Journal articles: 'Phase field fracture method'

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Xue, Tianju, Sigrid Adriaenssens, and Sheng Mao. "Mapped phase field method for brittle fracture." Computer Methods in Applied Mechanics and Engineering 385 (November 2021): 114046. http://dx.doi.org/10.1016/j.cma.2021.114046.

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Zhao, Jinzhou, Qing Yin, John McLennan, Yongming Li, Yu Peng, Xiyu Chen, Cheng Chang, Weiyang Xie, and Zhongyi Zhu. "Iteratively Coupled Flow and Geomechanics in Fractured Poroelastic Reservoirs: A Phase Field Fracture Model." Geofluids 2021 (December 20, 2021): 1–13. http://dx.doi.org/10.1155/2021/6235441.

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Fluid-solid coupling in fractured reservoirs plays a critical role for optimizing and managing in energy and geophysical engineering. Computational difficulties associated with sharp fracture models motivate phase field fracture modeling. However, for geomechanical problems, the fully coupled hydromechanical modeling with the phase field framework is still under development. In this work, we propose a fluid-solid fully coupled model, in which discrete fractures are regularized by the phase field. Specifically, this model takes into account the complex coupled interaction of Darcy-Biot-type fluid flow in poroelastic media, Reynolds lubrication governing flow inside fractures, mass exchange between fractures and matrix, and the subsequent geomechanical response of the solid. An iterative coupling method is developed to solve this multifield problem efficiently. We present numerical studies that demonstrate the performance of our model.

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Labanda, Nicolás A., Luis Espath, and Victor M. Calo. "A spatio-temporal adaptive phase-field fracture method." Computer Methods in Applied Mechanics and Engineering 392 (March 2022): 114675. http://dx.doi.org/10.1016/j.cma.2022.114675.

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Kakouris, E. G., and S. P. Triantafyllou. "Phase-field material point method for brittle fracture." International Journal for Numerical Methods in Engineering 112, no. 12 (August 14, 2017): 1750–76. http://dx.doi.org/10.1002/nme.5580.

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Choo, Jinhyun, and Fan Fei. "Phase-field modeling of geologic fracture incorporating pressure-dependence and frictional contact." E3S Web of Conferences 205 (2020): 03004. http://dx.doi.org/10.1051/e3sconf/202020503004.

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Geologic fractures such as joints and faults are central to many problems in energy geotechnics. Notable examples include hydraulic fracturing, injection-induced earthquakes, and geologic carbon storage. Nevertheless, our current capabilities for simulating the development and evolution of geologic fractures in these problems are still insufficient in terms of efficiency and accuracy. Recently, phase-field modeling has emerged as an efficient numerical method for fracture simulation which does not require any algorithm for tracking the geometry of fracture. However, existing phase-field models of fracture neglected two distinct characteristics of geologic fractures, namely, the pressure-dependence and frictional contact. To overcome these limitations, new phase-field models have been developed and described in this paper. The new phase-field models are demonstrably capable of simulating pressure-dependent, frictional fractures propagating in arbitrary directions, which is a notoriously challenging task.

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CHEN, Pengcheng, Yu'e MA, Fan PENG, and Linglong ZHOU. "Simulating hydrogen embrittlement fracture based on phase field method." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 40, no. 3 (June 2022): 504–11. http://dx.doi.org/10.1051/jnwpu/20224030504.

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The phase field hydrogen embrittlement fracture model is improved by introducing tension-compression split of strain energy. The numerical formulas of the model are provided, besides, the coupling term of concentration field and displacement field is deduced. The matlab software is used to compile the numerical program of phase field hydrogen embrittlement fracture. The modes I and II cracks of hydrogen embrittlement are simulated respectively. The simulation results show that hydrogen ions concentrate at the crack tip where stress concentration happens, and that the hydrogen concentration reduces the critical failure load of the square plate. Compared with the numerical results of the existing models, the improved model can accurately calculate the critical failure load in the mode I crack and capture the embrittlement fracture phenomenon when the phase field and the concentration field are accumulated near the crack tip. Moreover, the improved model can effectively simulate the mode II crack with hydrogen embrittlement.

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Feng, Yuan, Qihan Wang, Di Wu, Zhen Luo, Xiaojun Chen, Tianyu Zhang, and Wei Gao. "Machine learning aided phase field method for fracture mechanics." International Journal of Engineering Science 169 (December 2021): 103587. http://dx.doi.org/10.1016/j.ijengsci.2021.103587.

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Patil, R. U., B. K. Mishra, and I. V. Singh. "An adaptive multiscale phase field method for brittle fracture." Computer Methods in Applied Mechanics and Engineering 329 (February 2018): 254–88. http://dx.doi.org/10.1016/j.cma.2017.09.021.

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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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Jammoul, M., and M. F. Wheeler. "A Phase-Field-Based Approach for Modeling Flow and Geomechanics in Fractured Reservoirs." SPE Journal 27, no. 02 (December 21, 2021): 1195–208. http://dx.doi.org/10.2118/203906-pa.

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Summary Modeling the geomechanical deformations of fracture networks has become an integral part of designing enhanced geothermal systems and recovery mechanisms for unconventional reservoirs. Stress changes in the reservoir can cause variations in the apertures of fractures resulting in large changes in their transmissivities. At the same time, sustained high-injection pressures can induce shear slipping along existing fractures and faults and trigger seismic activity. In this work, we extend the phase-field method to solve for flow and geomechanical deformations in naturally fractured reservoirs. The framework can predict the opening/closure of fractures as well as their shear slipping because of induced stresses and poromechanical effects. The flow through fractures is modeled on spatially nonconforming grids using the enhanced velocity mixed finite element method. The geomechanics equations are discretized using the continuous Galerkin (CG) finite element method. The flow and mechanics equations are decoupled using the fixed stress iterative scheme. The implementation is validated against the analytical solutions of Mandel’s problem and Sneddon’s benchmark test. Two synthetic examples are presented to illustrate the impact of poroelastic deformations and the accompanying dynamic behavior of fractures on the safety and productivity of subsurface projects.

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Li, Liyong, and Seong H. Lee. "Efficient Field-Scale Simulation of Black Oil in a Naturally Fractured Reservoir Through Discrete Fracture Networks and Homogenized Media." SPE Reservoir Evaluation & Engineering 11, no. 04 (August 1, 2008): 750–58. http://dx.doi.org/10.2118/103901-pa.

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Summary This paper describes a hybrid finite volume method, designed to simulate multiphase flow in a field-scale naturally fractured reservoir. Lee et al. (WRR 37:443-455, 2001) developed a hierarchical approach in which the permeability contribution from short fractures is derived in an analytical expression that from medium fractures is numerically solved using a boundary element method. The long fractures are modeled explicitly as major fluid conduits. Reservoirs with well-developed natural fractures include many complex fracture networks that cannot be easily modeled by simple long fracture formulation and/or homogenized single continuity model. We thus propose a numerically efficient hybrid method in which small and medium fractures are modeled by effective permeability, and large fractures are modeled by discrete fracture networks. A simple, systematic way is devised to calculate transport parameters between fracture networks and discretized, homogenized media. An efficient numerical algorithm is also devised to solve the dual system of fracture network and finite volume grid. Black oil formulation is implemented in the simulator to demonstrate practical applications of this hybrid finite volume method. Introduction Many reservoirs are highly fractured due to the complex tectonic movement and sedimentation process the formation has experienced. The permeability of a fracture is usually much larger than that of the rock matrix; as a result, the fluid will flow mostly through the fracture network, if the fractures are connected. This implies that the fracture connectivities and their distribution will determine fluid transport in a naturally fractured reservoir (Long and Witherspoon 1985). Because of statistically complex distribution of geological heterogeneity and multiple length and time scales in natural porous media, three approaches (Smith and Schwartz 1993) are commonly used in describing fluid flow and solute transport in naturally fractured formations:discrete fracture models;continuum models using effective properties for discrete grids; andhybrid models that combine discrete, large features and equivalent continuum. Currently, most reservoir simulators use dual continuum formulations (i.e., dual porosity/permeability) for naturally fractured reservoirs in which matrix blocks are divided by very regular fracture patterns (Kazemi et al. 1976, Van Golf-Racht 1982). Part of the primary input into these simulation models is the permeability of the fracture system assigned to the individual grid-blocks. This value can only be reasonably calculated if the fracture systems are regular and well connected. Field characterization studies have shown, however, that fracture systems are very irregular, often disconnected, and occur in swarms (Laubach 1991, Lorenz and Hill 1991, Narr et al. 2003). Most naturally fractured reservoirs include fractures of multiple- length scales. The effective grid-block permeability calculated by the boundary element method becomes expensive as the number of fractures increases. The calculated effective properties for grid-blocks also underestimates the properties for long fractures whose length scale is much larger than the grid-block size. Lee et al. (2001) proposed a hierarchical method to model fluid flow in a reservoir with multiple-length scaled fractures. They assumed that short fractures are randomly distributed and contribute to increasing the effective matrix permeability. An asymptotic solution representing the permeability contribution from short fractures was derived. With the short fracture contribution to permeability, the effective matrix permeability can be expressed in a general tensor form. Thus, they also developed a boundary element method for Darcy's equation with tensor permeability. For medium-length fractures in a grid-block, a coupled system of Poisson equations with tensor permeability was solved numerically using a boundary element method. The grid-block effective permeabilities were used with a finite difference simulator to compute flow through the fracture system. The simulator was enhanced to use a control-volume finite difference formulation (Lee et al. 1998, 2002) for general tensor permeability input (i.e., 9-point stencil for 2-D and 27-point stencil for 3-D). In addition, long fractures were explicitly modeled by using the transport index between fracture and matrix in a gridblock. In this paper we adopt their transport index concept and extend the hierarchical method:to include networks of long fractures;to model fracture as a two-dimensional plane; andto allow fractures to intersect with well bore. This generalization allows us to model a more realistic and complex fracture network that can be found in naturally fractured reservoirs. To demonstrate this new method for practical reservoir applications, we furthermore implement a black oil formulation in the simulator. We explicitly model long fractures as a two-dimensional plane that can penetrate several layers. The method, presented in this paper, allows a general description of fracture orientation in space. For simplicity of computational implementation however, both the medium-length and long fractures considered in this paper are assumed to be perpendicular to bedding boundaries. In addition, we derive a source/sink term to model the flux between matrix and long fracture networks. This source/sink allows for coupling multiphase flow equations in long fractures and matrix. The paper is organized as follows. In Section 2 black oil formulation is briefly summarized and the transport equations for three phase flow are presented. The fracture characterization and hierarchical modeling approach, based on fracture length, are discussed in Section 3. In Section 4 we review homogenization of short and medium fractures, which is part of our hierarchical approach to modeling flow in porous media with multiple length-scale fractures. In Section 5 we discuss a discrete network model of long fractures. We also derive transfer indices between fracture and effective matrix blocks. In Section 6 we present numerical examples for tracer transport in a model with simple fracture network, interactions of fractures and wells, and black oil production in a reservoir with a complex fracture network system. Finally, the summary of our main results and conclusion follows.

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He, QiangSheng, and Chuang Liu. "Phase Field Modeling of Multiple Fracture Growth in Natural Fractured Reservoirs." Geofluids 2023 (March 4, 2023): 1–22. http://dx.doi.org/10.1155/2023/4846474.

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In recent years, hydraulic fracturing techniques have been widely used in extracting unconventional reservoir resources. During multicluster fracturing process, the stress shadowing effect can lead to a nonuniform distribution of fracturing fluid. In this paper, a two-dimensional multiple fracture propagation model is developed based on phase field method considering the distribution of fracturing fluid within each fracture during fracturing process. The distribution of fracturing fluid injected into each fracture is calculated through solving governing equations of perforation friction as well as wellbore friction. Numerical results demonstrate that the natural fractures in the reservoir have a significant influence on the distribution of injected fluid and the morphology of fracture network. In addition, higher injection rates and higher fluid viscosity stimulations are in favor of inducing uniform distribution of injected fluid into each cluster. The presented numerical model provides an effective tool to extend our understandings in generating fracture networks.

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Bourne, Stephen J., Lex Rijkels, Ben J. Stephenson, and Emanuel J. M. Willemse. "Predictive Modelling of Naturally Fractured Reservoirs Using Geomechanics and Flow Simulation." GeoArabia 6, no. 1 (January 1, 2001): 27–42. http://dx.doi.org/10.2113/geoarabia060127.

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ABSTRACT To optimise recovery in naturally fractured reservoirs, the field-scale distribution of fracture properties must be understood and quantified. We present a method to systematically predict the spatial distribution of natural fractures related to faulting and their effect on flow simulations. This approach yields field-scale models for the geometry and permeability of connected fracture networks. These are calibrated by geological, well test and field production data to constrain the distributions of fractures within the inter-well space. First, we calculate the stress distribution at the time of fracturing using the present-day structural reservoir geometry. This calculation is based on a geomechanical model of rock deformation that represents faults as frictionless surfaces within an isotropic homogeneous linear elastic medium. Second, the calculated stress field is used to govern the simulated growth of fracture networks. Finally, the fractures are upscaled dynamically by simulating flow through the discrete fracture network per grid block, enabling field-scale multi-phase reservoir simulation. Uncertainties associated with these predictions are considerably reduced as the model is constrained and validated by seismic, borehole, well test and production data. This approach is able to predict physically and geologically realistic fracture networks. Its successful application to outcrops and reservoirs demonstrates that there is a high degree of predictability in the properties of natural fracture networks. In cases of limited data, field-wide heterogeneity in fracture permeability can be modelled without the need for field-wide well coverage.

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Lerner, D. N., G. P. Wealthall, and A. Steele. "Assessing Risk from DNAPLs in Fractured Aquifers." Journal of Agricultural and Marine Sciences [JAMS] 7, no. 2 (June 1, 2002): 47. http://dx.doi.org/10.24200/jams.vol7iss2pp47-52.

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Chlorinated solvents are among the most widespread pollutants of groundwater. As DNAPLs (dense nonaqueous phase liquids), they can move rapidly and in complex patterns through fractures to reach and contaminate large volumes of aquifer, and then dissolve to cause significant pollution of groundwater. However, clean-up of DNAPLs in fractured rocks is virtually impossible and certainly expensive. Risk assessment should be used to decide whether the pollution is serious enough to justify major expenditure on clean-up or containment. A key aspect of risk assessment for DNAPLs in fractured aquifers is to understand how deep they are likely to have penetrated through the fracture network. This paper addresses two aspects of such predictions: measuring fracture apertures in situ and the connectivity of fracture networks with respect to DNAPLs. Fracture aperture is an in-situ field technique that has been developed and implemented to measure aperture variability and NAPL entry pressure in an undisturbed, water-saturated rock fracture. The field experiment also provided the opportunity to measure the wetting phase relative permeability at residual non-wetting phase saturation. The RADIO (Radial Aperture Determination by the Injection of Oil) method employs a constant rate injection of a non-toxic NAPL into a fracture isolated by a double packer array. The method was applied at the field site in Scotland, and measured apertures out to ~5m from the borehole. It showed that hydraulic aperture (from packer tests) was a poor estimator of the controlling aperture for DNAPL movement. This is the first time such large-scale aperture measurements have been made, and the technique is the first which can provide useful aperture estimates for risk analysis of DNAPL movement.Network connectivity is a fundamental property of the fracture system. DNAPL connectivity extends the concept to take account of the fluid properties.

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Khodadadian, Amirreza, Nima Noii, Maryam Parvizi, Mostafa Abbaszadeh, Thomas Wick, and Clemens Heitzinger. "A Bayesian estimation method for variational phase-field fracture problems." Computational Mechanics 66, no. 4 (July 14, 2020): 827–49. http://dx.doi.org/10.1007/s00466-020-01876-4.

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Abstract In this work, we propose a parameter estimation framework for fracture propagation problems. The fracture problem is described by a phase-field method. Parameter estimation is realized with a Bayesian approach. Here, the focus is on uncertainties arising in the solid material parameters and the critical energy release rate. A reference value (obtained on a sufficiently refined mesh) as the replacement of measurement data will be chosen, and their posterior distribution is obtained. Due to time- and mesh dependencies of the problem, the computational costs can be high. Using Bayesian inversion, we solve the problem on a relatively coarse mesh and fit the parameters. In several numerical examples our proposed framework is substantiated and the obtained load-displacement curves, that are usually the target functions, are matched with the reference values.

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Zhang, Yan, Xiaobing Lu, Xuhui Zhang, and Peng Li. "Proppant Transportation in Cross Fractures: Some Findings and Suggestions for Field Engineering." Energies 13, no. 18 (September 19, 2020): 4912. http://dx.doi.org/10.3390/en13184912.

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The proppant transportation is a typical two-phase flow process in a complex cross fracture network during hydraulic fracturing. In this paper, the proppant transportation in cross fractures is investigated by the computational fluid dynamics (CFD) method. The Euler–Euler two-phase flow model and the kinetic theory of granular flow (KTGF) are adopted. The dimensionless controlling parameters are derived by dimensional analysis. The equilibrium proppant height (EPH) and the ratio of the proppant mass (RPM) in the secondary fracture to that in the whole cross fracture network are used to describe the movement and settlement of proppants in the cross fractures. The main features of the proppant transportation in the cross fractures are given, and several relative suggestions are presented for engineering application in the field. The main controlling dimensionless parameters for relative EPH are the proppant Reynolds number and the inlet proppant volume fraction. The dominating dimensionless parameters for RPM are the relative width of the primary and the secondary fracture. Transportation of the proppants with a certain particle size grading into the cross fractures may be a good way for supporting the hydraulic fractures.

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Hu, Xiaofei, Xiangyu Huang, Weian Yao, and Peng Zhang. "Precise integration explicit phase field method for dynamic brittle fracture." Mechanics Research Communications 113 (April 2021): 103698. http://dx.doi.org/10.1016/j.mechrescom.2021.103698.

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Wu, Chi, Jianguang Fang, Zhongpu Zhang, Ali Entezari, Guangyong Sun, Michael V. Swain, and Qing Li. "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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Yin, Bo, and Michael Kaliske. "Fracture simulation of viscoelastic polymers by the phase-field method." Computational Mechanics 65, no. 2 (September 17, 2019): 293–309. http://dx.doi.org/10.1007/s00466-019-01769-1.

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Liu, Tong-Rui, Fadi Aldakheel, and M. H. Aliabadi. "Virtual element method for phase field modeling of dynamic fracture." Computer Methods in Applied Mechanics and Engineering 411 (June 2023): 116050. http://dx.doi.org/10.1016/j.cma.2023.116050.

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Kristensen, Philip K., Christian F. Niordson, and Emilio Martínez-Pañeda. "An assessment of phase field fracture: crack initiation and growth." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 379, no. 2203 (June 21, 2021): 20210021. http://dx.doi.org/10.1098/rsta.2021.0021.

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The phase field paradigm, in combination with a suitable variational structure, has opened a path for using Griffith’s energy balance to predict the fracture of solids. These so-called phase field fracture methods have gained significant popularity over the past decade, and are now part of commercial finite element packages and engineering fitness- for-service assessments. Crack paths can be predicted, in arbitrary geometries and dimensions, based on a global energy minimization—without the need for ad hoc criteria. In this work, we review the fundamentals of phase field fracture methods and examine their capabilities in delivering predictions in agreement with the classical fracture mechanics theory pioneered by Griffith. The two most widely used phase field fracture models are implemented in the context of the finite element method, and several paradigmatic boundary value problems are addressed to gain insight into their predictive abilities across all cracking stages; both the initiation of growth and stable crack propagation are investigated. In addition, we examine the effectiveness of phase field models with an internal material length scale in capturing size effects and the transition flaw size concept. Our results show that phase field fracture methods satisfactorily approximate classical fracture mechanics predictions and can also reconcile stress and toughness criteria for fracture. The accuracy of the approximation is however dependent on modelling and constitutive choices; we provide a rationale for these differences and identify suitable approaches for delivering phase field fracture predictions that are in good agreement with well-established fracture mechanics paradigms. This article is part of a discussion meeting issue ‘A cracking approach to inventing new tough materials: fracture stranger than friction’.

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Li, Qiangqiang, Dingxi Xue, Chongyang Feng, Xiongwen Zhang, and Guojun Li. "Fracture Simulation of Ni–YSZ Anode Microstructures of Solid Oxide Fuel Cells Using Phase Field Method." Journal of The Electrochemical Society 169, no. 7 (July 1, 2022): 073507. http://dx.doi.org/10.1149/1945-7111/ac7c3f.

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The performance degradation of solid oxide fuel cells (SOFC) is directly related to the damage and fracture of electrode microstructures. In this study, the phase field fracture method is used to simulate the fracture of anode microstructures, and the effects of boundary constraints, thermal load, and Ni phase on the fracture of Ni–YSZ anode microstructures are investigated. Results show that tensile stresses occur in the Ni and YSZ phases whether above or below the reference temperature. The cracks propagate along the direction perpendicular to the first principal stress, showing a brittle fracture characteristic. When the microstructure is cooled, all cracks appear in YSZ phase, and almost all cracks initiate at the lowest point of YSZ–pore concave interface. When the microstructure is heated, the tensile first principal stress induces few cracks at local positions but will not make the cracks propagate continuously. The thermal mismatch between Ni and YSZ is not enough to induce cracks, and the fracture of electrode microstructure is more likely to be caused by external tensile load or the thermal mismatch between anode and electrolyte layers. The presence of Ni increases the stiffness of the microstructure, and solid phase’s disconnection reduces the strength of the microstructure.

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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-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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Dou, Zhi, Zhifang Zhou, Yefei Tan, and Yanzhang Zhou. "Numerical Study of the Influence of Cavity on Immiscible Liquid Transport in Varied-Wettability Fractures." Journal of Chemistry 2015 (2015): 1–10. http://dx.doi.org/10.1155/2015/961256.

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Field evidence indicates that cavities often occur in fractured rocks, especially in a Karst region. Once the immiscible liquid flows into the cavity, the cavity has the immiscible liquid entrapped and results in a low recovery ratio. In this paper, the immiscible liquid transport in cavity-fractures was simulated by Lattice Boltzmann Method (LBM). The interfacial and surface tensions were incorporated by Multicomponent Shan-Chen (MCSC) model. Three various fracture positions were generated to investigate the influence on the irreducible nonwetting phase saturation and displacement time. The influences of fracture aperture and wettability on the immiscible liquid transport were discussed and analyzed. It was found that the cavity resulted in a long displacement time. Increasing the fracture aperture with the corresponding decrease in displacement pressure led to the long displacement time. This consequently decreased the irreducible nonwetting phase saturation. The fracture positions had a significant effect on the displacement time and irreducible saturation. The distribution of the irreducible nonwetting phase was strongly dependent on wettability and fracture position. Furthermore, this study demonstrated that the LBM was very effective in simulating the immiscible two-phase flow in the cavity-fracture.

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Tomić, Zoran, Tomislav Jarak, Tomislav Lesičar, Nenad Gubeljak, and Zdenko Tonković. "Modelling of Fatigue Microfracture in Porous Sintered Steel Using a Phase-Field Method." Materials 16, no. 11 (June 3, 2023): 4174. http://dx.doi.org/10.3390/ma16114174.

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Porosity in sintered materials negatively affects its fatigue properties. In investigating its influence, the application of numerical simulations reduces experimental testing, but they are computationally very expensive. In this work, the application of a relatively simple numerical phase-field (PF) model for fatigue fracture is proposed for estimation of the fatigue life of sintered steels by analysis of microcrack evolution. A model for brittle fracture and a new cycle skipping algorithm are used to reduce computational costs. A multiphase sintered steel, consisting of bainite and ferrite, is examined. Detailed finite element models of the microstructure are generated from high-resolution metallography images. Microstructural elastic material parameters are obtained using instrumented indentation, while fracture model parameters are estimated from experimental S–N curves. Numerical results obtained for monotonous and fatigue fracture are compared with data from experimental measurements. The proposed methodology is able to capture some important fracture phenomena in the considered material, such as the initiation of the first damage in the microstructure, the forming of larger cracks at the macroscopic level, and the total life in a high cycle fatigue regime. However, due to the adopted simplifications, the model is not suitable for predicting accurate and realistic crack patterns of microcracks.

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Zhang, Caihong, Wenqiang Xu, Jialing Yang, Kaizhong Cao, Debing Wen, and Xusheng Wang. "Application of phase-field method in corrosion fracture of reinforced concrete." Advances in Mechanical Engineering 14, no. 6 (June 2022): 168781322211082. http://dx.doi.org/10.1177/16878132221108282.

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The phase-field method was used to simulate the propagation of concrete cracks and failure caused by corrosion and expansion of steel bars, which provides ideas for accurate simulation of the corrosion failure process of reinforced concrete (RC) and evaluation of structural durability. In this study, the entire process of corrosion and expansion of steel bars, resulting in cracks and finally falling off of the concrete protective layer, was successfully simulated. The simulation results were in good agreement with the actual observations. By setting different thicknesses of the protective layer, it was found that the thickness of the concrete protective layer had no obvious effect on limiting concrete cracks caused by the corrosion of steel bars. However, increasing the thickness of the protective layer can delay the speed of crack propagation. Simultaneously, considering the corrosion and expansion of multiple steel bars, according to the thickness of the protective layer and the spacing between the reinforcing bars, two forms of wedge-shaped cracking and laminar spalling of the protective layer are simulated. The simulation result is consistent with the actual observation phenomenon. This fully illustrates the possibility of using the phase-field method to simulate the corrosion fracture of RC and provides a reference for the engineering design and durability research of concrete structures.

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Shen, Rilin, Haim Waisman, and Licheng Guo. "Fracture of viscoelastic solids modeled with a modified phase field method." Computer Methods in Applied Mechanics and Engineering 346 (April 2019): 862–90. http://dx.doi.org/10.1016/j.cma.2018.09.018.

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Li, Yihuan, Wenyu Lai, and Yongxing Shen. "Variational h-adaption method for the phase field approach to fracture." International Journal of Fracture 217, no. 1-2 (May 30, 2019): 83–103. http://dx.doi.org/10.1007/s10704-019-00372-y.

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Triantafyllou, Savvas P., and Emmanouil G. Kakouris. "A generalized phase field multiscale finite element method for brittle fracture." International Journal for Numerical Methods in Engineering 121, no. 9 (May 15, 2020): 1915–45. http://dx.doi.org/10.1002/nme.6293.

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Bobreneva, Yulia Olegovna, Parvin Ilgar gizi Rahimly, Victoria Olegovna Podryga, Svetlana Sergeevna Bazhitova, Ahmed Elsaid Ezeldin Bakeer Ali Bakeer, and Ahmed Kamal Ibrahim Abu-Nab. "On one method of numerical modeling of a two-phase fluid system in a fractured-porous reservoir." Keldysh Institute Preprints, no. 38 (2021): 1–20. http://dx.doi.org/10.20948/prepr-2021-38.

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In this work, the authors propose an algorithm for solving the problem of the process of mass transfer of a two-phase fluid in a fractured-porous reservoir in a one-dimensional formulation. The presence of natural fractures in such reservoirs impedes various types of exploration during field development. Fractured porous reservoirs are characterized by intense exchange fluid flow between fractures and porous blocks. Each system under consideration has its own individual set of filtration-capacity parameters that complicates the problem. To study the mass transfer of a two-phase liquid in a medium with double porosity, a four-block mathematical model with splitting by physical processes is proposed. The model is described by a system of partial differential equations. The method of splitting by physical processes forms two functional blocks: by water saturation and piezoconductivity. For the numerical solution of this system, an absolutely stable implicit finite-difference scheme is made in the spatially one-dimensional case. On the basis of the proposed difference scheme, pressures and saturations in the matrix and fracture system are calculated.

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Noii, Nima, Amirreza Khodadadian, Jacinto Ulloa, Fadi Aldakheel, Thomas Wick, Stijn François, and Peter Wriggers. "Bayesian inversion for unified ductile phase-field fracture." Computational Mechanics 68, no. 4 (August 26, 2021): 943–80. http://dx.doi.org/10.1007/s00466-021-02054-w.

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AbstractThe prediction of crack initiation and propagation in ductile failure processes are challenging tasks for the design and fabrication of metallic materials and structures on a large scale. Numerical aspects of ductile failure dictate a sub-optimal calibration of plasticity- and fracture-related parameters for a large number of material properties. These parameters enter the system of partial differential equations as a forward model. Thus, an accurate estimation of the material parameters enables the precise determination of the material response in different stages, particularly for the post-yielding regime, where crack initiation and propagation take place. In this work, we develop a Bayesian inversion framework for ductile fracture to provide accurate knowledge regarding the effective mechanical parameters. To this end, synthetic and experimental observations are used to estimate the posterior density of the unknowns. To model the ductile failure behavior of solid materials, we rely on the phase-field approach to fracture, for which we present a unified formulation that allows recovering different models on a variational basis. In the variational framework, incremental minimization principles for a class of gradient-type dissipative materials are used to derive the governing equations. The overall formulation is revisited and extended to the case of anisotropic ductile fracture. Three different models are subsequently recovered by certain choices of parameters and constitutive functions, which are later assessed through Bayesian inversion techniques. A step-wise Bayesian inversion method is proposed to determine the posterior density of the material unknowns for a ductile phase-field fracture process. To estimate the posterior density function of ductile material parameters, three common Markov chain Monte Carlo (MCMC) techniques are employed: (i) the Metropolis–Hastings algorithm, (ii) delayed-rejection adaptive Metropolis, and (iii) ensemble Kalman filter combined with MCMC. To examine the computational efficiency of the MCMC methods, we employ the $$\hat{R}{-}convergence$$ R ^ - c o n v e r g e n c e tool. The resulting framework is algorithmically described in detail and substantiated with numerical examples.

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Sulistyowati, E., and A. Haris. "Integration of Borehole Image and Sonic to Evaluate Critically-Stressed Fractures to Optimize Production at FORGE Geothermal Field." Journal of Physics: Conference Series 2019, no. 1 (October 1, 2021): 012085. http://dx.doi.org/10.1088/1742-6596/2019/1/012085.

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Abstract Geothermal integration solutions as unconventional environment have workflows or methods that must be able to optimize existing data and be adapted to overcome existing challenges. The integration method consists of geology, Petrophysics and Geomechanics domains. Geological analysis to identify fractures, fracture classification, knowing the dip azimuth and the magnitude of the fracture, quantitative analysis (intensity, aperture and porosity) by using the wellbore image log. Petrophysics analysis is to distinguish open / healed fractures that analysed from sonic data. Fracture orientation analysed further for the stress calculation on fracture planes and to determine the effective fractures (most likely to flow) that has a high ratio of shear to normal stress. Geomechanical analysis in geothermal fields, among others, is to determine the dynamic permeability behaviour of fractures during the production / injection phase, determine the orientation and productive fracture interval. The integration is using FORGE well 21-31 in 8.5in section with depth interval 6,226 – 7,920 ft-MD and well 58-32 in 8.5in section with depth interval 7,390-7,527 ft-MD. Well 21-31 shows dominant fracture strike orientation to NNE-SSW, while Well 58-32 shows slightly different set strike orientation to N-S with minor striking to NE-SW and NW-SE. Evaluation of critically stressed fracture intended to have knowledge on production mechanism and based on analysis, fracture/fault that has high potential of shearing is striking to NNE-SSW and dipping to Westerly.

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Azinpour, Erfan, Jose Cesar de Sa, and Abel Dias dos Santos. "Micromechanically-motivated phase field approach to ductile fracture." International Journal of Damage Mechanics 30, no. 1 (August 16, 2020): 46–76. http://dx.doi.org/10.1177/1056789520948933.

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Utilization of the phase-field diffusive crack approach in prediction of crack evolution in materials containing voids is investigated herein. It has been established that the ductile failure occurs predominantly due to nucleation, growth and coalescence of micro-voids and micro-cavities, which lead to initiation and propagation of cracks till final material collapse. This study is an attempt to model the material internal degradation with the Rousselier pressure-dependent plasticity law, assisted with the phase field diffusive crack approach for the first time, in order to account for the post-critical softening regime. Such treatment requires the utilization of a damage evolution law and a crack initiation criterion which triggers the succeeding crack propagation, whereby a modified crack driving force based on the sequence of internal damage is employed. In numerical terms, the proposed model is integrated within a fully-staggered framework for the mechanical and diffusive fields and is implemented via the finite element method. The verification tests on the model is processed by several examples with the focus on both qualitative monitoring of pathological crack patterns and the quantitative analysis on the material response, particularly in the post-critical range, complemented by relevant comparisons with the existing data from literature.

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Cui, Haitao, Chenyu Du, and Hongjian Zhang. "Applications of Phase Field Methods in Modeling Fatigue Fracture and Performance Improvement Strategies: A Review." Metals 13, no. 4 (April 5, 2023): 714. http://dx.doi.org/10.3390/met13040714.

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Fatigue fracture simulation based on phase field methods is a promising numerical approach. As a typical continuum approach, phase field methods can naturally simulate complex fatigue fracture behavior. Moreover, the cracking is a natural result of the simulation without additional fracture criterion. This study first introduced the phase field fracture principle, then reviewed some recent advances in phase field methods for fatigue fracture modeling, and gave representative examples in macroscale, microscale, and multiscale structural simulations. In addition, some strategies to improve the performance of phase field models were summarized from different perspectives. The applications of phase field methods to fatigue failure demonstrate the ability to handle complex fracture behaviors under multiple loading forms and their interactions, and the methods have great potential for development. Finally, an outlook was made in four aspects: loading form, fatigue degradation criterion, coupled crystal plasticity, and performance improvement.

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Chang, Ningdong, Jinan Wang, and Fei Li. "Research on Crack Propagation of Deep Geologic Mass Disturbed by Excavation Based on Phase Field Method." Geofluids 2022 (May 9, 2022): 1–13. http://dx.doi.org/10.1155/2022/5791006.

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In recent years, the phase field fracture model has been widely studied and applied. It has good convergence in crack propagation simulation. Comparing with other methods, the phase field method has advantages in simulating crack intersection, bifurcation, and three-dimensional propagation. Based on the phase field method, the influence of excavation disturbance on crack initiation of rock mass is realized in this paper. The phase field fracture variational model is built by using user-defined element interface (UEL) and user material subroutine (UMAT) in ABAQUS. Firstly, the prefabricated crack propagation simulation is carried out to verify the algorithm. The fracture initiates in a butterfly shape and then expands along the horizontal direction. The results show that the maximum support reaction decreases with the gradual increase of l , which is compared with the results obtained by Miehe et al. The result proved the correctness and reliability of the algorithm. In this paper, the phase field fracture model of a flat plate with a reserved small hole under the upper tension is established. The results show that the crack finally produces a crack in the lower left and upper right directions of the square hole and continues to extend to the model boundary, which proves the feasibility of crack independent initiation and propagation by the phase field method. The stress formed a butterfly region until the fracture occurs. And the butterfly stress distribution was still present at the end of crack propagation. The maximum vertical stress was 1.7 × 103 MPa. Based on the South-to-North Water Transfer Project, the simulation of tunnel crack propagation under excavation disturbance is realized for the first time, which is based on the phase field method. The results show that the influence area of excavation disturbance will increase after considering crack development. Comparing the simulation results without considering crack propagation with the simulation results considering crack propagation, it is found that the stress level in the excavation disturbance area around the tunnel is greatly affected by cracks. When the crack is not considered, the maximum vertical stress is 2.16 × 105 Pa, and the maximum horizontal stress is 9.35 × 105 Pa, which occurs at the waist of the tunnel on the horizontal axis. When the crack is considered, the maximum vertical stress is 2.53 × 105 Pa, and the maximum horizontal stress is 1.10 × 106 Pa. It shows that the stress at the dome increases greatly. The vertical stress reaches 3.68 × 105 Pa, and the horizontal stress is up to 3.07 × 103 Pa. For the rock mass far away from the excavation disturbance area, because part of the elastic strain energy is absorbed by the surface crack, the stress level considering the crack is lower than that without the crack. But it is basically similar, indicating the accuracy of the phase field fracture model. This paper realizes the simulation of crack propagation under excavation disturbance and provides a way for the application of phase field fracture model in rock mechanics. This paper proves that phase field method has broad prospects in simulating rock crack propagation and provides the possibility for the popularization of phase field method.

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Navidtehrani, Yousef, Covadonga Betegón, and Emilio Martínez-Pañeda. "A simple and robust Abaqus implementation of the phase field fracture method." Applications in Engineering Science 6 (June 2021): 100050. http://dx.doi.org/10.1016/j.apples.2021.100050.

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Feng, Ye, and Jie Li. "Phase-field method with additional dissipation force for mixed-mode cohesive fracture." Journal of the Mechanics and Physics of Solids 159 (February 2022): 104693. http://dx.doi.org/10.1016/j.jmps.2021.104693.

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Zhao, Zipeng, Kemeng Huang, Chen Li, Changbo Wang, and Hong Qin. "A Novel Plastic Phase‐Field Method for Ductile Fracture with GPU Optimization." Computer Graphics Forum 39, no. 7 (October 2020): 105–17. http://dx.doi.org/10.1111/cgf.14130.

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Yin, B. B., and L. W. Zhang. "Phase field method for simulating the brittle fracture of fiber reinforced composites." Engineering Fracture Mechanics 211 (April 2019): 321–40. http://dx.doi.org/10.1016/j.engfracmech.2019.02.033.

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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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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 (July 9, 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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Mittermeir, Georg M. "Material-Balance Method for Dual-Porosity Reservoirs With Recovery Curves To Model the Matrix/Fracture Transfer." SPE Reservoir Evaluation & Engineering 18, no. 02 (February 9, 2015): 171–86. http://dx.doi.org/10.2118/174082-pa.

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Summary This paper presents a material-balance (MB) method applicable to naturally fractured dual-porosity reservoirs by considering the matrix/fracture transfer. The method is based on the recognition that the performance of water and gas displacement from matrix blocks can be depicted in the form of recovery factor vs. time. These recovery curves determine the matrix/fracture oil transfer. The reservoir pressure change depends on the original fluids in place and the strength of the aquifer. Thus, a close relationship between the recovery curves and the observed reservoir state (e.g., pressure, position of the phase contacts, water cut, and gas/oil ratio), the aquifer parameters, and the matrix/fracture oil transfer exists. Concerning the matrix blocks, the surrounding fracture continuum sets the boundary conditions by acting as an injector. The injection rates are predefined by the provided recovery curves, which one can obtain with different methods. They can be calculated by fine-scale single matrix-block models (Pirker et al. 2007), derived from conventional full-field numerical models, measured in a laboratory autoclave (Mattax and Kyte 1962), or determined by theoretical means (Davis and Hill 1982). The recovery curves can be scaled and normalized, making them applicable within a certain rock type to a wide range of rock parameters, namely shape factor, permeability, and porosity (Amiry 2014). While in a full-field model, various rock types can be identified; in MB calculations, however, they must be reduced to a single rock type. MB calculations—irrespective of conventional single-porosity methods or the herein-presented approach for dual-porosity naturally fractured reservoirs—are always conducted on a homogenized reservoir model. Therefore, variations in rock and pressure/volume/temperature properties cannot be taken into account. The recovery process is governed by two parameters—the asymptotic value of the recovery function and the time-scaling factor. These two parameters can be used for matching the observed reservoir performance. The new MB method matches both the reservoir pressure and the positions of the phase contacts. It also provides aquifer and matrix/fracture fluid-transfer models. Applying the parameters of those models in prediction mode and assuming a future production strategy, reservoir-pressure decline and phase-contact movements can be forecasted. The paper presents the calculation schema and the successful application to a field with more than 500 million STB of original oil in place and a 35-year production history. For the first time, it becomes possible to realistically—this means by fully considering the governing recovery mechanisms and thus the matrix/fracture transfer—calculate MB for naturally fractured dual-porosity reservoirs.

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Leggett, Smith Edward, Ding Zhu, and Alfred Daniel Hill. "Thermal Effects on Far-Field Distributed Acoustic Strain-Rate Sensors." SPE Journal 27, no. 02 (November 23, 2021): 1036–48. http://dx.doi.org/10.2118/205178-pa.

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Summary Fiber-optic cables cemented outside of the casing of an unconventional well measure crosswell strain changes during fracturing of neighboring wells with low-frequency distributed acoustic sensing (LF-DAS). As a hydraulic fracture intersects an observation well instrumented with fiber-optic cables, the fracture fluid injected at ambient temperatures can cool a section of the sensing fiber. Often, LF-DAS and distributed temperature sensing (DTS) cables are run in tandem, enabling the detection of such cooling events. The increasing use of LF-DAS for characterizing unconventional hydraulic fracture completions demands an investigation of the effects of temperature on the measured strain response by LF-DAS. Researchers have demonstrated that LF-DAS can be used to extract the temporal derivative of temperature for use as a differential-temperature-gradient sensor. However, differential-temperature-gradient sensing is predicated on the ability to filter strain components out of the optical signal. In this work, beginning with an equation for optical phase shift of LF-DAS signals, a model relating strain, temperature, and optical phase shift is explicitly developed. The formula provides insights into the relative strength of strain and temperature effects on the phase shift. The uncertainty in the strain-rate measurements due to thermal effects is estimated. The relationship can also be used to quantify uncertainties in differential-temperature-gradient sensors due to strain perturbations. Additionally, a workflow is presented to simulate the LF-DAS response accounting for both strain and temperature effects. Hydraulic fracture geometries are generated with a 3D fracture simulator for a multistage unconventional completion. The fracture width distributions are imported by a displacement discontinuity method (DDM) program to compute the strain rates along an observation well. An analytic model is used to approximate the temperature in the fracture. Using the derived formulae for optical phase shift, the model outputs are then used to compute the LF-DAS response at a fiber-optic cable, enabling the generation of waterfall plots including both strain and thermal effects. The model results suggest that before, during, and immediately following a fracture intersecting a well instrumented with fiber, the strain on the fiber drives the LF-DAS signal. However, at later times, as completion fluid cools the observation well, the temperature component of the LF-DAS signal can be equal to or exceed the strain component. The modeled results are compared to a published field case in an attempt to enhance the interpretation of LF-DAS waterfall plots. Finally, we propose a sensing configuration to identify the events when “wet fractures” (fractures with fluids) intersect the observation well.

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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 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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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 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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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 (July 17, 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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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 (June 8, 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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Huang, Kai, Jia Yan, Rilin Shen, Yulin Wan, Yukun Li, Hao Ge, Hongjun Yu, and Licheng Guo. "Investigation on fracture behavior of polymer-bonded explosives under compression using a viscoelastic phase-field fracture method." Engineering Fracture Mechanics 266 (May 2022): 108411. http://dx.doi.org/10.1016/j.engfracmech.2022.108411.

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Gong, Xun, Xinhua Ma, Yuyang Liu, and Guanfang Li. "Advances in Hydraulic Fracture Propagation Research in Shale Reservoirs." Minerals 12, no. 11 (November 12, 2022): 1438. http://dx.doi.org/10.3390/min12111438.

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The characterization of artificial fracture propagation law in the fracturing process of shale reservoirs is the basis for evaluating the fracture conductivity and a key indicator of the reservoir stimulated effect. In order to improve the fracture stimulated volume of shale reservoirs, this paper systematically discusses the current status of research on artificial fracture propagation law from the research methods and main control factors and provides an outlook on its future development direction. The analysis finds that the study of fracture propagation law by using indoor physical simulation experiments has the advantages of simple operation and intuitive image, and the introduction of auxiliary technologies such as acoustic emission monitoring and CT scanning into indoor physical model experiments can correct the experimental results so as to better reveal the propagation mechanism of artificial fractures. At present, the numerical simulation methods commonly used to study the propagation law of artificial fractures include the finite element method, extended finite element method, discrete element method, boundary element method and phase field method, etc. The models established based on these numerical simulation methods have their own advantages and applicability, so the numerical algorithms can be integrated and the numerical methods selected to model and solve the different characteristics of the propagation law of artificial fractures in different regions at different times can greatly improve the accuracy of the model solution and better characterize the propagation law of artificial fractures. The propagation law of artificial fracture in the fracturing process is mainly influenced by geological factors and engineering factors, so when conducting research, geological factors should be taken as the basis, and through detailed study of geological factors, the selection of the fracturing process can be guided and engineering influencing factors can be optimized.

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Li, Yicong, Tiantang Yu, and Sundararajan Natarajan. "An adaptive isogeometric phase-field method for brittle fracture in rock-like materials." Engineering Fracture Mechanics 263 (March 2022): 108298. http://dx.doi.org/10.1016/j.engfracmech.2022.108298.

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Journal articles on the topic 'Phase field fracture method'

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