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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'optimisationThe 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'améliorationIn 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 propagationInconel 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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Cavuoto, Riccardo. "Phase-field and reduced peridynamic theories for fracture problems." Doctoral thesis, Università degli studi di Trento, 2021. http://hdl.handle.net/11572/322187.
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Several aspects of fracture nucleation and growth in brittle porous ceramics and in thin films are investigated, through analytical, numerical modelling, and experimental validation. A mechanical experimental characterization has been developed for a porous ceramic, namely, a 3D apatite, characterised by an oriented porosity and used for biomedical applications. The ceramic is produced from wood, so that the resulting porosity evidences a multi-scale nature, a feature determining peculiar failure mechanisms and an unprecedented porosity/strength ratio. In particular, the material exhibits an exfoliation-type failure, resulting in a progressive loss in mechanical properties, occurring for compression tests parallel to the grains and for highly slender specimens. Similar cohesive-brittle behaviour is also found when the compression is applied in the direction orthogonal to the porous channels, regardless of the shape ratio of the specimen. An in-depth analysis of this response is performed by means of a phase-field model. After calibrating the model, stress-strain curves and fracturing patterns are accurately reproduced. Furthermore, the effects of multi-scale porosity on mechanical behaviour are determined. Various strategies available in the literature for evaluating the properties of porous materials are compared to the proposed phase-field approach. The results open new possibilities for the prediction and characterization of complex fracturing phenomena occurring in highly porous ceramics, so to facilitate medical applications as structural bone repair. An application of the peridynamic theory of continuum mechanics is developed to obtain a dimensional reduced formulation for the characterisation of through-thickness delamination of plates. The kinematic of the plate is carefully chosen to be composed of an absolutely continuous part and a zone where jumps in the displacements are allowed; in this way, the reduced form of the elastic bond-based peridynamic energy and the reduced Lagrangian are explicitly retrieved in a closed-form. The reduction generates a hierarchy of terms, characterizing the energy stored inside the plane element. A semi-analytical solution, obtained by means of a minimization procedure, is obtained for a test case and compared with finite element simulations. Despite the fact that the numerical model is fully three-dimensional (in other words, it is not reduced), this model leads to the same moment-curvature diagrams and nucleation/growth of the delamination surface found with the reduced formulation. Finally, the convergence of the proposed reduced model to local elastic theory at vanishing internal length is determined, so that a reduced-localized cohesive model for fracture is retrieved.
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Li, Yichen. "Phase-field Modeling of Phase Change Phenomena." Thesis, Virginia Tech, 2020. http://hdl.handle.net/10919/99148.
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The phase-field method has become a popular numerical tool for moving boundary problems in recent years. In this method, the interface is intrinsically diffuse and stores a mixing energy that is equivalent to surface tension. The major advantage of this method is its energy formulation which makes it easy to incorporate different physics. Meanwhile, the energy decay property can be used to guide the design of energy stable numerical schemes.
In this dissertation, we investigate the application of the Allen-Cahn model, a member of the phase-field family, in the simulation of phase change problems. Because phase change is usually accompanied with latent heat, heat transfer also needs to be considered. Firstly, we go through different theoretical aspects of the Allen-Cahn model for nonconserved interfacial dynamics. We derive the equilibrium interface profile and the connection between surface tension and mixing energy. We also discuss the well-known convex splitting algorithm, which is linear and unconditionally energy stable. Secondly, by modifying the free energy functional, we give the Allen-Cahn model for isothermal phase transformation. In particular, we explain how the Gibbs-Thomson effect and the kinetic effect are recovered. Thirdly, we couple the Allen-Chan and heat transfer equations in a way that the whole system has the energy decay property. We also propose a convex-splitting-based numerical scheme that satisfies a similar discrete energy law. The equations are solved by a finite-element method using the deal.ii library. Finally, we present numerical results on the evolution of a liquid drop in isothermal and non-isothermal settings. The numerical results agree well with theoretical analysis.Master of Science
Phase change phenomena, such as freezing and melting, are ubiquitous in our everyday life. Mathematically, this is a moving boundary problem where the phase front evolves based on the local temperature. The phase change is usually accompanied with the release or absorption of latent heat, which in turn affects the temperature. In this work, we develop a phase-field model, where the phase front is treated as a diffuse interface, to simulate the liquid-solid transition. This model is consistent with the second law of thermodynamics. Our finite-element simulations successfully capture the solidification and melting processes including the interesting phenomenon of recalescence.
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Ziaei-Rad, Vahid. "Phase field approach to fracture : massive parallelization and crack identification." Doctoral thesis, Universitat Politècnica de Catalunya, 2016. http://hdl.handle.net/10803/396154.
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The phase field method has proven to be an important tool in computational fracture mechanics in that it does not require complicated crack tracking and is able to predict crack nucleation and branching. However, the computational cost of such a method is high due to a small regularization length parameter, which in turns restricts the maximum element size that can be used in a finite element mesh. In this work, we developed a massively parallel algorithm on the graphical processing unit (GPU) to alleviate this difficulty in the case of dynamic brittle fracture. In particular, we adopted the standard finite element method on an unstructured mesh combined with second order explicit integrators.
As the explicit methods fit nicely with the GPU paradigm especially in terms of thread and memory hierarchy, we solve an elastodynamic problem when the phase field update is based on a gradient flow, so that a fully explicit implementation is feasible. To ensure stability, we designed a time adaptivity strategy to account for the decreasing critical time step during the evolution of the fields.
We demonstrated the performance of the GPU-implemented phase field models by means of representative numerical examples, with which we studied the effect of the artificial viscosity, an artificial parameter to be input, and compared the crack path branching predictions from three popular phase field models. Moreover, we verified the method with convergence studies and performed a scalability study to demonstrate the desired linear scaling of the program in terms of the wall time per physical time as a function of the number of degrees of freedom.
One of the main ideas of the phase field method is to employ a smeared representation of discrete cracks. However, in some applications it is still convenient to have the explicit crack path available, or even to develop a mechanism to introduce crack paths to partially replace a smeared crack propagation model.
In this work, we presents a variational method to identify the crack path from phase field approaches to fracture. The method is proven to be successful not only for a simple curved crack but also for multiple and branched cracks. The algorithm employs the non-maximum suppression technique, a procedure borrowed from the image processing field, to detect a bounding area which covers the ridge of the phase field profile. After that, it is continued with the step to determine a cubic spline to represent the crack path and to improve it via a constrained optimization process. To demonstrate the performance of our method, we provide the results with three sets of representative examples. The developed algorithm can be combined with one on crack opening, for more elaborate interpretation of phase field simulations. This is the topic of the next part of the work.
In this dissertation, we also provide a variational way to calculate the crack opening from phase field approaches to fracture. We also demonstrate the performance of our method with three sets of representative examples, and verify the results with a proper benchmark.
Having the crack geometry available from a phase field approach can provide more elaborate interpretation of the phase field simulations. It may also offer a possibility of developing less expensive numerical schemes for a fluid-driven crack propagation of impermeable solids. This will be the topic of our future work.El método de phase field ha demostrado ser una herramienta importante en la mecánica de fractura computacional el cual no requiere el seguimiento complicado de una fractura y es capaz de predecir la nucleación y la ramificación. Sin embargo, el coste computacional de un método de este tipo es alto debido a un pequeño parámetro de regularización de longitud, que a su vez limita el tamaño del elemento máximo que se puede utilizar en una malla de los elementos finitos. En esta disertación, hemos desarrollado un algoritmo paralelo de forma masiva en la unidad de procesamiento gráfico (GPU) para aliviar esta dificultad en el caso de rotura frágil dinámica. En particular, hemos adoptado el método de los elementos finitos en una malla no estructurada combinada con integradores explícitos de segundo orden. A medida que los métodos explícitos encajan adecuadamente con el paradigma de la GPU especialmente en términos de hilo y la jerarquía de memoria, se resuelve un problema de elastodinámica cuando la actualización de phase field se basa en un flujo de gradiente, de modo que una implementación totalmente explícita es factible. Para asegurar la estabilidad, se diseñó una estrategia adaptativa de tiempo para tener en cuenta la disminución del paso de tiempo crítico durante la evolución de los campos. Hemos demostrado el rendimiento de los modelos de phase field GPU-implementado por medio de ejemplos numéricos representativos, con los que se estudió el efecto de la viscosidad artificial, un parámetro artificial que sirva como entrada, y se compara las predicciones de la trayectoria ramificada de la grieta a partir de tres modelos de phase field populares. Por otra parte, se verificó el método de convergencia con los estudios y se realizó un estudio para demostrar la escala lineal deseada del programa en términos del tiempo de reloj de pared por el tiempo físico en función del número de grados de libertad. Una de las ideas principales del método de phase field es emplear una representación distribuida de una grieta discreta. Sin embargo, en algunas aplicaciones todavía es conveniente tener la ruta de grieta explícita disponible, o incluso desarrollar un mecanismo para introducir caminos de crack con el objetivo de sustituir en parte un modelo de fisura distribuida de propagación. En esta disertación, se presenta un método variacional para identificar la ruta de grietas en los enfoques de phase field en problemas de fractura. El método ha demostrado ser un éxito no sólo por una simple grieta curvada, sino también por múltiples grietas y ramificadas. El algoritmo emplea la técnica de supresión no máxima, un procedimiento tomado del campo de procesamiento de imágenes, para detectar un área de delimitación que cubre la cresta del perfil de phase field. A continuación, se continúa con la etapa de determinar un spline cúbico para representar la trayectoria de la grieta y mejorarlo a través de un proceso de optimización restringida. Para demostrar la eficacia de nuestro método, proporcionamos los resultados con tres conjuntos de ejemplos representativos. El algoritmo desarrollado se puede combinar con uno en apertura crack, para la interpretación más elaborada de simulaciones de phase field. Este es el tema de la siguiente parte de la tesis. En esta tesis, también ofrecemos una forma variacional para calcular la apertura de grietas de los enfoques de phase field a la fractura. También demostramos el rendimiento de nuestro método con tres conjuntos de ejemplos representativos, y verificar los resultados con un valor de referencia apropiado. Tener la geometría grieta disponible a partir de un enfoque de phase field puede proporcionar una interpretación más elaborada de las simulaciones de phase field. También puede ofrecer una posibilidad de desarrollar esquemas numéricos con menos costes para una propagación de la grieta de accionamiento hidráulico de sólidos impermeables. Este será el tema de nuestro futuro trabajo.
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Omatuku, Emmanuel Ngongo. "Phase field modeling of dynamic brittle fracture at finite strains." Master's thesis, Faculty of Engineering and the Built Environment, 2019. http://hdl.handle.net/11427/30172.
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Fracture is the total or partial separation of an initially intact body through the propagation of one or several cracks. Computational methods for fracture mechanics are becoming increasingly important in dealing with the nucleation and propagation of these cracks. One method is the phase field approach, which approximates sharp crack discontinuities with a continuous scalar field, the so-called phase field. The latter represents the smooth transition between the intact and broken material phases. The evolution of the phase field due to external loads describes the fracture process. An original length scale is used to govern the diffusive approximation of sharp cracks. This method further employs a degradation function to account for the loss of the material stiffness during fracture by linking the phase field to the body’s bulk energy. To prevent the development of unrealistic crack patterns and interpenetration of crack faces under compression, this study uses the anisotropic split of the bulk energy, as proposed by Amor et al. [5], to model the different fracture behavior in tension, shear and compression. This research is part of a larger project aimed at the modeling of Antarctic sea ice dynamics. One aspect of this project is the modeling of the gradual break-up of the consolidated ice during spring. As a first step, this study reviews a phase field model used for dynamic brittle fracture at finite strains. Subsequently, this model is implemented into the in-house finite element software SESKA to solve the benchmark tension and shear tests on a single-edge notched block. The implementation adopts the so-called monolithic scheme, which computes the displacement and phase field solutions simultaneously, with a Newmark time integration scheme. The results of the solved problems demonstrate the capabilities of the implemented dynamic phase field model to capture the nucleation and propagation of cracks. They further confirm that the choice of length-scale and mesh size influences the solutions. In this regard, a small value of the length-scale converges to the sharp crack topology and yields a larger stress value. On the other hand, a large length-scale parameter combined with a too coarse mesh size can yield unrealistic results.
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Schlueter, Alexander [Verfasser], and Charlotte [Akademischer Betreuer] Kuhn. "Phase Field Modeling of Dynamic Brittle Fracture / Alexander Schlueter ; Betreuer: Charlotte Kuhn." Kaiserslautern : Technische Universität Kaiserslautern, 2018. http://d-nb.info/116213397X/34.
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Tanne, Erwan. "Variational phase-field models from brittle to ductile fracture : nucleation and propagation." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLX088/document.
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Les simulations numériques des fissures fragiles par les modèles d’endommagement à gradient deviennent main- tenant très répandues. Les résultats théoriques et numériques montrent que dans le cadre de l’existence d’une pre-fissure la propagation suit le critère de Griffith. Alors que pour le problème à une dimension la nucléation de la fissure se fait à la contrainte critique, cette dernière propriété dimensionne le paramètre de longueur interne.Dans ce travail, on s’attarde sur le phénomène de nucléation de fissures pour les géométries communément rencontrées et qui ne présentent pas de solutions analytiques. On montre que pour une entaille en U- et V- l’initiation de la fissure varie continument entre la solution prédite par la contrainte critique et celle par la ténacité du matériau. Une série de vérifications et de validations sur diffèrent matériaux est réalisée pour les deux géométries considérées. On s’intéresse ensuite à un défaut elliptique dans un domaine infini ou très élancé pour illustrer la capacité du modèle à prendre en compte les effets d’échelles des matériaux et des structures.Dans un deuxième temps, ce modèle est étendu à la fracturation hydraulique. Une première phase de vérification du modèle est effectuée en stimulant une pré-fissure seule par l’injection d’une quantité donnée de fluide. Ensuite on étudie la simulation d’un réseau parallèle de fissures. Les résultats obtenus montrent qu’il a qu’une seule fissure qui se propage et que ce type de configuration minimise mieux l’énergie la propagation d’un réseau de fractures. Le dernier exemple se concentre sur la stabilité des fissures dans le cadre d’une expérience d’éclatement à pression imposée pour l’industrie pétrolière. Cette expérience d’éclatement de la roche est réalisée en laboratoire afin de simuler les conditions de confinement retrouvées lors des forages.La dernière partie de ce travail se concentre sur la rupture ductile en couplant le modèle à champ de phase avec les modèles de plasticité parfaite. Grâce à l’approche variationnelle du problème on décrit l’implantation numérique retenue pour le calcul parallèle. Les simulations réalisées montrent que pour une géométrie légèrement entaillée la phénoménologie des fissures ductiles comme par exemple la nucléation et la propagation sont en concordances avec ceux reportées dans la littératurePhase-field models, sometimes referred to as gradient damage, are widely used methods for the numerical simulation of crack propagation in brittle materials. Theoretical results and numerical evidences show that they can predict the propagation of a pre-existing crack according to Griffith’s criterion. For a one- dimensional problem, it has been shown that they can predict nucleation upon a critical stress, provided that the regularization parameter is identified with the material’s internal characteristic length.In this work, we draw on numerical simulations to study crack nucleation in commonly encountered geometries for which closed-form solutions are not available. We use U- and V-notches to show that the nucleation load varies smoothly from the one predicted by a strength criterion to the one of a toughness criterion when the strength of the stress concentration or singularity varies. We present validation and verification of numerical simulations for both types of geometries. We consider the problem of an elliptic cavity in an infinite or elongated domain to show that variational phase field models properly account for structural and material size effects.In a second movement, this model is extended to hydraulic fracturing. We present a validation of the model by simulating a single fracture in a large domain subject to a control amount of fluid. Then we study an infinite network of pressurized parallel cracks. Results show that the stimulation of a single fracture is the best energy minimizer compared to multi-fracking case. The last example focuses on fracturing stability regimes using linear elastic fracture mechanics for pressure driven fractures in an experimental geometry used in petroleum industry which replicates a situation encountered downhole with a borehole called burst experiment.The last part of this work focuses on ductile fracture by coupling phase-field models with perfect plasticity. Based on the variational structure of the problem we give a numerical implementation of the coupled model for parallel computing. Simulation results of a mild notch specimens are in agreement with the phenomenology of ductile fracture such that nucleation and propagation commonly reported in the literature
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Senay, Aras Betul. "Investigation of Some Cell Morphology Using Phase Field Method." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1503067908468122.
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Argyropoulos, Christos. "A combined immersed boundary/phase-field method for simulating two-phase pipe flows." Thesis, Imperial College London, 2015. http://hdl.handle.net/10044/1/51089.
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The investigation of the flow in a pipe is a major issue for the pipeline capacity but also plays an important role for the control and prevention of phenomena that could damage the pipe, such as corrosion, erosion, and the potential formation of wax or their deposits. Therefore, the characterization of the flow patterns is also a major issue for the prediction of the distribution over the cross-section of the pipe, in order to understand any problems that may interrupt or shut down the operation of the production line. The main purpose of the present effort is to develop an appropriate numerical method for simulating two-phase pipe flows. Advanced Computational Fluid Dynamics (CFD) methods are employed as Navier-Stokes solver, while a Phase-Field method is used to simulate the interfacial region between the two fluids. A Ghost-Cell Immersed Boundary Method (GCIBM) was developed and implemented for the reconstruction of smooth rigid boundaries (pipe wall) based on the work of Tseng and Ferziger (2003). The method was also modified in order to incorporate appropriate boundary conditions for coupling the Phase-Field and Navier-Stokes solvers for two-phase pipe flows. Tseng and Ferziger (2003) used the GCIBM for turbulent single-phase flows; the present modified version comprises a continuation of the method for handling two-phase pipe flows. The computational model is capable of handling large density and viscosity ratios with good accuracy. The developed GCIBM algorithm was validated against analytical solutions for single and two-phase pipe flow, presenting very good agreement. The computational model was compared to available experimental data from the literature for single rising bubbles and bubble coalescence in vertical pipe also with good agreement. The numerical method was used to investigate the lateral wall effects of a 3-D single bubble in a viscous liquid for different pipe diameters and bubble flow regimes. The dynamics of 3-D Taylor bubbles was also examined in vertical pipes for different properties of fluids (e.g. air-water system) and dimensionless parameters relevant to the problem (e.g. ReB, Eo, Mo). The numerical results were compared with available experimental and numerical data from the literature, presenting good agreement.
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Ammar, Kais. "Modelling and simulation of phase transformation-mechanics coupling using a phase field method." Paris, ENMP, 2010. https://theses.hal.science/tel-00508677.
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Nous proposons un cadre générique, permettant l'incorporation des différentes lois de comportement de mécanique linéaires ou non-linéaires (i. E. Elastoviscoplastique) dans les approches des champs de phases utilisées pour la modélisation et la simulation de la mobilité d'interfaces diffuses. Dans ce cadre, une formulation par éléments finis des modèles couplés champ de phases-élastoplasticité pour les alliages binaires est développée dans le formalisme général de la thermodynamique des milieux continus. Cette formulation est basée sur la théorie d'équilibre des microforces, proposée par Gurtin, où une équation supplémentaire, fonction du paramètre d'ordre et de son gradient, est introduite. La formulation est employée pour simuler les évolutions morphologiques complexes des microstructures hétérogènes et décrire l'interface diffuse entre deux phases en présence des contraintes induites par transformation de phase. En utilisant les principes de la thermodynamique des processus irréversibles, les lois de comportement et les équations d'évolution sont clairement exposées et séparées dans la formulation de sorte que des modèles non-linéaires et fortement couplés puissent être implantés plus facilement dans un code par éléments finis. Cette formulation peut être appliquée aux corps finis périodiques et non périodiques, aux microstructures hétérogènes. Les conditions initiales et les conditions aux limites en paramètre d'ordre et en concentration ainsi que leurs quantités duales sont clairement énoncées. Des techniques d'homogénéisation ont été utilisées pour décrire le comportement dans les interfaces diffuses. Les conséquences de ces choix de modélisation ont été déterminées en ce qui concerne les effets des contraintes mécaniques sur les équilibres de phases et la cinétique de transformation. L'ensemble des équations d'évolution couplées, à savoir l'équation d'équilibre statique local, l'équation de champ de phases et l'équation de conservation de la masse, est résolu en utilisant la méthode des éléments finis pour la discrétisation spatiale et un schéma implicite des différences finies pour la discrétisation temporelle. Afin d'illustrer l'intérêt de l'approche proposée, des calculs par éléments finis ont été effectués sur des situations élémentaires telles que le calcul des concentrations d'équilibre des phases en présence de contraintes et la croissance de précipités dans une matrice élastique ou élasto-plastique, situations pour lesquelles des solutions analytiques pour des interfaces parfaites sont disponiblesA general constitutive framework is proposed to incorporate linear and nonlinear mechanical behaviour laws (i. G. Elastoviscoplasticity) into a standard phase field model. A finite element formulation of a coupled phase field/diffusion/mechanical problem for alloys is proposed within the general framework of continuum thermodynamics. This formulation is based on the concept of generalized stresses as proposed by Gurtin, where an additional balance equation for generalized stresses, called microforces, associated with the order parameter and its first gradient, is postulated. The formulation is used to simulate the complex morphological evolutions of the heterogeneous microstructures and to describe the diffuse interface between two phases in the presence of the stresses induced by phase transformation. Using the principles of the thermodynamics of irreversible processes, the balance and constitutive equations are clearly separated in the formulation. Also, boundary and initial conditions for the displacement, concentration and order parameter and their dual quantities are clearly stated within the formulation. The theory is shown to be well-suited for a finite element formulation of the initial boundary value problems on nite size specimens with arbitrary geometries and for very general non-periodic or periodic boundary conditions. In the diffuse interface region where both phases coexist, mixture rules taken from homogenization theory are introduced into the formulation. The consequences of the choice of a specific interface behaviour is investigated, with regard to the mechanical effect on phase equilibria (equilibrium compositions and volume fractions of the coexisting phases), as well as on the transformation kinetics. The set of coupled evolution equations, which are the local static equilibrium, the balance of generalized stresses and the balance of mass, is solved using a finite element method for the space discretization and a finite difference method for the temporal discretization. To validate the numerical finite element implementation and to illustrate the ability of the proposed model to handle precipitation together with mechanical contribution effect, some elementary initial boundary value problem in coupled diusion-elasto-plasticity on finite size specimens has been solved and validated against corresponding sharp interface analytical solutions
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Hou, Yue. "Computational Analysis of Asphalt Binder based on Phase Field Method." Diss., Virginia Tech, 2014. http://hdl.handle.net/10919/47783.
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The mechanical performance evaluation of asphalt binder has always been a challenging issue for pavement engineers. Recently, the Phase Field Method (PFM) has emerged as a powerful computational tool to simulate the microstructure evolution of asphalt binder. PFM analyzes the structure from the free energy aspect and can provide a view of the whole microstructure evolution process. In this dissertation, asphalt binder performance is analyzed by PFM in three aspects: first, the relationship between asphalt chemistry and performance is investigated. The components of asphalt are simplified to three: asphaltene, resin and oil. Simulation results show that phase separation will occur under certain thermal conditions and result in an uneven distribution of residual thermal stress. Second, asphalt cracking is analyzed by PFM. The traditional approach to analyze crack propagation is Classic Fracture Mechanics first proposed by Griffith, which needs to clearly depict the crack front conditions and may cause complex cracking topologies. PFM describes the microstructure using a phase-field variable which assumes positive one in the intact solid and negative one in the crack void. The fracture toughness is modeled as the surface energy stored in the diffuse interface between the intact solid and crack void. To account for the growth of cracks, a non-conserved Allen-Cahn equation is adopted to evolve the phase-field variable. The energy based formulation of the phase-field method handles the competition between the growth of surface energy and release of elastic energy in a natural way: the crack propagation is a result of the energy minimization in the direction of the steepest descent. Both the linear elasticity and phase-field equation are solved in a unified finite element frame work, which is implemented in the commercial software COMSOL. Different crack mode simulations are performed for validation. It was discovered that the onset of crack propagation agrees very well with the Griffith criterion and experimental results. Third, asphalt self-healing phenomenon is studied based on the Atomic Force Microscopy (AFM) technology. The self-healing mechanism is simulated in two ways: thermodynamic approach and mechanical approach. Cahn-Hilliard dynamics and Allen-Cahn dynamics are adopted, respectively.Ph. D.
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Shen, Chen. "The fundamentals and applications of phase field method in quantitative microstructural modeling." Columbus, Ohio : Ohio State University, 2004. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1080249965.
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Thesis (Ph. D.)--Ohio State University, 2004.Title from first page of PDF file. Document formatted into pages; contains xx, 217 p.; also includes graphics (some col.). Includes abstract and vita. Advisor: Yunzhi Wang, Dept. of Materials Science and Engineering. Includes bibliographical references (p. 209-217).
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Xu, Ying. "TWO-DIMENSIONAL SIMULATION OF SOLIDIFICATION IN FLOW FIELD USING PHASE-FIELD MODEL|MULTISCALE METHOD IMPLEMENTATION." Lexington, Ky. : [University of Kentucky Libraries], 2006. http://lib.uky.edu/ETD/ukymeen2006d00524/YingXu_Dissertation_2006.pdf.
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Thesis (Ph. D.)--University of Kentucky, 2006.Title from document title page (viewed on January 25, 2007). Document formatted into pages; contains: xiii, 162 p. : ill. (some col.). Includes abstract and vita. Includes bibliographical references (p. 151-157).
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Düsing, Martin [Verfasser]. "Simulation of bainitic transformation with the phase field method / Martin Düsing." Paderborn : Universitätsbibliothek, 2018. http://d-nb.info/1171305648/34.
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Wang, Heyu. "Moving finite element methods for phase-field models of solidification." HKBU Institutional Repository, 2007. http://repository.hkbu.edu.hk/etd_ra/882.
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Parrinello, Antonino. "A rate-pressure-dependent thermodynamically-consistent phase field model for the description of failure patterns in dynamic brittle fracture." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:c6590f4f-f4e2-40e3-ada1-49ba35c2a594.
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The investigation of failure in brittle materials, subjected to dynamic transient loading conditions, represents one of the ongoing challenges in the mechanics community. Progresses on this front are required to support the design of engineering components which are employed in applications involving extreme operational regimes. To this purpose, this thesis is devoted to the development of a framework which provides the capabilities to model how crack patterns form and evolve in brittle materials and how they affect the quantitative description of failure. The proposed model is developed within the context of diffusive interfaces which are at the basis of a new class of theories named phase field models. In this work, a set of additional features is proposed to expand their domain of applicability to the modelling of (i) rate and (ii) pressure dependent effects. The path towards the achievement of the first goal has been traced on the desire to account for micro-inertia effects associated with high rates of loading. Pressure dependency has been addressed by postulating a mode-of-failure transition law whose scaling depends upon the local material triaxiality. The governing equations have been derived within a thermodynamically-consistent framework supplemented by the employment of a micro-forces balance approach. The numerical implementation has been carried out within an updated lagrangian finite element scheme with explicit time integration. A series of benchmarks will be provided to appraise the model capabilities in predicting rate-pressure-dependent crack initiation and propagation. Results will be compared against experimental evidences which closely resemble the boundary value problems examined in this work. Concurrently, the design and optimization of a complimentary, improved, experimental characterization platform, based on the split Hopkinson pressure bar, will be presented as a mean for further validation and calibration.
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Kuhn, Charlotte [Verfasser], and Ralf [Akademischer Betreuer] Müller. "Numerical and Analytical Investigation of a Phase Field Model for Fracture / Charlotte Kuhn. Betreuer: Ralf Müller." Kaiserslautern : Technische Universität Kaiserslautern, 2013. http://d-nb.info/1035405563/34.
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Rosam, Jan. "A fully implicit, fully adaptive multigrid method for multiscale phase-field modelling." Thesis, University of Leeds, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.445357.
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Yamada, Takayuki. "A Level Set-Based Topology Optimization Incorporating Concept of the Phase-Field Method." 京都大学 (Kyoto University), 2010. http://hdl.handle.net/2433/126804.
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Bhowmick, Sauradeep. "Advanced Smoothed Finite Element Modeling for Fracture Mechanics Analyses." University of Cincinnati / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1623240613376967.
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Yeddu, Hemantha Kumar. "Martensitic Transformations in Steels : A 3D Phase-field Study." Doctoral thesis, KTH, Metallografi, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-95316.
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Martensite is considered to be the backbone of the high strength of many commercial steels. Martensite is formed by a rapid diffusionless phase transformation, which has been the subject of extensive research studies for more than a century. Despite such extensive studies, martensitic transformation is still considered to be intriguing due to its complex nature. Phase-field method, a computational technique used to simulate phase transformations, could be an aid in understanding the transformation. Moreover, due to the growing interest in the field of “Integrated computational materials engineering (ICME)”, the possibilities to couple the phase-field method with other computational techniques need to be explored. In the present work a three dimensional elastoplastic phase-field model, based on the works of Khachaturyan et al. and Yamanaka et al., is developed to study the athermal and the stress-assisted martensitic transformations occurring in single crystal and polycrystalline steels. The material parameters corresponding to the carbon steels and stainless steels are considered as input data for the simulations. The input data for the simulations is acquired from computational as well as from experimental works. Thus an attempt is made to create a multi-length scale model by coupling the ab-initio method, phase-field method, CALPHAD method, as well as experimental works. The model is used to simulate the microstructure evolution as well as to study various physical concepts associated with the martensitic transformation. The simulation results depict several experimentally observed aspects associated with the martensitic transformation, such as twinned microstructure and autocatalysis. The results indicate that plastic deformation and autocatalysis play a significant role in the martensitic microstructure evolution. The results indicate that the phase-field simulations can be used as tools to study some of the physical concepts associated with martensitic transformation, e.g. embryo potency, driving forces, plastic deformation as well as some aspects of crystallography. The results obtained are in agreement with the experimental results. The effect of stress-states on the stress-assisted martensitic microstructure evolution is studied by performing different simulations under different loading conditions. The results indicate that the microstructure is significantly affected by the loading conditions. The simulations are also used to study several important aspects, such as TRIP effect and Magee effect. The model is also used to predict some of the practically important parameters such as Ms temperature as well as the volume fraction of martensite formed. The results also indicate that it is feasible to build physically based multi-length scale model to study the martensitic transformation. Finally, it is concluded that the phase-field method can be used as a qualitative aid in understanding the complex, yet intriguing, martensitic transformations.QC 20120525
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Cajuhi, Tuanny Verfasser], Lorenzis Laura [Akademischer Betreuer] De, and Pietro [Akademischer Betreuer] [Lura. "Fracture in porous media : phase-field modeling, simulation and experimental validation / Tuanny Cajuhi ; Laura De Lorenzis, Pietro Lura." Braunschweig : Technische Universität Braunschweig, 2019. http://d-nb.info/1180601521/34.
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Sridhar, Ashish [Verfasser], and Marc-André [Akademischer Betreuer] Keip. "Phase-field modeling of microstructure and fracture evolution in magneto-electro-mechanics / Ashish Sridhar ; Betreuer: Marc-André Keip." Stuttgart : Universitätsbibliothek der Universität Stuttgart, 2020. http://d-nb.info/1232727903/34.
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Asp, Grönhagen Klara. "Phase-field modeling of surface-energy driven processes." Doctoral thesis, KTH, Metallografi, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-11036.
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Surface energy plays a major role in many phenomena that are important in technological and industrial processes, for example in wetting, grain growth and sintering. In this thesis, such surface-energy driven processes are studied by means of the phase-field method. The phase-field method is often used to model mesoscale microstructural evolution in materials. It is a diffuse interface method, i.e., it considers the surface or phase boundary between two bulk phases to have a non-zero width with a gradual variation in physical properties such as energy density, composition and crystalline structure. Neck formation and coarsening are two important diffusion-controlled features in solid-state sintering and are studied using our multiphase phase-field method. Inclusion of Navier-Stokes equation with surface-tension forces and convective phase-field equations into the model, enables simulation of reactive wetting and liquid-phase sintering. Analysis of a spreading liquid on a surface is investigated and is shown to follow the dynamics of a known hydrodynamic theory. Analysis of important capillary phenomena with wetting and motion of two particles connected by a liquid bridge are studied in view of important parameters such as contact angles and volume ratios between the liquid and solid particles. The interaction between solute atoms and migrating grain boundaries affects the rate of recrystallization and grain growth. The phenomena is studied using a phase-field method with a concentration dependent double-well potential over the phase boundary. We will show that with a simple phase-field model it is possible to model the dynamics of grain-boundary segregation to a stationary boundary as well as solute drag on a moving boundary. Another important issue in phase-field modeling has been to develop an effective coupling of the phase-field and CALPHAD methods. Such coulping makes use of CALPHAD's thermodynamic information with Gibbs energy function in the phase-field method. With the appropriate thermodynamic and kinetic information from CALPHAD databases, the phase-field method can predict mictrostructural evolution in multicomponent multiphase alloys. A phase-field model coupled with a TQ-interface available from Thermo-Calc is developed to study spinodal decomposition in FeCr, FeCrNi and TiC-ZrC alloys.QC 20100622
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Yang, Fan. "Quantitative Study Of Precipitate Growth In Ti-6al-4v Using The Phase Field Method." The Ohio State University, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=osu1211902429.
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Aldakheel, Fadi [Verfasser], and Christian [Akademischer Betreuer] Miehe. "Mechanics of nonlocal dissipative solids : gradient plasticity and phase field modeling of ductile fracture / Fadi Aldakheel ; Betreuer: Christian Miehe." Stuttgart : Universitätsbibliothek der Universität Stuttgart, 2016. http://d-nb.info/1118370228/34.
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Gavagnin, Claudio. "Modeling and computation of cracking in multiphase porous media with the phase-field approach." Doctoral thesis, Università degli studi di Padova, 2019. http://hdl.handle.net/11577/3427308.
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The development of mathematical and numerical models for the study of the problem of fracture in porous media is motivated by several real-world applications. In particular, the phase-field approach to fracture, based on the regularization of the variational formulation of the Griffith's theory, seems to be one of the most promising, due to its ability to model complicated fracture processes, such as nucleation and branching, and preserve the continuity of the displacement field. The majority of the phase-field models for fracture in porous media present in the literature are mainly oriented to the study the problem of fracture in saturated porous media. Anyway, certain phenomena, such as the cracking of clayey soils during a desiccation process, suggest the importance of the extension of these models to a partially saturated framework, in which also the flow of the gaseous phase can influence the mechanical behavior of the porous medium, and thus the process of formation and evolution of fractures.
Abstract The aim of this work is to develop a finite element model for the phase-field analysis of fracture in three-phase porous media, in which both the flux of the water and the flux of the dry air are taken into account. In the first part of the thesis particular attention is payed to the study of some numerical difficulties that such modeling implies, such as the errors in the evaluation of the mass conservation of the water and the occurrence of numerical locking when a volumetric-deviatoric energy split for the phase-field model is used. An original mass conservative formulation, which takes into account the deformability of the solid skeleton, and a new stabilized mixed finite element formulation for the phase-field model of fracture in saturated porous media have been proposed, and tested with different numerical applications. In the last part of the thesis the finite element discretization of the proposed three-phase model is derived and applied to the numerical simulation of two different desiccation problems, in order to to study the influence of the balance equation of the air in the development of fractures in the porous medium.Lo sviluppo di modelli matematici e numerici per lo studio della frattura nei mezzi porosi è motivato da numerose applicazioni nel mondo reale. In particolare, lo studio della frattura con la tecnica del phase-filed, basata sulla regolarizzazione della formulazione variazionale della teoria di Griffith, sembra essere una delle più promettenti, grazie alla sua abilità di modellare fenomeni complessi, come la formazione e la ramificazione di fratture, a preservare la continuità del campo di spostamenti. La maggior parte dei modelli phase-field presenti in letteratura sono principalmente orientati allo studio della frattura in mezzi porosi saturi. D'altro canto, alcuni fenomeni, come la formazione di fratture in argille durante un processo di essicazione, indicano l'importanza di estendere questi modelli in condizione di parziale saturazione, tenendo in considerazione la possibile influenza del flusso della fase gassosa sul comportamento meccanico dello scheletro solido e, di conseguenza, sul processo di formazione e evoluzione della frattura. Lo scopo di questa tesi è la formulazione di un modello numerico agli elementi finiti per lo studio, con la tecnica del phase-field, della frattura in mezzi porosi trifase, in cui si considerino sia il flusso d'acqua che il flusso dell'aria all'interno del mezzo. Particolare attenzione è rivolta ad un approfondimento di alcune problematiche numeriche che tale modellazione comporta, come gli errori nella conservazione della massa della fase liquida e il locking numerico dovuto ad un eccesso di rigidezza volumetrica, quando lo split volumetrico-deviatorico dell'energia viene utilizzato nel modello phase-field. In particolare, vengono proposte e testate attraverso varie applicationi numeriche una nuova formulazione conservativa che tenga conto della deformabilità dello scheletro solido, e una nuova stabilizzazione per la formulazione mista del modello phase-field per la frattura in mezzi porosi saturi. Nell'ultima parte la discretizzazione agli elementi finiti del modello trifase proposto viene derivata, e applicata alla simulazione numerica di due problemi di essicazione, con l'obiettivo di studiare l'influenza dell'equazione di bilancio dell'aria sullo sviluppo di fratture nel mezzo poroso.
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Moraes, Alves Celso Luiz [Verfasser]. "Investigations on Microsegregation and Peritectic Phase Transformation with and without Elastic Effects Utilizing Phase-Field Method / Celso Luiz Moraes Alves." Aachen : Shaker, 2015. http://d-nb.info/1080761934/34.
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Luo, Weiqi. "Fundamental and practical applications of phase field method to the study of alloy microstructure evolutions." The Ohio State University, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=osu1407398850.
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Li, Shi-Ming. "Mean-Field Free-Energy Lattice Boltzmann Method for Liquid-Vapor Interfacial Flows." Diss., Virginia Tech, 2007. http://hdl.handle.net/10919/29621.
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This dissertation includes a theoretical and numerical development to simulate liquid-vapor flows and the applications to microchannels.
First, we obtain a consistent non-local pressure equation for simulating liquid-vapor interfacial flows using mean-field free-energy theory. This new pressure equation is shown to be the general form of the classical van der Waals" square-gradient theory. The new equation is implemented in two-dimensional (2D) D2Q7, D2Q9, and three-dimensional (3D) D3Q19 lattice Boltzmann method (LBM). The three LBM models are validated successfully in a number of analytical solutions of liquid-vapor interfacial flows.
Second, we have shown that the common bounceback condition in the literature leads to an unphysical velocity at the wall in the presence of surface forces. A few new consistent mass and energy conserving velocity-boundary conditions are developed for D2Q7, D2Q9, and D3Q19 LBM models, respectively. The three LBM models are shown to have the capabilities to successfully simulate different wall wettabilities, the three typical theories or laws for moving contact lines, and liquid-vapor channel flows.
Third, proper scaling laws are derived to represent the physical system in the framework of the LBM. For the first time, to the best of the author's knowledge, we obtain a flow regime map for liquid-vapor channel flows with a numerical method. Our flow map is the first flow regime map so far for submicrochannel flows, and also the first iso-thermal flow regime map for CO₂ mini- and micro-channel flows. Our results show that three major flow regimes occur, including dispersed, bubble/plug, and liquid strip flow. The vapor and liquid dispersed flows happen at the two extremities of vapor quality. When vapor quality increases beyond a threshold, bubble/plug patterns appear. The bubble/plug regimes include symmetric and distorted, submerged and non-wetting, single and train bubbles/plugs, and some combination of them. When the Weber number<10, the bubble/plug flow regime turns to a liquid strip pattern at the increased vapor quality of 0.5~0.6. When the Weber number>10, the regime transition occurs around a vapor quality of 0.10~0.20. In fact, when an inertia is large enough to destroy the initial flow pattern, the transition boundary between the bubble and strip regimes depends only on vapor quality and exists between x=0.10 and 0.20. The liquid strip flow regimes include stratified strip, wavy-stratified strip, intermittent strip, liquid lump, and wispy-strip flow. We also find that the liquid-vapor interfaces become distorted at the Weber number of 500~1000, independent of vapor quality. The comparisons of our flow maps with two typical experiments show that the simulations capture the basic and important flow mechanisms for the flow regime transition from the bubble/plug regimes to the strip regimes and from the non-distorted interfaces to the distorted interfaces.
Last, our available results show that the flow regimes of both 2D and 3D fall in the same three broad categories with similar subdivisions of the flow regimes, even though the 3D duct produces some specific 3D corner flow patterns. The comparison between 2D and 3D flows shows that the flow map obtained from 2D flows can be generally applied to a 3D situation, with caution, when 3D information is not available. In addition, our 3D study shows that different wettabilities generate different flow regimes. With the complete wetting wall, the flow pattern is the most stable.Ph. D.
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Malik, Amer. "Phase change with stress effects and flow." Doctoral thesis, KTH, Fysiokemisk strömningsmekanik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-118451.
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In this thesis two kinds of phase change i.e., solid state phase transformation in steels and solid-to-liquid phase transformation in paraffin, have been modeled and numerically simulated. The solid state phase transformation is modeled using the phase field theory while the solid-to-liquid phase transformation is modeled using the Stokes equation and exploiting the viscous nature of the paraffin, by treating it as a liquid in both states.The theoretical base of the solid state, diffusionless phase transformation or the martensitic transformation comes from the Khachaturyan's phase field microelasticity theory. The time evolution of the variable describing the phase transformation is computed using the time dependent Ginzburg-Landau equation. Plasticity is also incorporated into the model by solving another time dependent equation. Simulations are performed both in 2D and 3D, for a single crystal and a polycrystal. Although the model is valid for most iron-carbon alloys, in this research an Fe-0.3\%C alloy is chosen.In order to simulate martensitic transformation in a polycrystal, it is necessary to include the effect of the grain boundary to correctly capture the morphology of the microstructure. One of the important achievements of this research is the incorporation of the grain boundary effect in the Khachaturyan's phase field model. The developed model is also employed to analyze the effect of external stresses on the martensitic transformation, both in 2D and 3D. Results obtained from the numerical simulations show good qualitative agreement with the empirical observations found in the literature.The microactuators are generally used as a micropump or microvalve in various miniaturized industrial and engineering applications. The phase transformation in a paraffin based thermohydraulic membrane microactuator is modeled by treating paraffin as a highly viscous liquid, instead of a solid, below its melting point. The fluid-solid interaction between paraffin and the enclosing membrane is governed by the ALE technique. The thing which sets apart the presented model from the previous models, is the use of geometry independent and realistic thermal and mechanical properties. Numerical results obtained by treating paraffin as a liquid in both states show better conformity with the experiments, performed on a similar microactuator. The developed model is further employed to analyze the time response of the system, for different input powers and geometries of the microactuator.QC 20130219
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Schänzel, Lisa-Marie [Verfasser], and Christian [Akademischer Betreuer] Miehe. "Phase field modeling of fracture in rubbery and glassy polymers at finite thermo-viscoelastic deformations / Lisa-Marie Schänzel. Betreuer: Christian Miehe." Stuttgart : Universitätsbibliothek der Universität Stuttgart, 2015. http://d-nb.info/1069107409/34.
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Schwaab, Marie-Émeline. "Growth of interacting cracks : numerical approach to "En-passant" fracture." Thesis, Lyon, 2018. http://www.theses.fr/2018LYSE1276/document.
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La rupture macroscopique d’un matériau intervient généralement lorsque des micro-défauts coalescent, plutôt que par la propagation catastrophique d’une seule fissure. Il est donc souhaitable d’étudier des configurations de rupture où de multiples fissures interagissent. Les paires de fissures en-passant (EP), où deux fissures parallèles croissent l’une vers l’autre, sont particulièrement intéressantes d’un point de vue applicatif. Cette configuration de rupture se retrouve aussi bien dans des situations naturelles (os, dorsales océaniques,…) qu’industrielles (génie civil, pièces métalliques,…). Malgré la diversité de tailles et de matériaux dans lesquels ces fissures existent, leurs trajectoires ont une forme typique en crochet quasi-universelle dont l’origine, résultant de l’interaction fissure-fissure répulsive puis attractive, est mal comprise. En particulier, le comportement répulsif initial semble mettre à mal la mécanique élastique linéaire de la rupture (MELR). Dans cette thèse, nous avons d’abord étudié les fissures EP dans le cadre de la MELR. L’étude de l’angle initial de déviation et la simulation de trajectoires a montré contre toute attente que la MELR permet de reproduire qualitativement la forme en crochet. Prédire précisément certaines caractéristiques, comme l’intensité de la phase répulsive, nécessite plus de finesse au niveau de la représentation du comportement matériau. Nous avons ensuite utilisé un modèle par champ de phase pour enrichir le modèle matériau. Les nouvelles trajectoires simulées étant fortement influencées par la longueur caractéristique du champ de phase, il est possible d’obtenir un modèle plus juste quantitativement. Une perspective intéressante reste de relier cette longueur à la microstructure du matériauMacroscopic failure of a material happens generally through the coalescence of micro-defects rather than the catastrophic propagation of a single crack. It is therefore advisable to study fracture problems in which many cracks interact. The case of en-passant crack pairs (EP-cracks), two parallel and offset cracks approaching each other by propagating through their inner tips, presents a marked interest as these cracks can be found in various natural (bones, oceanic rifts,..) or industrial (civil engineering,…) situations. Despite the large variety of scales and materials in which these cracks are observed, their trajectories present a remarkably self-similar hook-shape. This shape result from the crack-crack interaction, first repulsive before becoming attractive, and its origin is poorly understood. In particular, the initial repulsive behaviour seems to question the validity of linear elastic fracture mechanics (LEFM). In this thesis, we first studied EP-cracks in the LEFM framework. The study of the initial kink angle and the simulation of crack paths showed against all expectations that LEFM is able to reproduce qualitatively the hook-shaped paths. Precise predictions of specific characteristics, such as the magnitude of repulsion, requires a more refined model of the material behaviour. We then used a phase-field model to augment the material representation. As they are strongly influenced by the characteristic length scale of the phase-field, the new simulated trajectories indicate that it is possible to develop a more quantitatively correct model. An attractive prospect is to link this characteristic length to the material microstructure
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Vondrous, Alexander [Verfasser]. "Grain growth behavior and efficient large scale simulations of recrystallization with the phase-field method / Alexander Vondrous." Karlsruhe : KIT Scientific Publishing, 2014. http://www.ksp.kit.edu.
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Gu, Hanfeng. "Multigrid methods for 3D composite material simulation and crack propagation modelling based on a phase field method." Thesis, Lyon, 2016. http://www.theses.fr/2016LYSEI090/document.
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Avec le développement des techniques d’imagerie telles que la tomographie par rayons X au cours des dernières années, il est maintenant possible de prendre en compte la microstructure réelle dans les simulations des matériaux composites. Cependant, la complexité des composites tels que des fibres inclinées et brisées, les vides, exige un grand nombre des données à l’échelle microscopique pour décrire ces détails et amène ainsi des problèmes difficiles en termes de temps de calcul et de mémoire lors de l’utilisation de méthodes de simulation traditionnelles comme la méthode Eléments Finis. Ces problèmes deviennent encore plus sérieux dans la simulation de l’endommagement, comme la propagation des fissures. Par conséquent, il est nécessaire d’étudier des méthodes numériques plus efficaces pour ce genre de problèmes à grande échelle. La méthode Multigrille (MG) est une méthode qui peut être efficace parce que son coût de calcul est proportionnel au nombre d’inconnues. Dans cette thèse, un solveur de MG efficace pour ces problèmes est développé. La méthode MG est appliquée pour résoudre le problème d’élasticité statique basé sur l’équation de Lamé et aussi le problème de la propagation de fissures basé sur une méthode de champ de phase. La précision des solutions MG est validée par une solution analytique classique d’Eshelby. Ensuite, le solveur MG est développé pour étudier le processus d’homogénéisation des composites et ses solutions sont comparées avec des solutions existantes de la littérature. Après cela, le programme de calcul MG est appliqué pour simuler l’effet de bord libre dans les matériaux composites stratifiés. Une structure stratifiée réelle donnée par tomographie X est d’abord simulé. Enfin, le solveur MG est encore développé, combinant une méthode de champ de phase, pour simuler la rupture quasi-fragile. La méthode MG présente l’efficacité à la fois en temps de calcul et en mémoire pour résoudre les problèmes ci-dessusWith the development of imaging techniques like X-Ray tomography in recent years, it is now possible to take into account the microscopic details in composite material simulations. However, the composites' complex nature such as inclined and broken fibers, voids, requires rich data to describe these details and thus brings challenging problems in terms of computational time and memory when using traditional simulation methods like the Finite Element Method. These problems become even more severe in simulating failure processes like crack propagation. Hence, it is necessary to investigate more efficient numerical methods for this kind of large scale problems. The MultiGrid (MG) method is such an efficient method, as its computational cost is proportional to the number of unknowns. In this thesis, an efficient MG solver is developed for these problems. The MG method is applied to solve the static elasticity problem based on the Lame's equation and the crack propagation problem based on a phase field method. The accuracy of the MG solutions is validated with Eshelby's classic analytic solution. Then the MG solver is developed to investigate the composite homogenization process and its solutions are compared with existing solutions in the literature. After that, the MG solver is applied to simulate the free-edge effect in laminated composites. A real laminated structure using X-Ray tomography is first simulated. At last, the MG solver is further developed, combined with a phase field method, to simulate the brittle crack propagation. The MG method demonstrates its efficiency both in time and memory dimensions for solving the above problems
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Fromm, Bradley S. "Linking phase field and finite element modeling for process-structure-property relations of a Ni-base superalloy." Thesis, Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/45789.
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Establishing process-structure-property relationships is an important objective in the paradigm of materials design in order to reduce the time and cost needed to develop new materials. A method to link phase field (process-structure relations) and microstructure-sensitive finite element (structure-property relations) modeling is demonstrated for subsolvus polycrystalline IN100. A three-dimensional (3D) experimental dataset obtained by orientation imaging microscopy performed on serial sections is utilized to calibrate a phase field model and to calculate inputs for a finite element analysis. Simulated annealing of the dataset realized through phase field modeling results in a range of coarsened microstructures with varying grain size distributions that are each input into the finite element model. A rate dependent crystal plasticity constitutive model that captures the first order effects of grain size, precipitate size, and precipitate volume fraction on the mechanical response of IN100 at 650°C is used to simulate stress-strain behavior of the coarsened polycrystals. Model limitations and ideas for future work are discussed.
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Wu, Chi. "Time-dependent Topology Optimisation for Implantable Devices." Thesis, The University of Sydney, 2022. https://hdl.handle.net/2123/29237.
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Implantable load-bearing devices signify a class of major biomechanical devices that replace damaged organs/tissue to restore desired functionalities. So far, implant designs often follow trial-and-error or experience-based protocols rather than patient-specific designs. In addition, in-vivo studies have demonstrated that implant design can substantially determine long-term treatment outcomes and longevity. Therefore, rather than empirical guidelines, efficient and elegant design approaches are urgently required to consider both initial conditions and time-dependent behaviours to promise an optimal outcome over time. One of the critical issues associated with implant devices is fracture failure due to low tensile strength and low fracture toughness at initial conditions or over time. Thus, topology optimisation for implantable devices considering path/time-dependent fracture failure was explored in this thesis. Then, a level-set based topology optimisation approach was developed to maximise fracture resistance of composite biomaterials. Load-bearing implants can change local biomechanical conditions, notably affecting long-term treatment outcomes. Considering this time-dependent nature, the thesis proposed a time-dependent topology optimisation framework for design of bone fixation plates and tissue scaffolds by incorporating bone adaptation and regeneration. Accurately predicting bone growth and remodelling results rely on the inverse-identification of tissue ingrowth/remodelling-related parameters from in-vivo data. To tackle this issue, the thesis investigated a novel machine learning-based multiscale model to predict bone growth in scaffolds efficiently. The inversely identified remodelling-related parameters were then used for a machine learning-based design of patient-specific scaffolds by incorporating ceramic additive manufacturing.
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Paranjape, Harshad Madhukar. "Modeling of Shape Memory Alloys: Phase Transformation/Plasticity Interaction at the Nano Scale and the Statistics of Variation in Pseudoelastic Performance." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1417605178.
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Msekh, Mohammed Abdulrazzak Verfasser], Timon [Akademischer Betreuer] Rabczuk, Lorenzis Laura [Gutachter] De, and Tom [Gutachter] [Lahmer. "Phase Field Modeling for Fracture with Applications to Homogeneous and Heterogeneous Materials / Mohammed Abdulrazzak Msekh ; Gutachter: Laura De Lorenzis, Tom Lahmer ; Betreuer: Timon Rabczuk." Weimar : Bauhaus-Universität Weimar, 2017. http://d-nb.info/1135592950/34.
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Msekh, Mohammed Abdulrazzak Verfasser], Timon [Akademischer Betreuer] [Rabczuk, Lorenzis Laura Gutachter] De, and Tom [Gutachter] [Lahmer. "Phase Field Modeling for Fracture with Applications to Homogeneous and Heterogeneous Materials / Mohammed Abdulrazzak Msekh ; Gutachter: Laura De Lorenzis, Tom Lahmer ; Betreuer: Timon Rabczuk." Weimar : Bauhaus-Universität Weimar, 2017. http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170615-32291.
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Bansel, Gurvinder Singh. "Advanced operator splitting based semi-implicit spectral method to solve the binary and single component phase-field crystal model." Thesis, Brunel University, 2011. http://bura.brunel.ac.uk/handle/2438/5900.
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We present extensive testing in order to find the optimum balance among errors associated with time integration, spatial discretization, and splitting for a fully spectral semi implicit scheme of the phase field crystal model. The scheme solves numerically the equations of dissipative dynamics of the binary phase field crystal model proposed by Elder et al. [Elder et al, 2007]. The fully spectral semi implicit scheme uses the operator splitting method in order to decompose the complex equations in the phase field crystal model into sub-problems that can be solved more efficiently. Using the combination of non-trivial splitting with the spectral approach, the scheme leads to a set of algebraic equations of diagonal matrix form and thus easier to solve. Using this method developed by the BCAST research team we are able to show that it speeds up the computations by orders of magnitude relative to the conventional explicit finite difference scheme, while the costs of the pointwise implicit solution per timestep remains low. Comparing both the finite difference scheme used by Elder et al [Elder et al, 2007] to the spectral semi implicit scheme, we are also able to show that the finite differencing cannot compete with the spectral differencing in regards to accuracy. This is mainly due to numerical dissipation in finite differencing. In addition the results show that this method can efficiently be parallelized for distributed memory systems, where an excellent scalability with the number of CPUs. We have applied the semi-implicit spectral scheme for binary alloys to explore polycrystalline dendritic solidification. The kinetics of transformation has been analysed in terms of Johnson-Mehl-Avrami-Kolmogorov formalism. We show that Avrami plots are not linear, and the respective Avrami-Kolmogorov exponents (PAK) vary with the transformed fraction (or time). Using the semi-implicit spectral scheme we have been able to provide extensive numerical testing of methods in solving the single component case. This has been demonstrated by using unconditional time stepping with comparable simulations using conditional time stepping. We show the accuracy of the solution for unconditional time stepping is not compromised and furthermore computational efficiency can be significantly increased with the introduction of this scheme. Finally we have investigated how the composition of the initial liquid phase influences the eutectic morphology evolving during solidification. This is the first study that addresses this question using the dynamical density functional theory.