejc, Hermann G. Matthies und 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 (Dezember 2020): 113353. http://dx.doi.org/10.1016/j.cma.2020.113353.

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38

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

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39

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

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40

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

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41

Clayton, John D. „Modeling Deformation and Fracture of Boron-Based Ceramics with Nonuniform Grain and Phase Boundaries and Thermal-Residual Stress“. Solids 3, Nr. 4 (16.11.2022): 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 carbide (B4C) and boron carbide-titanium diboride (B4C-TiB2), the latter a dual-phase composite. Recent advancements in processing technology enable the production of these materials via spark-plasma sintering (SPS) at nearly full theoretical density. Numerical simulations invoking biaxial loading (e.g., pure shear) demonstrate how properties and mechanisms at the scale of the microstructure influence overall strength and ductility. In agreement with experimental inferences, simulations show that plasticity is more prevalent in the TiB2 phase of the composite and reduces the tendency for transgranular fracture. The composite demonstrates greater overall strength and ductility than monolithic B4C in both simulations and experiments. Toughening of the more brittle B4C phase from residual stress, in addition to crack mitigation from the stronger and more ductile TiB2 phase are deemed advantageous attributes of the composite.

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42

Reinoso, José, Percy Durand, Pattabhi Budarapu und Marco Paggi. „Crack Patterns in Heterogenous Rocks Using a Combined Phase Field-Cohesive Interface Modeling Approach: A Numerical Study“. Energies 12, Nr. 6 (13.03.2019): 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 patterns in heterogenous rock masses with brittle response is accomplished through the current methodology by combining the phase field approach for intact rock failure and the cohesive interface-like modeling approach for its application in joint fracture. Predictions from the present technique are first validated against Brazilian test results, which were developed using alternative phase field methods, and with respect to specimens subjected to different loading case and whose corresponding definitions are characterized by the presence of single and multiple flaws. Subsequently, the numerical study is extended to the analysis of heterogeneous rock masses including joints that separate different potential lithologies, leading to tortuous crack paths, which are observed in many practical situations.

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43

Nguyen, Ngoc-Hien, Vinh Phu Nguyen, Jian-Ying Wu, Thi-Hong-Hieu Le und Yan Ding. „Mesh-Based and Meshfree Reduced Order Phase-Field Models for Brittle Fracture: One Dimensional Problems“. Materials 12, Nr. 11 (08.06.2019): 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 the Discrete Empirical Interpolation Method (DEIM) and the Matrix Discrete Empirical Interpolation Method ((M)DEIM) are adopted to approximate the nonlinear vectors and matrices. The second one is a meshfree Krigingmodel. For one-dimensional problems, served as proof-of-concept demonstrations, in which Young’s modulus and the fracture energy vary, the POD-based model can speed up the online computations eight-times, and for the Kriging model, the speed-up factor is 1100, albeit with a slightly lower accuracy. Another merit of the Kriging’s model is its non-intrusive nature, as one does not need to modify the full-order model code.

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Zhao, Han, Xiangguo Zeng, Jingbo Wu, Huayan Chen, Wei Li und 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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45

Choo, Jinhyun, und 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 (März 2018): 1–32. http://dx.doi.org/10.1016/j.cma.2017.10.009.

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46

Li, Bin, Christian Peco, Daniel Millán, Irene Arias und 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, Nr. 3-4 (15.07.2014): 711–27. http://dx.doi.org/10.1002/nme.4726.

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47

Aldakheel, Fadi, Ramish Satari und Peter Wriggers. „Feed-Forward Neural Networks for Failure Mechanics Problems“. Applied Sciences 11, Nr. 14 (14.07.2021): 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 conditions. As an outcome, promising results close to the exact solutions are produced.

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48

Novelli, Larissa, Lapo Gori und Roque Luiz da Silva Pitangueira. „Phase-field modelling of brittle fracture with Smoothed Radial Point Interpolation Methods“. Engineering Analysis with Boundary Elements 138 (Mai 2022): 219–34. http://dx.doi.org/10.1016/j.enganabound.2022.01.011.

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49

Kriaa, Yosra, Yassine Hersi, Amine Ammar und Bassem Zouari. „Quasi-Static and Dynamic Crack Propagation by Phase Field Modeling: Comparison with Previous Results and Experimental Validation“. Applied Sciences 14, Nr. 10 (08.05.2024): 4000. http://dx.doi.org/10.3390/app14104000.

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In this paper, experimental tensile tests for pre-cracked high Carbon steel ‘C90’ specimens were performed for quasi-static and dynamic loading. High loading velocity affects the crack patterns by preventing deflection. On the other hand, an efficient numerical tool based on the phase field model was developed and validated to predict brittle fracture trajectories. A staggered numerical scheme was adopted to solve the displacement and damage fields separately. Implementation efficiency in initiating and propagating cracks, even from an undamaged microstructure, was proved. The effect of the critical fracture energy density Gc on the crack path was tested; with smaller Gc, the crack patterns become more complex. In addition, the impact of loading velocities was examined, and earlier and faster crack formation and greater crack branching is observed with higher impact velocity. In this study, bidimensional plane stress cases were treated. The phase field model with hybrid formulation was able to predict crack pattern and especially crack arrest and branching found in the literature. The developed model accurately determined the transition zone of the crack path topology that has been observed experimentally.

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Schmidt, Jaroslav, Alena Zemanová, Jan Zeman und Michal Šejnoha. „Phase-Field Fracture Modelling of Thin Monolithic and Laminated Glass Plates under Quasi-Static Bending“. Materials 13, Nr. 22 (16.11.2020): 5153. http://dx.doi.org/10.3390/ma13225153.

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A phase-field description of brittle fracture is employed in the reported four-point bending analyses of monolithic and laminated glass plates. Our aims are: (i) to compare different phase-field fracture formulations applied to thin glass plates, (ii) to assess the consequences of the dimensional reduction of the problem and mesh density and refinement, and (iii) to validate for quasi-static loading the time-/temperature-dependent material properties we derived recently for two commonly used polymer foils made of polyvinyl butyral or ethylene-vinyl acetate. As the nonlinear response prior to fracture, typical of the widely used Bourdin–Francfort–Marigo model, can lead to a significant overestimation of the response of thin plates under bending, the numerical study investigates two additional phase-field fracture models providing the linear elastic phase of the stress-strain diagram. The typical values of the critical fracture energy and tensile strength of glass lead to a phase-field length-scale parameter that is challenging to resolve in the numerical simulations. Therefore, we show how to determine the fracture energy concerning the applied dimensional reduction and the value of the length-scale parameter relative to the thickness of the plate. The comparison shows that the phase-field models provide very good agreement with the measured stresses and resistance of laminated glass, despite the fact that only one/two cracks are localised using the quasi-static analysis, whereas multiple cracks evolve during the experiment. It was also observed that the stiffness and resistance of the partially fractured laminated glass can be well approximated using a 2D plane-stress model with initially predefined cracks, which provides a better estimation than the one-glass-layer limit.

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