Relevant bibliographies by topics / Phase field fracture method

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Academic literature on the topic 'Phase field fracture method'

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Published: 15 June 2023

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Journal articles on the topic "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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Dissertations / Theses on the topic "Phase field fracture method"

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Deogekar, Sai Sharad. "A Computational Study of Dynamic Brittle Fracture Using the Phase-Field Method." University of Cincinnati / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1439455086.

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Nigro, Claudio F. "Phase field modeling of flaw-induced hydride precipitation kinetics in metals." Licentiate thesis, Malmö högskola, Institutionen för materialvetenskap och tillämpad matematik (MTM), 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:mau:diva-7787.

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Hydrogen embrittlement can manifest itself as hydride formation in structures when in contact with hydrogen-rich environments, e.g. in space and nuclear power applications. To supplant experimentation, modeling of such phenomena is beneficial to make life prediction reduce cost and increase the understanding. In the present work, two different approaches based on phase field theory are employed to study the precipitation kinetics of a second phase in a metal, with a special focus on the application of hydride formation in hexagonal close-packed metals. For both presented models, a single component of the non-conserved order parameter is utilized to represent the microstructural evolution. Throughout the modelling the total free energy of the system is minimized through the time-dependent Ginzburg-Landau equation, which includes a sixth order Landau potential in the first model, whereas one of fourth order is used for the second model. The first model implicitly incorporates the stress field emanating from a sharp crack through the usage of linear elastic fracture mechanics and the governing equation is solved numerically for both isotropic and anisotropic bodies by usage of the finite volume method. The second model is applied to plate and notched cantilever geometries, and it includes an anisotropic expansion of the hydrides that is caused by the hydride precipitation. For this approach, the mechanical and phase transformation aspects are coupled and solved simultaneously for an isotropic material using the finite element method. Depending on the Landau potential coefficients and the crack-induced hydrostatic stress, for the first model the second-phase is found to form in a confined region around the crack tip or in the whole material depending on the material properties. From the pilot results obtained with the second model, it is shown that the applied stress and considered anisotropic swelling induces hydride formation in preferential directions and it is localized in high stress concentration areas. The results successfully demonstrate the ability of both approaches to model second-phase formation kinetics that is triggered by flaw-induced stresses and their capability to reproduce experimentally observed hydride characteristics such as precipitation location, shape and direction.
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Wu, Yi. "Topology optimization in structural dynamics : vibrations, fracture resistance and uncertainties." Thesis, Paris Est, 2022. http://www.theses.fr/2022PESC2007.

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L'objectif de cette thèse est de développer des méthodes d'optimisation topologiques basées sur la densité pour plusieurs problèmes difficiles de structure en dynamique. Premièrement, nous proposons une stratégie de normalisation en élasto-dynamique en vue d'obtenir une distribution optimale de matériau dans la structure qui réduit la réponse aux excitations dynamiques en fréquence et améliore la stabilité numérique dans la méthode BESO (bi-directional evolutionary structural optimisation). Ensuite, pour décrire les incertitudes de paramètres pouvant intervenir dans des problèmes réalistes en ingénierie, un modèle d'incertitudes à intervalle hybride est développé pour prendre en compte les incertitudes dans le problème d'optimisation en dynamique. Une méthode de perturbation est développée pour une optimisation topologique robuste vis-à-vis des incertitudes et permettant des gains de temps de calculs importants. De plus, nous introduisons un modèle d'incertitude de champ d'intervalle dans ce cadre. L'approche est appliquée à l'optimisation topologique des structures mono-matériaux, composites et multi-échelles. Enfin, nous développons un cadre d'optimisation topologique pour la résistance des structures à la fissuration quasi-fragile dans un cadre dynamique, par combinaison avec la méthode de champs de phase. Ce cadre est étendu à la conception de structures résistantes à des impacts. Contrairement aux approches basées sur les contraintes, la totalité de la propagation des fissures est prise en compte dans le processus d'optimisation
The objective of this thesis is to develop density based-topology optimization methods for several challenging dynamic structural problems. First, we propose a normalization strategy for elastodynamics to obtain optimized material distributions of the structures that reduces frequency response and improves the numerical stabilities of the bi-directional evolutionary structural optimization (BESO). Then, to take into account uncertainties in practical engineering problems, a hybrid interval uncertainty model is employed to efficiently model uncertainties in dynamic structural optimization. A perturbation method is developed to implement an uncertainty-insensitive robust dynamic topology optimization in a form that greatly reduces the computational costs. In addition, we introduce a model of interval field uncertainty into dynamic topology optimization. The approach is applied to single material, composites and multi-scale structures topology optimization. Finally, we develop a topology optimization for dynamic brittle fracture structural resistance, by combining topology optimization with dynamic phase field fracture simulations. This framework is extended to design impact-resistant structures. In contrast to stress-based approaches, the whole crack propagation is taken into account into the optimization process
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Li, Tianyi. "Gradient-damage modeling of dynamic brittle fracture : variational principles and numerical simulations." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLX042/document.

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Une bonne tenue mécanique des structures du génie civil en béton armé sous chargements dynamiques sévères est primordiale pour la sécurité et nécessite une évaluation précise de leur comportement en présence de propagation dynamique de fissures. Dans ce travail, on se focalise sur la modélisation constitutive du béton assimilé à un matériau élastique-fragile endommageable. La localisation des déformations sera régie par un modèle d'endommagement à gradient où un champ scalaire réalise une description régularisée des phénomènes de rupture dynamique. La contribution de cette étude est à la fois théorique et numérique. On propose une formulation variationnelle des modèles d'endommagement à gradient en dynamique. Une définition rigoureuse de plusieurs taux de restitution d'énergie dans le modèle d'endommagement est donnée et on démontre que la propagation dynamique de fissures est régie par un critère de Griffith généralisé. On décrit ensuite une implémentation numérique efficace basée sur une discrétisation par éléments finis standards en espace et la méthode de Newmark en temps dans un cadre de calcul parallèle. Les résultats de simulation de plusieurs problèmes modèles sont discutés d'un point de vue numérique et physique. Les lois constitutives d'endommagement et les formulations d'asymétrie en traction et compression sont comparées par rapport à leur aptitude à modéliser la rupture fragile. Les propriétés spécifiques du modèle d'endommagement à gradient en dynamique sont analysées pour différentes phases de l'évolution de fissures : nucléation, initiation, propagation, arrêt, branchement et bifurcation. Des comparaisons avec les résultats expérimentaux sont aussi réalisées afin de valider le modèle et proposer des axes d'amélioration
In civil engineering, mechanical integrity of the reinforced concrete structures under severe transient dynamic loading conditions is of paramount importance for safety and calls for an accurate assessment of structural behaviors in presence of dynamic crack propagation. In this work, we focus on the constitutive modeling of concrete regarded as an elastic-damage brittle material. The strain localization evolution is governed by a gradient-damage approach where a scalar field achieves a smeared description of dynamic fracture phenomena. The contribution of the present work is both theoretical and numerical. We propose a variationally consistent formulation of dynamic gradient damage models. A formal definition of several energy release rate concepts in the gradient damage model is given and we show that the dynamic crack tip equation of motion is governed by a generalized Griffith criterion. We then give an efficient numerical implementation of the model based on a standard finite-element spatial discretization and the Newmark time-stepping methods in a parallel computing framework. Simulation results of several problems are discussed both from a computational and physical point of view. Different damage constitutive laws and tension-compression asymmetry formulations are compared with respect to their aptitude to approximate brittle fracture. Specific properties of the dynamic gradient damage model are investigated for different phases of the crack evolution: nucleation, initiation, propagation, arrest, kinking and branching. Comparisons with experimental results are also performed in order to validate the model and indicate its further improvement
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Goswami, Somdatta [Verfasser], Timon [Akademischer Betreuer] Rabczuk, Stephane [Gutachter] Bordas, and Magd Abel [Gutachter] Wahab. "Phase field modeling of fracture with isogeometric analysis and machine learning methods / Somdatta Goswami ; Gutachter: Stephane Bordas, Magd Abel Wahab ; Betreuer: Timon Rabczuk." Weimar : Bauhaus-Universität Weimar, 2021. http://d-nb.info/122878924X/34.

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Kramer, Sharlotte Lorraine Bolyard Ravichandran G. (Guruswami) Ravichandran G. (Guruswami) Bhattacharya Kaushik. "Phase-shifting full-field interferometric methods for in-plane tensorial stress determination for fracture studies /cSharlotte Lorraine Bolyard Kramer ; Guruswami Ravichandran, committee chair and advisor ; Kaushik Bhattacharya, co-advisor." Diss., Pasadena, Calif. : California Institute of Technology, 2009. http://resolver.caltech.edu/CaltechETD:etd-05272009-094456.

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Agrawal, Vaibhav. "Multiscale Phase-field Model for Phase Transformation and Fracture." Research Showcase @ CMU, 2016. http://repository.cmu.edu/dissertations/850.

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We address two problems in this thesis. First, a phase-field model for structural phase transformations in solids and second, a model for dynamic fracture. The existing approaches for both phase transformations and fracture can be grouped into two categories. Sharp-interface models, where interfaces are singular surfaces; and regularized-interface models, such as phase-field models, where interfaces are smeared out. The former are challenging for numerical solutions because the interfaces or crack needs to be explicitly tracked, but have the advantage that the kinetics of existing interfaces or cracks and the nucleation of new interfaces can be transparently and precisely prescribed. The diffused interface models such as phasefield models do not require explicit tracking of interfaces and makes them computationally attractive. However, the specification of kinetics and nucleation is both restrictive and extremely opaque in such models. This prevents straightforward calibration of phase-field models to experiment and/or molecular simulations, and breaks the multiscale hierarchy of passing information from atomic to continuum. Consequently, phase-field models cannot be confidently used in dynamic settings. We present a model which has all the advantages of existing phase-field models but also allows us to prescribe kinetics and nucleation criteria. We present a number of examples to characterize and demonstrate the features of the model. We also extend it to the case of multiple phases where preserving kinetics of each kind of interface is more complex. We use the phase transformation model with certain changes to model dynamic fracture. We achieve the advantage of prescribing nucleation and kinetics independent of each other. We demonstrate examples of anisotropic crack propagation and crack propagation on an interface in a composite material. We also report some limitations of phase-field models for fracture which have not been mentioned in the existing literature. These limitations include dependence of effective crack width and hence the effective surface energy on the crack speed, lack of a reasonable approximation for the mechanical response of cracked region and inability to model large deformations.
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Riad, Soukaina. "Vers une modélisation de la corrosion sous contrainte assistée par l'irradiation du superalliage 718." Electronic Thesis or Diss., Ecole centrale de Nantes, 2022. http://www.theses.fr/2022ECDN0039.

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Le superalliage base nickel 718 est réputé pour présenter une excellente tenue à la corrosion, une très forte résistancemécanique et une bonne tenue sous irradiation. De ce fait, il s’agit d’un matériau de choix au sein d’un réacteur électronucléaire pour les pièces soumises à des sollicitations extrêmes (ressorts, systèmes de maintien. . . ).Pourtant des ruptures en service ont été observées de ce matériau sous le phénomène de corrosion sous contraintes assistée par l’irradiation. La présente thèse vise à apporter de nouveaux éléments de compréhension de ce phénomène complexe sous l’angle de la modélisation numérique. Le processus de fissuration par corrosion sous contrainte est modélisé par la méthode des champs de phase. Une implémentation unifiée, apte à traiter lesfissurations intra et intergranulaires, est proposée et permet de coupler efficacement différentes échelles de travail (du milieu continu au polycristal) et différents physiques (mécanique des milieux continus et généralisés et oxydation interne). Cette modélisation permet de proposer des simulations des étapes complexes de la corrosion sous contrainte, à savoirl’amorçage, la coalescence et la propagation
Inconel 718 alloy is renowned for having excellent corrosion resistance, very high mechanical strength and good resistance to irradiation. Thus, it is a material of choice within a nuclear power reactor for parts subjected to extreme stresses (springs, retaining systems,...). However, failures in service have been observed in this material under irradiationassisted stress corrosion cracking phenomenon. This thesis aims to bring new elements of understanding of this complex phenomenon from the point of view of numerical modeling. The stress corrosion cracking process is modeled by the phase field fracture method. A unified implementation, able to deal with inter and intergranular fracture, is proposedand allows to couple efficiently different scales of work (from continuous medium to polycrystal) and different physics (mechanics of continuous and generalized media and internal oxidation). This modeling allows to propose simulations of the complex stages of stress corrosion cracking, namely initiation, coalescence and propagation
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Abdollahi, Amir. "Phase-field modeling of fracture in ferroelectric materials." Doctoral thesis, Universitat Politècnica de Catalunya, 2012. http://hdl.handle.net/10803/285833.

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The unique electro-mechanical coupling properties of ferroelectrics make them ideal materials for use in micro-devices as sensors, actuators and transducers. Nevertheless, because of the intrinsic brittleness of ferroelectrics, the optimal design of the electro-mechanical devices is strongly dependent on the understanding of the fracture behavior in these materials. Fracture processes in ferroelectrics are notoriously complex, mostly due to the interactions between the crack tip stress and electric fields and the localized switching phenomena in this zone (formation and evolution of domains of different crystallographic variants). Phase-field models are particularly interesting for such a complex problem, since a single partial differential equation governing the phase-field accomplishes at once (1) the tracking of the interfaces in a smeared way (cracks, domain walls) and (2) the modeling of the interfacial phenomena such as domain-wall energies or crack face boundary conditions. Such a model has no difficulty for instance in describing the nucleation of domains and cracks or the branching and merging of cracks. Furthermore, the variational nature of these models makes the coupling of multiple physics (electrical and mechanical fields in this case) very natural. The main contribution of this thesis is to propose a phase-field model for the coupled simulation of the microstructure formation and evolution, and the nucleation and propagation of cracks in single crystal ferroelectric materials. The model naturally couples two existing energetic phase-field approaches for brittle fracture and ferroelectric domain formation and evolution. The finite element implementation of the theory is described. Simulations show the interactions between the microstructure and the crack under mechanical and electro-mechanical loadings. Another objective of this thesis is to encode different crack face boundary conditions into the phase-field framework since these conditions strongly affect the fracture behavior of ferroelectrics. The smeared imposition of these conditions are discussed and the results are compared with that of sharp crack models to validate the proposed approaches. Simulations show the effects of different conditions, electro-mechanical loadings and media filling the crack gap on the crack propagation and the microstructure of the material. In a third step, the coupled model is modified by introducing a crack non-interpenetration condition in the variational approach to fracture accounting for the asymmetric behavior in tension and compression. The modified model makes it possible to explain anisotropic crack growth in ferroelectrics under Vickers indentation loading. This model is also employed for the fracture analysis of multilayer ferroelectric actuators, which shows the potential of the model for future application. The coupled phase-field model is also extended to polycrystals by introducing realistic polycrystalline microstructures in the model. Inter- and trans-granular crack propagation modes are observed in the simulations. Finally and for completeness, the phase-field theory is extended for the simulation of conducting cracks and some preliminary simulations are also performed in three dimensions. Salient features of the crack propagation phenomenon predicted by the simulations of this thesis are directly compared with experimental observations.
Los materiales ferroeléctricos poseen únicas propiedades electro-mecánicas y por eso se utilizan para los micro-dispositivos como sensores, actuadores y transductores. No obstante, debido a la fragilidad intrínseca de los ferroeléctricos, el diseño óptimo de los dispositivos electro-mecánicos es altamente dependiente de la comprensión del comportamiento de fractura en estos materiales. Los procesos de fractura en ferroeléctricos son notoriamente complejos, sobre todo debido a las interacciones entre campos de tensión y eléctricos y los fenómenos localizados en zona de fractura (formación y evolución de los dominios de las diferentes variantes cristalográficas). Los modelos de campo de fase son particularmente útiles para un problema tan complejo, ya que una sola ecuación diferencial parcial que gobierna el campo de fase lleva a cabo a la vez (1) el seguimiento de las interfaces de una manera suave (grietas, paredes de dominio) y (2) la modelización de los fenómenos interfaciales como las energías de la pared de dominio o las condiciones de las caras de grieta. Tal modelo no tiene ninguna dificultad, por ejemplo en la descripción de la nucleación de los dominios y las grietas o la ramificación y la fusión de las grietas. Además, la naturaleza variacional de estos modelos facilita el acoplamiento de múltiples físicas (campos eléctricos y mecánicos en este caso). La principal aportación de esta tesis es la propuesta de un modelo campo de fase para la simulación de la formación y evolución de la microestructura y la nucleación y propagación de grietas en materiales ferroeléctricos. El modelo aúna dos modelos de campo de fase para la fractura frágil y para la formación de dominios ferroeléctricos. La aplicación de elementos finitos a la teoría es descrita. Las simulaciones muestran las interacciones entre la microestructura y la fractura del bajo cargas mecánicas y electro-mecánicas. Otro de los objetivos de esta tesis es la codificación de diferentes condiciones de contorno de grieta porque estas condiciones afectan en gran medida el comportamiento de la fractura de ferroeléctricos. La imposición de estas condiciones se discuten y se comparan con los resultados de modelos clasicos para validar los modelos propuestos. Las simulaciones muestran los efectos de diferentes condiciones, cargas electro-mecánicas y medios que llena el hueco de la grieta en la propagación de las fisuras y la microestructura del material. En un tercer paso, el modelo se modifica mediante la introducción de una condición que representa el comportamiento asimétrico en tensión y compresión. El modelo modificado hace posible explicar el crecimiento de la grieta anisotrópica en ferroeléctricos. Este modelo también se utiliza para el análisis de la fractura de los actuadores ferroeléctricos, lo que demuestra el potencial del modelo para su futura aplicación. El modelo se extiende también a policristales mediante la introducción de microestructuras policristalinas realistas en el modelo. Modos de fractura inter y trans-granulares de propagación se observan en las simulaciones. Por último y para completar, la teoría del campo de fase se extiende para la simulación de las grietas conductivas y algunas simulaciones preliminares también se realizan en tres dimensiones. Principales características del fenómeno de la propagación de la grieta predicho por las simulaciones de esta tesis se comparan directamente con las observaciones experimentales.
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Muixí, Ballonga Alba. "Locally adaptive phase-field models and transition to fracture." Doctoral thesis, Universitat Politècnica de Catalunya, 2020. http://hdl.handle.net/10803/669747.

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This thesis proposes a new computational model for the efficient simulation of crack propagation, through the combination of a phase-field model in small subdomains around crack tips and a discontinuous model in the rest of the domain. The combined model inherits the advantages of both approaches. The phase-field model determines crack propagation at crack tips, and the discontinuous model explicitly describes the crack elsewhere, enabling to use a coarser discretization and thus reducing the computational cost. In crack-tip subdomains, the discretization is refined to capture the phase-field solution, while in the discontinuous part, sharp cracks are incorporated into the coarse background discretization by the eXtended Finite Element Method (XFEM). As crack-tip subdomains move with crack growth, the discretization is automatically updated and phase-field bands are replaced by sharp cracks in the wake of cracks. The first step is the development of an adaptive refinement strategy for phase-field models. To this end, two alternatives are proposed. Both of them consider two types of elements, standard and refined, which are mapped into a fixed background mesh. In refined elements, the space of approximation is uniformly $h$-refined. Continuity between elements of different type is imposed in weak form to handle the non-conformal approximations in a natural way, without spreading of refinement nor having to deal with hanging nodes, leading to a very local refinement along cracks. The first adaptive strategy relies on a Hybridizable Discontinuous Galerkin (HDG) formulation of the problem, in which continuity between elements is imposed in weak form. The second one is based on a more efficient Continuous Galerkin (CG) formulation; a continuous FEM approximation is used in the standard and refined regions and, then, continuity on the interface between regions is imposed in weak form by Nitsche's method. The proposed strategies robustly refine the discretization as cracks propagate and can be easily incorporated into a working code for phase-field models. However, the computational cost can be further reduced by transitioning to the discontinuous in the combined model. In the wake of crack tips, the phase-field diffuse cracks are replaced by XFEM discontinuous cracks and elements are derefined. The combined model is studied within the adaptive CG formulation. Numerical experiments include branching and coalescence of cracks, and a fully 3D test.
En aquesta tesi es proposa un nou model computacional per a simular la propagació de fractures de manera eficient, a partir de la combinació d’un model de camp de fase en petits subdominis al voltant dels extrems de les fissures, i d’un model discontinu a la resta del domini. El model combinat manté els avantatges de tots dos tipus de model. El model continu determina la propagació de la fissura, i el model discontinu descriu explícitament la fissura en gairebé tot del domini, amb una discretització més grollera i el conseqüent estalvi en cost computacional. Als subdominis de camp de fase, la discretització es refina per tal d’aproximar bé la solució, mentre que a la part discontínua, les fissures s’incorporen a la discretització grollera a partir de l’eXtended Finite Element Method (XFEM). A mesura que les fissures es propaguen pel domini, la discretització s’actualitza automàticament i, lluny dels extrems, la representació suavitzada de les fissures a partir del camp de fase es reemplaça per una representació discontínua. El primer pas és definir una estratègia de refinament adaptatiu pels models continus de camp de fase. En aquesta tesi es proposen dues alternatives diferents. Totes dues consideren dos tipus d’elements, estàndards i refinats, que es mapen a la malla inicial. Als elements refinats, l’espai d’aproximació es refina uniformement. La continuïtat entre elements de tipus diferent s’imposa en forma feble per facilitar el tractament de les aproximacions no conformes, sense que s’escampi el refinament ni haver d’imposar restriccions als nodes de la interfície, donant lloc a un refinament molt localitzat. La primera estratègia adaptativa es basa en una formulació Hybridizable Discontinuous Galerkin (HDG) del problema, que imposa continuïtat entre elements en forma feble. La segona es basa en una formulació contínua més eficient; es fa servir una aproximació contínua del Mètode dels Elements Finits a les regions estàndards i refinades i, aleshores, a la interfície entre les dues regions s’imposa la continuïtat en forma feble amb el mètode de Nitsche. Les estratègies adaptatives refinen la discretització a mesura que les fissures es propaguen, i es poden afegir a un codi per a models de camp de fase de manera senzilla. No obstant, el cost computacional es pot reduir encara més fent servir el model combinat. Lluny dels extrems de les fissures, la representació suavitzada del camp de fase es substitueix per discontinuïtats en una discretització de XFEM, i els elements es desrefinen. El model combinat es formula a partir de l’estratègia adaptativa contínua. Els exemples numèrics inclouen bifurcació i coalescència de fissures, i un exemple en 3D.
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Books on the topic "Phase field fracture method"

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Miguel Torre do Vale Arriaga e Cunha. Stability Analysis of Metals Capturing Brittle and Ductile Fracture through a Phase Field Method and Shear Band Localization. [New York, N.Y.?]: [publisher not identified], 2016.

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service), SpringerLink (Online, ed. Field Theoretic Method in Phase Transformations. New York, NY: Springer New York, 2012.

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Umantsev, Alexander. Field Theoretic Method in Phase Transformations. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-1487-2.

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Corsi, Daniele, and Cèlia Nadal Pasqual. Studi Iberici. Dialoghi dall’Italia. Venice: Fondazione Università Ca’ Foscari, 2021. http://dx.doi.org/10.30687/978-88-6969-505-6.

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Iberian Studies have developed in the last quarter of a century to the point of making one speak of a real Iberian Turn. Starting from the rejection of the classic scheme that places the two states (Portugal and Spain) as privileged agents of the representation of the Iberian space, the proposal of the Iberian Studies is to work on the system of historical exchanges and interferences that have shaped the cultural fabric of the peninsula, investigating both the points of connection as much as those of the fracture between its different realities (such as the Basque, Catalan and Galician ones, as well as the Castilian and Lusitanian ones). Accompanied by a “Reasoned Bibliography on Iberian Studies and Iberian Studies from Italy”, this volume examines the state of the art, with particular attention to the Italian context, in which these researches show a still unequal rooting and diffusion. A first section, dedicated to a general framework of the discipline and the exposition of theoretical issues and method problems, is followed by a second that presents critical contributions that address individual case studies. Born in part as a reaction to the so-called “crisis of Hispanism”, Iberian Studies offer themselves as an alternative to the traditional model of peninsular Hispanism, to its uninational and monolingual paradigm. They also place the emphasis on diversity and the relational aspect, looking with suspicion at every hegemonic design aimed at establishing a “centre” within a heterogeneous cultural landscape. Attentive to the phenomena of immigration and linguistic minorities, to the colonial past and relations with the Latin American world, but also to the themes of comparativism, translation, theory and the rethinking of criticism, Iberian Studies are a field in which not only debates about literature and the arts are included, but also about ideology.
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Mazo, Aleksandr, and Konstantin Potashev. The superelements. Modeling of oil fields development. ru: INFRA-M Academic Publishing LLC., 2020. http://dx.doi.org/10.12737/1043236.

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This monograph presents the basics of super-element modeling method of two-phase fluid flows occurring during the development of oil reservoir. The simulation is performed in two stages to reduce the spatial and temporal scales of the studied processes. In the first stage of modeling of development of oil deposits built long-term (for decades) the model of the global dynamics of the flooding on the super-element computational grid with a step equal to the average distance between wells (200-500 m). Local filtration flow, caused by the action of geological and technical methods of stimulation, are modeled in the second stage using a special mathematical models using computational grids with high resolution detail for the space of from 0.1 to 10 m and time — from 102 to 105 C. The results of application of the presented models to the solution of practical tasks of development of oil reservoir. Special attention is paid to the issue of value transfer in filtration-capacitive properties of the reservoir, with a detailed grid of the geological model on the larger grid reservoir models. Designed for professionals in the field of mathematical and numerical modeling of fluid flows occurring during the development of oil fields and using traditional commercial software packages, as well as developing their own software. May be of interest to undergraduate and graduate students studying in areas such as "Mechanics and mathematical modeling", "Applied mathematics", "Oil and gas".
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Wick, Thomas. Multiphysics Phase-Field Fracture: Modeling, Adaptive Discretizations, and Solvers. de Gruyter GmbH, Walter, 2020.

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Field Theoretic Method In Phase Transformations. Springer, 2012.

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Umantsev, Alexander. Field Theoretic Method in Phase Transformations. Springer, 2012.

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Vondrous, Alexander. Grain Growth Behavior and Efficient Large Scale Simulations of Recrystallization With the Phase-field Method. Saint Philip Street Press, 2020.

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Boudreau, Joseph F., and Eric S. Swanson. Quantum field theory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198708636.003.0024.

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Markov chain Monte Carlo techniques are developed to compute properties of a variety of quantum field theories. The method is introduced with a simple scalar field theory and used to evaluate the particle spectrum and phase diagram for parity symmetry breaking. The technique of micorcanonical updating is introduced to increase efficiency. The important topic of gauge theory is then introduced via the gauged Z2 model. Development of the gauge theory formalism continues with Abelian gauge theory in two dimensions. The interaction between static charges is computed and compared to the exact result. The string tension in nonableian SU(2) gauge theory is explored with the aid of the renormalization group, which gives an entrée to a discussion of the Higgs mechanism. Finally, the formalism for including fermions is briefly reviewed.
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Book chapters on the topic "Phase field fracture method"

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Borden, Michael J., Thomas J. R. Hughes, Chad M. Landis, Amin Anvari, and Isaac J. Lee. "Phase-Field Formulation for Ductile Fracture." In Computational Methods in Applied Sciences, 45–70. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-60885-3_3.

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Bilgen, C., A. Kopaničáková, R. Krause, and K. Weinberg. "A Phase-Field Approach to Pneumatic Fracture." In Non-standard Discretisation Methods in Solid Mechanics, 217–41. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-92672-4_9.

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Hudobivnik, Blaž, Fadi Aldakheel, and Peter Wriggers. "Adaptive Virtual Element Method for Large-Strain Phase-Field Fracture." In Current Trends and Open Problems in Computational Mechanics, 195–206. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-87312-7_20.

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Kuhn, Charlotte, Timo Noll, Darius Olesch, and Ralf Müller. "Phase Field Modeling of Brittle and Ductile Fracture." In Non-standard Discretisation Methods in Solid Mechanics, 283–325. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-92672-4_11.

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De Lorenzis, Laura, and Tymofiy Gerasimov. "Numerical Implementation of Phase-Field Models of Brittle Fracture." In Modeling in Engineering Using Innovative Numerical Methods for Solids and Fluids, 75–101. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-37518-8_3.

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Alessi, R., M. Ambati, T. Gerasimov, S. Vidoli, and L. De Lorenzis. "Comparison of Phase-Field Models of Fracture Coupled with Plasticity." In Computational Methods in Applied Sciences, 1–21. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-60885-3_1.

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Dimaki, Andrey V., and Evgeny V. Shilko. "Theoretical Study of Physico-mechanical Response of Permeable Fluid-Saturated Materials Under Complex Loading Based on the Hybrid Cellular Automaton Method." In Springer Tracts in Mechanical Engineering, 485–501. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-60124-9_21.

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AbstractWe give a brief description of the results obtained by Prof. Sergey G. Psakhie and his colleagues in the field of theoretical studies of mechanical response, including fracture, of permeable fluid-saturated materials. Such materials represent complex systems of interacting solid and liquid phases. Mechanical response of such a medium is determined by processes taking place in each phase as well as their interaction. This raised a need of developing a new theoretical approach of simulation of such media—the method of hybrid cellular automaton that allowed describing stress-strain fields in solid skeleton, transfer of a fluid in crack-pore volume and influence of fluid pressure on the stress state of the solid phase. The new method allowed theoretical estimation of strength of liquid-filled permeable geomaterials under complex loading conditions. Governing parameters controlling strength of samples under uniaxial loading and shear in confined conditions were identified.
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Rabczuk, Timon, Huilong Ren, and Xiaoying Zhuang. "Nonlocal Operator Method for Dynamic Brittle Fracture Based on an Explicit Phase Field Model." In Computational Methods Based on Peridynamics and Nonlocal Operators, 243–69. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-20906-2_9.

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Yoshioka, Keita, Mathias Nest, Daniel Pötschke, Amir Shoarian Sattari, Patrick Schmidt, and David Krach. "Numerical Platform." In GeomInt–Mechanical Integrity of Host Rocks, 63–95. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-61909-1_3.

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AbstractAn essential scientific goal of the GeomInt project is the analysis of potentials and limitations of different numerical approaches for the modelling of discontinuities in the rocks under consideration in order to improve the understanding of methods and their synergies with regard to theoretical and numerical fundamentals. As numerical methods, the “Lattice Element Method” (LEM), the non-continuous discontinuum methods “Discrete Element Method” (DEM), the “Smoothed Particle Hydrodynamics” (SPH), the “Forces on Fracture Surfaces” (FFS) as well as the continuum approaches “Phase-Field Method” (PFM), “Lower-Interface-Method” (LIE), “Non-Local Deformation” (NLD) and the “Hybrid-Dimensional Finite-Element-Method” (HDF) will be systematically investigated and appropriately extended based on experimental results (Fig. 3.1).
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Steinke, Christian, Imadeddin Zreid, and Michael Kaliske. "Modelling of Ductile Fracture of Strain-hardening Cement-based Composites - Novel Approaches Based on Microplane and Phase-field Method." In Plasticity, Damage and Fracture in Advanced Materials, 175–99. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-34851-9_10.

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Conference papers on the topic "Phase field fracture method"

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Sondershaus, R., and R. Müller. "Phase field model for simulating fracture of ice." In 8th European Congress on Computational Methods in Applied Sciences and Engineering. CIMNE, 2022. http://dx.doi.org/10.23967/eccomas.2022.219.

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Liao, Minmao, and Peng Ma. "Computation of brittle phase field fracture by the quadrature element method." In BIC 2022: 2022 2nd International Conference on Bioinformatics and Intelligent Computing. New York, NY, USA: ACM, 2022. http://dx.doi.org/10.1145/3523286.3524557.

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Yvonnet, J. "Phase field method for microcracking simulations in concrete microstructure models obtained from 3D microtomography images." In 10th International Conference on Fracture Mechanics of Concrete and Concrete Structures. IA-FraMCoS, 2019. http://dx.doi.org/10.21012/fc10.233759.

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Fei, Fan, Andre Costa, John E. Dolbow, Randolph R. Settgast, and Matteo Cusini. "Phase-Field Simulation of Near-Wellbore Nucleation and Propagation of Hydraulic Fractures in Enhanced Geothermal Systems (EGS)." In SPE Reservoir Simulation Conference. SPE, 2023. http://dx.doi.org/10.2118/212251-ms.

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Abstract Enhanced geothermal systems (EGS) rely on the artificial creation of fractures (i.e., hydraulic fractures) to enhance the permeability of the formation which would, otherwise, be too low to allow for fluid circulation. Hydraulic fracturing involves complex nucleation and propagation processes, which are key to the analysis and prediction of well productivity. Numerical simulations are commonly employed to understand the specific mechanisms behind nucleation and propagation of hydraulic fractures. However, most numerical approaches face tremendous challenges in tracking and accommodating the evolving fracture geometry, especially when curved and branched fractures occur. The phase-field method can overcome this obstacle, as it can model fracture propagation without the need for tracking the fracture tip nor for remeshing. However, the most common phase-field formulation is unable to accurately capture fracture nucleation. In this work, we develop a new phase-field approach for hydraulic fracturing that accounts for fracture nucleation due to the strengths of geologic material and the existence of small defects. Verification examples show that the proposed formulation can accurately predict near-wellbore nucleation and propagation of hydraulic fractures and the wellbore breakdown pressure. Simulation of a three-dimensional wellbore problem further demonstrates the efficiency of the proposed phase-field method in handling fracture nucleation and propagation.
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He, Xupeng, Zhen Zhang, Marwah AlSinan, Yiteng Li, Hyung Kwak, and Hussein Hoteit. "Uncertainty and Sensitivity Analysis of Multi-Phase Flow in Fractured Rocks: A Pore-To-Field Scale Investigation." In SPE Annual Technical Conference and Exhibition. SPE, 2022. http://dx.doi.org/10.2118/210131-ms.

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Abstract Despite recent advancements in computational methods, it is still challenging to properly model fracture properties, such as relative permeability and hydraulic aperture, at the field scale. The challenge is in determining the most representative fracture properties, concluded from multi-scale data. In this study, we demonstrate how to capture fracture properties at the field scale from core-scale and pore-scale data through multi-scale uncertainty quantification, and assess how pore-scale processes can significantly impact the recovery factor. There are three components within our workflow: 1) performing high-resolution Navier-Stokes (NS) simulation at pore-scale to obtain hydraulic aperture of discrete single fractures, 2) embedding pore-scale parameters into core-scale for predicting field-scale objective, such as recovery factor, and 3) performing Monte Carlo simulations to determine the relationship effect of the pore-scale parameters to the field scale responding. At pore-scale, we start with four parameters that characterize the fractures: mean aperture, relative roughness, tortuosity, and the ratio of minimum to mean apertures. We then construct hydraulic aperture surrogates using an Artificial Neural Network (ANN). At the field scale, we deploy Long Short-Term Memory (LSTM) to capture the recovery factor at field-scale. The final results are the time-varying recovery factor and its sensitivity analysis. Monte Carlo simulation is performed on the final surrogate to produce the recovery factor value for various time-step. The result is beneficial for risk assessment and decision-making during the development of fractured reservoirs. Our method is the first to quantitatively estimate multi-scale parameters’ effect on recovery factors in two-phase flow in fractured media. This method also shows how we accommodate and deal with multi-scale parameters.
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Tsitova, A. "Experimental and numerical study of crack propagation with the phase field method: application to three-point bending test." In 10th International Conference on Fracture Mechanics of Concrete and Concrete Structures. IA-FraMCoS, 2019. http://dx.doi.org/10.21012/fc10.233322.

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Li, Wei. "Phase-Field Fracture Simulation of Dual-Cooled Annular Fuel Pellet." In 2022 29th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/icone29-92230.

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Abstract The dual-cooled annular nuclear fuel is an advanced design that is expected to greatly lower fuel temperature even under high linear power density, as compared to traditional cylindrical fuel pin. Although fuel temperature can be much lower, the annular pellet also receives much higher neutron fluence, which may induce severe cracking during normal operation. This work deals with quasi-static cracking of dual-cooled annular UO2 pellet under neutron radiation. The analysis is based on the phase-field fracture model coupled with an oxygen diffusion model, heat conduction model and mechanical equilibrium model. The considered thermo-mechanical properties and irradiation behaviors of the nuclear fuel are both temperature and irradiation dependent. Especially, the acceleration of fuel creep due to oxygen redistribution is included. The fracture is represented by a scalar phase-field variable governed by a cohesive phase-field fracture method. These models are numerically implemented in the multi-physics coupling simulation framework MOOSE. For the first time, the diffusion-thermo-mechanical coupled fracture model is applied to the dual-cooled annular UO2 fuel pellet cracking during reactor startup, power ramp and reactor shutdown. Preliminarily, UO2 irradiation creep is found to play an important role on the fuel pellet fragmentation. The developed capability supports interpretation of experimental data and can guide material design of advanced ceramic nuclear fuel.
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Jammoul, Mohamad, and Mary Wheeler. "A Phase-Field Based Approach for Modeling the Cementation and Shear Slip of Fracture Networks." In SPE Reservoir Simulation Conference. SPE, 2021. http://dx.doi.org/10.2118/203906-ms.

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Abstract 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 large variations in the apertures of fractures resulting in drastic 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, a novel approach is introduced for the simulation of cementation and shear slip of fractures on very general semi-structured grids. Natural fracture networks are represented in large scale reservoirs using the phase-field approach. The fluid flow through fractures is simulated on spatially non-conforming grids using the enhanced velocity mixed finite element method. The geomechanics equations are discretized using the continuous Galerkin finite element method. The single-phase flow and mechanics equations are decoupled using the fixed stress iterative scheme. The model can predict shear slipping and opening/closure of fractures due to induced stresses and poromechanical effects. Two synthetic examples are presented to model the effects of injection/production processes on the cementation and shear slip of fractures. The impact of the fractures' orientation and their connectivity on the hydromechanical response of the reservoir is also considered. The examples illustrate the strong impact of the dynamic behavior of fractures and the accompanying poroelastic deformations on the safety and productivity of subsurface projects.
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Franke, Marlon, Christian Hesch, and Maik Dittmann. "A HIGHER ORDER PHASE-FIELD APPROACH TO FRACTURE FOR FINITE-DEFORMATION CONTACT PROBLEMS." In VII European Congress on Computational Methods in Applied Sciences and Engineering. Athens: Institute of Structural Analysis and Antiseismic Research School of Civil Engineering National Technical University of Athens (NTUA) Greece, 2016. http://dx.doi.org/10.7712/100016.2295.9907.

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KUMAR, AKASH, and TRISHA SAIN. "PHASE FIELD BASED COHESIVE ZONE FRACTURE APPROACH TO MODEL ANISOTROPIC EFFECT AND INTERFACE FRACTURE IN FIBER REINFORCED POLYMER COMPOSITES." In Proceedings for the American Society for Composites-Thirty Seventh Technical Conference. Destech Publications, Inc., 2022. http://dx.doi.org/10.12783/asc37/36400.

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Among multiple damage mechanisms in fiber reinforced polymer composites (FRPCs), delamination is the major failure mode that occurs very often due to low interlaminar strength of these materials. Prediction of this failure mode through computational modeling is not straight forward. In this work we aim to use the phase field fracture method (PFF) to model interfacial fracture in FRPCs. In PFF, the crack is assumed as a diffused entity rather than discrete discontinuities. In the present work, a unified phase field based cohesive zone model (PF-CZM) has been utilized to characterize the interlaminar fracture of carbon fiber reinforced epoxy composite. A Double cantilever beam (DCB) geometry has been simulated for 0◦ fiber orientation to determine mode I interfacial fracture toughness. To meet the requirement, two laminas of unidirectional FRP were bonded together using an adhesive (resin rich region) for different adhesive layer thicknesses and the corresponding energy release rates are computed. The area method suggested by Whitney [1982] was used to measure the energy release rate (R-curve). The results show different GI values for different thickness of adhesive layer and remains within a specified limit. The peak load is also different for different thicknesses of adhesive. Prior to the DCB simulations, open hole tension (OHT) simulations for different fiber orientations (0◦, 45◦ and 90◦) were also performed for carbon-fiber reinforced epoxy composite to validate the PF-CZM model prediction with the experimental data available in literature.
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Reports on the topic "Phase field fracture method"

1

Robertson, Brett Anthony. Phase Field Fracture Mechanics. Office of Scientific and Technical Information (OSTI), November 2015. http://dx.doi.org/10.2172/1227184.

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Biner, Bullent, Michael Tonks, Paul C. Millett, Yulan Li, Shenyang Y. Hu, Fei Gao, Xin Sun, E. Martinez, and D. Anderson. PROGRESS ON GENERIC PHASE-FIELD METHOD DEVELOPMENT. Office of Scientific and Technical Information (OSTI), September 2012. http://dx.doi.org/10.2172/1059624.

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Tupek, Michael R. Cohesive phase-field fracture and a PDE constrained optimization approach to fracture inverse problems. Office of Scientific and Technical Information (OSTI), June 2016. http://dx.doi.org/10.2172/1409369.

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Author, Not Given. Brittle fracture phase-field modeling of a short-rod specimen. Office of Scientific and Technical Information (OSTI), September 2015. http://dx.doi.org/10.2172/1225864.

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Landis, Chad M., and Thomas J. Hughes. Phase-Field Modeling and Computation of Crack Propagation and Fracture. Fort Belvoir, VA: Defense Technical Information Center, April 2014. http://dx.doi.org/10.21236/ada603638.

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Culp, David, Nathan Miller, and Laura Schweizer. Application of Phase-Field Techniques to Hydraulically- and Deformation-Induced Fracture. Office of Scientific and Technical Information (OSTI), August 2017. http://dx.doi.org/10.2172/1378175.

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Yue, Dick K. Assimilation of Three-Dimensional Phase-Resolved Wave-Field Data Using an Efficient High-Order Spectral Method. Fort Belvoir, VA: Defense Technical Information Center, August 2001. http://dx.doi.org/10.21236/ada626896.

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Fried, Eliot, and Morton E. Gurtin. Continuum mechanical and computational aspects of phase field elasticity as applied to phase transitions and fracture. Final report: DE-FG02-97ER25318, June 1, 1997 - May 31, 2000. Office of Scientific and Technical Information (OSTI), April 2001. http://dx.doi.org/10.2172/808066.

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Allen, Jeffrey, Robert Moser, Zackery McClelland, Md Mohaiminul Islam, and Ling Liu. Phase-field modeling of nonequilibrium solidification processes in additive manufacturing. Engineer Research and Development Center (U.S.), December 2021. http://dx.doi.org/10.21079/11681/42605.

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This project models dendrite growth during nonequilibrium solidification of binary alloys using the phase-field method (PFM). Understanding the dendrite formation processes is important because the microstructural features directly influence mechanical properties of the produced parts. An improved understanding of dendrite formation may inform design protocols to achieve optimized process parameters for controlled microstructures and enhanced properties of materials. To this end, this work implements a phase-field model to simulate directional solidification of binary alloys. For applications involving strong nonequilibrium effects, a modified antitrapping current model is incorporated to help eject solute into the liquid phase based on experimentally calibrated, velocity-dependent partitioning coefficient. Investigated allow systems include SCN, Si-As, and Ni-Nb. The SCN alloy is chosen to verify the computational method, and the other two are selected for a parametric study due to their different diffusion properties. The modified antitrapping current model is compared with the classical model in terms of predicted dendrite profiles, tip undercooling, and tip velocity. Solidification parameters—the cooling rate and the strength of anisotropy—are studied to reveal their influences on dendrite growth. Computational results demonstrate effectiveness of the PFM and the modified antitrapping current model in simulating rapid solidification with strong nonequilibrium at the interface.
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Conrady, Morgan, Markus Bauer, Kyoo Jo, Donald Cropek, and Ryan Busby. Solid-phase microextraction (SPME) for determination of geosmin and 2-methylisoborneol in volatile emissions from soil disturbance. Engineer Research and Development Center (U.S.), October 2021. http://dx.doi.org/10.21079/11681/42289.

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Abstract:
A method is described here for the concentration and determination of geosmin and 2-methylisoborneol (2-MIB) from the gaseous phase, with translation to field collection and quantification from soil disturbances in situ. The method is based on the use of solid-phase microextraction (SPME) fibers for adsorption of volatile chemicals from the vapor phase, followed by desorption into a gas chromatograph-mass spectrometer (GC-MS) for analysis. The use of a SPME fiber allows simple introduction to the GC-MS without further sample preparation. Several fiber sorbent types were studied and the 50/30 μm DVB/CAR/PDMS was the best performer to maximize the detected peak areas of both analytes combined. Factors such as extraction temperature and time along with desorption temperature and time were explored with respect to analyte recovery. An extraction temperature of 30 ◦C for 10 min, with a desorption temperature of 230 ◦C for 4 min was best for the simultaneous analysis of both geosmin and 2-MIB without complete loss of either one. The developed method was used successfully to measure geosmin and 2-MIB emission from just above disturbed and undisturbed soils, indicating that this method detects both compounds readily from atmospheric samples. Both geosmin and 2-MIB were present as background concentrations in the open air, while disturbed soils emitted much higher concentrations of both compounds. Surprisingly, 2-MIB was always detected at higher concentrations than geosmin, indicating that a focus on its detection may be more useful for soil emission monitoring and more sensitive to low levels of soil disturbance.
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