Dissertations / Theses on the topic 'Localised failure'

This thesis explains on the numerical study of localized damage mechanism in concrete pedestals supporting bridge girder bearings. It examined the structural response of concrete pedestals dealing with complex contact interaction behaviour between steel bearing plate and concrete. Three dimensional nonlinear explicit finite element micro models of concrete pedestals were analyzed with various pedestal heights, edge clearance distances, loading geometries, confinement reinforcements and loading eccentricities. Also included are few mitigation strategies had been proposed to minimize the effect of localized failure and therefore which can then improve the structural performance of concrete pedestals.

High wind events such as tropical cyclones, severe storms and tornadoes are more likely to impact the Australian coastal regions due to possible climate changes. Such events can be extremely destructive to building structures, in particular, low-rise buildings with lightweight roofing systems that are commonly made of thin steel roof sheeting and battens. Large wind suction loads that act on the roofs during high wind events cause premature failures of roof connections (fixings), leading to complete roof failures. Past wind damage investigations showed that the roof sheeting to batten connection failed frequently during high wind events. These local connection failures have been extensively investigated by many researchers and suitable recommendations to eliminate such failures have been proposed. However, this meant the weakest point has now shifted to the batten to truss/rafter connection. These connections are predominantly subjected to localised pull-through failures in which the screw fastener head pulls through the bottom flanges of thin steel roof battens. However, these failures have not been investigated adequately despite the many roof batten pull-through failures and eventual losses of both roof sheeting and battens observed after recent high wind events. Currently available design rules for the pull-through capacity of cold-formed steel screw fastener connections do not address the specific pull-through failures in thin steel roof battens under wind uplift loading. Current design practice of roof battens is based on using the design wind uplift capacity tables published by their manufacturers. However, it is unclear whether these design capacity tables developed for specific roof battens adequately included the effects of pull-through failures. As for the roof sheeting to batten connections, batten to rafter/truss connections are also subjected to both static and fatigue failures due to static and cyclic wind uplift loads, respectively. Although some experimental studies were conducted in the past using simulated static and cyclic wind loading, they were incomplete and no design rules were developed. Since the climate predictions indicate the likelihood of severe storm events with increased intensity in the future, they are more likely to cause static pull-through failures of roof battens. In addition, a thorough understanding of the static behaviour is first needed to evaluate the fatigue behaviour in depth. Hence this research was aimed at investigating the localised pull-through failures of thin steel roof battens under simulated static wind uplift loads, using laboratory experiments and finite element modelling. A preliminary and detailed experimental study was first conducted using industrial roof battens and full scale air-box tests and three small scale tests such as two-span batten tests, cantilever batten tests and short batten tests. Suitable small scale test methods were identified to accurately simulate the localised pull-through failures of roof battens. The applicability of the proposed small scale test methods for other roof battens was verified using two-span and short batten tests undertaken using roof battens made at the university workshop. Based on the test results, a suitable modification factor was recommended for use with the pull-through capacity equation presented in the current Australian (AS/NZS 4600: 2005) and American (AISI S100: 2012) cold-formed steel standards to accurately determine the pullthrough failure loads of roof battens. The main and extensive experimental study was then undertaken using two-span and short batten tests to examine the pull-through failures of roof battens. The tests were conducted to investigate the effects of many critical parameters such as screw fastener tightening, batten height, web angle, steel grade, batten thickness, screw fastener head size, screw fastener location, batten bottom flange width, underside and edge details of the screw fastener head, and screw fastener types on the roof batten pull-through failure behaviour and capacity. Since the test results showed that the pull-through failure behaviour of high strength and low strength steel roof battens significantly differed from each other due to the differences in ductility, two new design rules and relevant capacity reduction factors were developed to accurately determine the design pull-through capacities of roof battens. The finite element models of both two-span batten and short batten test specimens were modelled and analysed using ABAQUS software. A suitable failure criterion was developed based on constitutive model inputs and employed in the finite element analyses to accurately predict the initiation of pull-through failures of thin steel roof battens associated with the tearing fracture of bottom flange around the screw fastener head edge. The finite element models were validated using the test results, and additional parametric studies were conducted to investigate the parameters which were not considered in the experimental study due to their lower importance on pullthrough failure behaviour and capacity of roof battens. A large pull-through capacity data base was developed using the pull-through failure loads obtained from the tests and finite element analyses. Suitable design rules were then developed using them and finally recommended with suitable capacity reduction factors for the accurate determination of the design pull-through capacities of thin-walled steel roof battens. This study also investigated the strengthening methods recommended by the roof batten manufacturers and builders and showed that they are inadequate to provide a significant improvement based on the governing pull-through failures of roof battens. A reliable strengthening method using overlapping short battens as brackets at the supports was recommended and a series of roof batten tests was conducted using two-span batten tests and two types of industrial roof battens. The test results confirmed the adequacy of the proposed strengthening method. Suitable fragility curves were developed using detailed probabilistic analyses and Monte Carlo simulations based on the governing pull-through failures of thin steel roof battens to predict the likely level of roof damages to a large community for a given wind speed. The pull-through failure behaviour of roof battens was examined by defining eight different cases that are likely to occur during high wind events (for example, with and without dominant openings) and developing relevant fragility curves. The effects of using different batten span and spacing were also investigated using fragility curves. Fragility curves were also used to evaluate the enhancement level that could be achieved with the proposed strengthening method. In summary, this research study has developed suitable test, design and strengthening methods and fragility curves for thin steel roof battens subject to localised pullthrough failures under high wind uplift loads.

Failure modes for sandwich beams of GFRP laminate skins and Nomex honeycomb core are investigated. Theoretical models using honeycomb mechanics and classical beam theory are described. A failure mode map for loading under 3-point bending, is constructed, showing the dependence of failure mode and load on the ratio of skin thickness to span length and honeycomb relative density. Beam specimens are tested in 3-point bending. The effect of honeycomb direction is also examined. The experimental data agree satisfactorily with the theoretical predictions. The results reveal the important role of core shear in a sandwich beam's bending behaviour and the need for a better understanding of indentation failure mechanism. High order sandwich beam theory (HOSBT) is implemented to extract useful information about the way that sandwich beams respond to localised loads under 3-point bending. 'High-order' or localised effects relate to the non-linear patterns of the in-plane and vertical displacements fields of the core through its height resulting from the unequal deformations in the loaded and unloaded skins. The localised effects are examined experimentally by Surface Displacement Analysis of video images recorded during 3-point bending tests. A new parameter based on the intrinsic material and geometric properties of a sandwich beam is introduced to characterise its susceptibility to localised effects. Skin flexural rigidity is shown to play a key role in determining the way that the top skin allows the external load to pass over the core. Furthermore, the contact stress distribution in the interface between the central roller and the top skin, and its importance to an indentation stress analysis, are investigated. To better model the failure in the core under the vicinity of localised loads, an Arcan- type test rig is used to test honeycomb cores under simultaneous compression and shear loading. The experimental measurements show a linear relationship between the out-of-plane compression and shear in honeycomb cores. This is used to derive a failure criterion for applied shear and compression, which is combined with the high order sandwich beam theory to predict failure caused by localised loads in sandwich beams made of GFRP laminate skins and Nomex honeycomb under 3-point bending loading. Short beam tests with three different indenter's size are performed on appropriately prepared specimens. Experiments validate the theoretical approach and reveal the nature of pre- and post-failure behaviour of these sandwich beams. HOSBT is used as a compact computational tool to reconstruct failure mode maps for sandwich panels. Superposition of weight and stiffness contours on these failure maps provide carpet plots for design optimisation procedures.

Cette thèse aborde le problème de la rupture localisée dans les roches, qui caractérise un grand nombre d'applications dans le domaine du génie civil, tels que la rupture du barrage, effondrement des fondations, la stabilité des excavations ou les tunnels, les glissements de terrain et les éboulements. Le risque de rupture localisée devrait être mieux appréhendé pour mieux l'éviter. La rupture localisée dans les roches est généralement caractérisée par une une rupture soudaine et quasi-fragile sans avertissement sous forme de grandes déformations et visibles avant la rupture elle-même. Cela se produit également sous l'influence des hétérogénéités matériels, des fissures existantes et d'autres défauts initiaux.Les trois nouveaux modèles numériques, intégrant les mécanismes de ruptures localisées, l'hétérogénéité de la roche et des fissures existantes et d'autres défauts, sont présentés dans cette thèse. Le premier modèle propose une représentation en 2D de roche composite à deux phases, où la phase solide représente la roche intacte et la faible phase indique les défauts initiaux. Le deuxième modèle représente l'extension du modèle précédent vers un espace 3D, où est considéré un ensemble complet de mécanismes de ruptures en 3D. Les propriétés hétérogènes sont considérées ici par une distribution aléatoire en accord avec la variation statistique de Gausse. Ce modèle est également utilisé pour l'analyse de la roche intacte par spécimens possédant des écarts de formes géométriques qui influencent la résistance à la compression uni-axiale. Le troisième modèle est un modèle en 2D, traitant l’interaction volumétrique entre un fluide et la structure sous l’influence de l’écoulement du fluide à travers le milieu de la roche poreuse.L'approche des lattices discrètes est choisie pour construire un cadre général pour les trois modèles, où les cellules de Voronoï représentent les grains de roche tenus ensemble par les poutres de Timoshenko comme des liens de cohésion. La cinématique améliorée est caractérisée par l'approche intégrée des discontinuités comme un supplément à la cinématique standard de liens cohérents. Cela sert pour la propagation de la macro fissure dans tous les modes de ruptures et de leurs combinaisons, entre les grains de la roche. La formation de la zone du processus de rupture suivie par des microfissures coalescentes, précédant la rupture localisée, est aussi considérée dans les modèles. L’écoulement du fluide est régi par la loi de Darcy, tandis que les conditions de couplage obéissent à la théorie de poroélasticité de Biot.Les résultats des modèles numériques ont été vérifiés par des exemples de la littérature dans le cas des modèles en 2D. Le modèle en 3D a été validé suite aux résultats expérimentaux effectués sur 90 échantillons de roches, où sont considérées de légères déviations géométriques des spécimens.La présentation de ces modèles, ainsi que leurs aspects de mise en œuvre sont présentés en détail. L’approche avec une discontinuité intrinsèque et le caractère local des améliorations nécessaires à la simulation des discontinuités de déplacement orientent vers la condensation statique des degrés de liberté améliorés sont efficacement intégrés dans l’architecture des éléments finis
This thesis deals with the problem of localized failure in rocks, which occurs often in civil engineering practice like in dam failure, foundation collapse, stability of excavaations, slopes and tunnels, landslides and rock falls. The risk of localized failure should be better understood in order to be prevented. The localized failure in rocks is usually characterized by a sudden and brittle failure without warning in a sense of larger and visible deformations prior to failure. This happens also under the strong influence of material heterogeneities, preexisting cracks and other defects.The three novel numerical models, incorporating the localized failure mechanisms, heterogeneity of rock and preexisting cracks and other defects, are presented in this thesis. First model deals with 2D plane strain two-phase rock composite, where stronger phase represents the intact rock and weaker phase initial defects. Second model represents the extension of the previous model towards the 3D space, where full set of 3D failure mechanisms is considered. Heterogeneous properties are taken here through the random distribution and Gauss statistical variation of material properties. The latter model is also used for the analysis of intact rock core specimens geometrical shape deviations influencing the uni-axial compressive strength. Third model is a 2D, dealing with volumetric fluid-structure interaction and localized failure under the influence of fluid flow throughthe porous rock medium.The discrete beam lattice approach is chosen for general framework for three models, where Voronoi cells represent the rock grains kept together by Timoshenko beams as cohesive links. The enhanced kinematics characterized for embedded discontinuity approach is added upon standard kinematics of cohesive links. This serves for the macro crack propagation in all failure modes and their combinations, between the rock grains. The fracture process zone formation followed by micro-cracks coalescence, preceding the localized failure, is considered as well. Fluid flow is governed by a Darcy law, while coupling conditions obey Biot's theory of poroplasticity. The results of the numerical models were verified by the benchmarks available from literature in 2D case. The 3D model was validated against the experimental results conducted on 90 rock specimens, where even slight geometrical deviations of specimens are considered.Presentation of these models, as well as their implementation aspects are given in full detail. Embedded discontinuity concept and the local nature of enhancements required to capture the displacement discontinuities leads to the very efficient approach with static condensation of enhanced degrees of freedom and technique that can be efficiently incorporated into finite element code architecture

La défaillance des matériaux et structures d'ingénierie peut être considéré comme le résultat d'une interaction complexe entre différents phénomènes physiques tels que la nucléation des cavités, les microfissures, les microvides et d'autres processus irréversibles. Ces micro-défauts se fondent éventuellement en une ou plusieurs macro-fissures conduisant à une diminution de la capacité portante et finalement à une défaillance de la structure considérée. La prévention des défaillances des structures et des composants structurels a toujours été un sujet important et une préoccupation majeure en ingénierie. Cette thèse vise à représenter une défaillance localisée dans des matériaux non linéaires sans dépendance de maillage. Un intérêt particulier sera le cas de l’adoucissement dynamique des déformations. Les phénomènes localisés sont pris en compte en utilisant l'approche des discontinuités embarquées fortes dans laquelle le champ de déplacement est amélioré pour capturer la discontinuité. Sur la base de cette approche, on a d'abord développé un modèle unidimensionnel de barres élasto-plastique capable de représenter une défaillance pour des matériaux ductiles avec un durcissement combiné dans une zone de processus de fracture FPZ et un adoucissement avec des discontinuités fortes encastrées. Les résultats comparant le modèle unidimensionnel proposé aux travaux (semi-) analytiques sont présentés. Il a été démontré que la stratégie proposée offre des solutions indépendantes de maillage. La déformation augmente dans le domaine de l’adoucissement avec une diminution simultanée de la contrainte. Le problème se décharge élastiquement à l'extérieur de la zone d’adoucissement de déformation. L'énergie dissipée se trouve à disparaître. Le modèle a également été comparé à un modèle de dommage unidimensionnel capable de représenter la fracture dynamique de la barre d'endommagementélasto-endommagée dans la zone de traitement de fracture - FPZ et de adoucissement avec de discontinuités fortes encastrées pour trouver un bon accord entre deux modèles. Un modèle d'éléments finis bidimensionnel a été développé, capable de décrire à la fois le mécanisme de dommage diffus accompagné d'un durcissement initial et d'une réponse d’adoucissement ultérieure de la structure. On a analysé les résultats de plusieurs simulations numériques effectuées sur des essais mécaniques classiques sous des charges progressivement croissantes telles que le test Brésilien ou le test de flexion en trois points. Le cadre de dynamique proposé est montré pour augmenter la robustesse de calcul. On a constaté que la direction finale des macro-fissures est assez bien prédite et que l'influence des effets d'inertie sur les solutions obtenues est assez modeste notamment en comparaison entre différentes mailles. Ce modèle bidimensionnel a été étendu plus loin dans le modèle bidimensionnel de discontinuité intégrée en viscodamage pour aider à explorer brièvement la mise en œuvre du schéma de point intermédiaire de second ordre qui peut fournir des résultats améliorés sous limitation de la régularisation visqueuse du modèle de dégâts localisés
Failure of engineering materials and structures can be considered as a result of a complex interplay between different physical phenomena such as nucleation of cavities, microcracks,microvoids and other irreversible processes. These micro-defects eventually coalesce into one or more macro-cracks leading to a decrease in the load-bearing capability and finally, to failure of the structure under consideration. Prevention of failure of structures and structural parts has always been a critical subject and a major concern in engineering. This thesis aims to represent localized failure in non linear materials without mesh dependency. Of special interest will be the case of dynamic strain-softening. Localized phenomena are taken into account by using the embedded strong discontinuities approach in which the displacement field is enhanced to capture the discontinuity. Based upon this approach, a one-dimensional model for elasto-plastic bar capable of representing failure for ductile materials with combined hardening in FPZ-fracture process zone and softening with embedded strong discontinuities was first developed. Results comparing the proposed one-dimensional model to (semi-) analytical works are presented. It was shown that the proposed strategy provides mesh independent solutions. Strain increases in the softening domain with a simultaneous decrease of stress. The problem unloads elastically outside the strain softening region. The strain energy is found to vanish. The model was also compared with a one dimensional damage model capable of representing the dynamic fracture for elasto-damage bar with combined hardening in fracture process zone - FPZ and softening with strong embedded discontinuities to find a good agreement between two models. A two-dimensional finite element model was developed, capable of describing both the diffuse damage mechanism accompanied by initial strain hardening and subsequent softening response of the structure. The results of several numerical simulations, performed on classical mechanical tests under slowly increasing loads such as Brazilian test or three-point bending test were analyzed. The proposed dynamics framework is shown to increase computational robustness. It was found that the final direction of macro-cracks is predicted quite well and that influence of inertia effects on the obtained solutions is fairly modest especially in comparison among different meshes. This two-dimensional model was expanded further into the two dimensional continuum viscodamage-embedded discontinuity model to help briefly explore the implementation of the second order mid-point scheme that can provide improved results under limitation of viscous regularization of localized failure damage model

Localization studies arise from the need to accurately model the behaviour of materials which exhibit instabilities due to strain softening or geometric effects. Localization in finite element modelling of brittle materials such as concrete and rock is a relatively unexplored area in computational mechanics, and this work applies current concepts to an isotropic damage model. The onset of localization is characterised by a bifurcation, where spatially uniform deformation is replaced by highly localized bands of large strain. Simple bifurcation analysis techniques are used, and are shown to extend the present predictive capability of the damage model and to indicate the direction of further refinement. Numerical studies of localization in concrete and norite are presented, together with boundary value problems of importance in mining applications. It is shown that qualitative agreement is obtained with experimental results.

In this work, several beam finite element formulations are proposed for failure analysis of planar reinforced concrete beams and frames under monotonic static loading. The localized failure of material is modeled by the embedded strong discontinuity concept, which enhances standard interpolation of displacement (or rotation) with a discontinuous function, associated with an additional kinematic parameter representing jump in displacement (or rotation). The new parameters are local and are condensed on the element level. One stress resultant and two multi-layer beam finite elements are derived. The stress resultant Euler-Bernoulli beam element has embedded discontinuity in rotation. Bending response of the bulk of the element is described by elasto-plastic stress resultant material model. The cohesive relation between the moment and the rotational jump at the softening hinge is described by rigid-plastic model. Axial response is elastic. In the multi-layer beam finite elements, each layer is treated as a bar, made of either concrete or steel. Regular axial strain in a layer is computed according to Euler-Bernoulli or Timoshenko beam theory. Additional axial strain is produced by embedded discontinuity in axial displacement, introduced individually in each layer. Behavior of concrete bars is described by elastodamage model, while elasto-plasticity model is used for steel bars. The cohesive relation between the stress at the discontinuity and the axial displacement jump is described by rigid-damage softening model in concrete bars and by rigid-plastic softening model in steel bars. Shear response in the Timoshenko element is elastic. Finally, the multi-layer Timoshenko beam finite element is upgraded by including viscosity in the softening model. Computer code implementation is presented in detail for the derived elements. An operator split computational procedure is presented for each formulation. The expressions, required for the local computation of inelastic internal variables and for the global computation of the degrees of freedom, are provided. Performance of the derived elements is illustrated on a set of numerical examples, which show that the multi-layer Euler-Bernoulli beam finite element is not reliable, while the stress-resultant Euler-Bernoulli beam and the multi-layer Timoshenko beam finite elements deliver satisfying results.

During the last decades, the localized failure of massive structures under thermo-mechanical loads becomes the main interest in civil engineering due to a number of construction damaged and collapsed due to fire accident. Two central questions were carried out concerning the theoretical aspect and the solution aspect of the problem. In the theoretical aspect, the central problem is to introduce a thermo-mechanical model capable of modeling the interaction between these two physical effects, especially in localized failure. Particularly, we have to find the answer to the question: how mechanical loading affect the temperature of the material and inversely, how thermal loading result in the mechanical response of the structure. This question becomes more difficult when considering the localized failure zone, where the classical continuum mechanics theory can not be applied due to the discontinuity in the displacement field and, as will be proved in this thesis, in the heat flow. In terms of solution aspect, as this multi-physical problem is mathematical represented by a differential system, it can not be solved by an 'exact' analytical solution and therefore, numerical approximation solution should be carried out. This thesis contributes in both two aspects. Particularly, thermomechanical models for both steel and concrete (the two most important materials in civil engineering), which capable of controling the hardening behavior due to plasticity and/or damage and also the softening behavior due to the localized failure, are carried out and discussed. Then, the thermomechanical problems are solved by 'adiabatic' operator split procedure, which 'separates' the multi-physical process into the 'mechanical' part and the 'thermal' part. Each part is solved individually by another operator split procedure in the frame-work of embbed-discontinuity finite element method. In which, the 'local' discontinuities of the displacement field and the heat flow is solved in the element level, for each element where localized failure is detected. Then, these discontinuities are brought into the 'static condensation' form of the overall equilibrium equation, which is used to solved the displacement field and the temperature field of the structure at the global level. The thesis also contributes to determine the ultimate response of a reinforced concrete frame submitted to fire loading. In which, we take into account not only the degradation of material properties due to temperature but also the thermal effect in identifying the total response of the structure. Moreover, in the proposed method, the shear failure is also considered along with the bending failure in forming the overal failure of the reinforced structure. The thesis can also be extended and completed to solve the behavior of reinforced concrete in 2D or 3D case considering the behavior bond interface or to take into account other type of failures in material such as fatigue or buckling. The proposed models can also be improved to determine the dynamic response of the structure when subjected to earthquake and/or impact.

Ce travail a pour objet l’analyse limite des structures par la méthode des éléments finis. Lorsqu’une structure atteint sa charge limite, certaines de ses composantes sont dans la phase inélastique de leur comportement, alors que dans les parties les plus critiques, du fait de la localisation des déformations inélastiques, se produit la rupture du matériau. Les effets de localisation sont, dans les matériaux fragiles liés à l’apparition et au développement de macro fissures alors qu’ils sont, dans les matériaux ductiles, gouvernés par les bandes de cisaillement localisées. L’étude de la charge limite est ainsi reliée à la modélisation du comportement inélastique standard du matériau mais également à la modélisation des effets localisés correspondant au comportement adoucissant des matériaux. Le comportement inélastique standard du matériau est, dans ce travail, décrit par des modèles élastoplastiques, élastoviscoplastiques ou élastiques non linéaires. Tous les modèles de comportement sont définis en termes d’efforts généralisés. Un certain nombre d’approches mathématiques et d’algorithmes numériques sont disponibles mais sont bien souvent inefficaces et manquent de précision. Ainsi, nous utilisons une approche développée plus récemment s’appuyant sur une méthode d’éléments finis enrichis de discontinuités. Nous avons développé de nouvelles formulations d’éléments standards prenant en compte des cinématiques et des descriptions des champs de déplacements discontinus complexes. Plusieurs formulations d’éléments finis ont été développées pour l’analyse de différents composants structurels. Nous présentons, dans un premier temps, un élément fini dédié à l’analyse limite des plaques en béton armé. La formulation d’un élément de plaque élastoplastique et élastoviscoplastique écrite en efforts généralisés associée à une procédure commune d’intégration sont présentées ensuite. Un élément de coque non linéaire, faisant intervenir une fonction seuil à deux surfaces incluant à la fois un écrouissage isotrope et un écrouissage cinématique est ensuite présenté. Les deux derniers éléments finis développés dans ce travail sont dédiés à la modélisation de la rupture localisée dans les poutres planes et les solides bidimensionnels. L’élément de poutre d’Euler-Bernouilli est enrichi par une discontinuité en rotation. Une stratégie s’appuyant sur l’analyse préalable, par un modèle raffiné, d’une partie de la structure est proposée afin d’obtenir les paramètres du modèle constitutif de la poutre. Enfin, nous présentons la formulation d’un élément quadrangulaire à discontinuité forte dont la cinématique permet de prendre en compte des sauts de déplacements linéaires dans les deux directions normale et tangentielle le long de la surface de discontinuité. Des résultats numériques montrent que les éléments développés ainsi que les algorithmes associés constituent un outil efficace et robuste d’analyse de la charge limite et de la rupture des structures. Parmi les exemples, nous présentons la simulation de la propagation d’une fissure dans un matériau fragile ainsi que le développement d’une bande de cisaillement dans un matériau ductile. Les codes numériques associés aux formulations présentées dans ce travail ont été générés par l’outil de programmation symbolique et d’optimisation de code AceGen. Les performances des éléments sont présentés à travers un grand nombre d’exemples numériques réalisés à partir du code AceFem
The dissertation deals with limit load and limit ductility analysis of structures by the finite element method. When structure is at its limit load, several structural components behave inelastically, while in the critical parts of the structure, due to localization of inelastic strains, failure of material appears. Localized effects in brittle materials are related to appearance and formation of a large (macro) crack, while failure in ductile materials is governed by localized shear bands. The study of limit load is thus related to modeling both standard inelastic material effects, as well as modeling of localized failure of material, often reffered to as material softening. Standard inelastic material effects are in this work described with elastoplastic, elastoviscoplastic and nonlinear elastic material models. All the material models are defined at the level of stress-resultants. Several mathematical approaches and numerical algorithms for modeling localized effects are at hand, but they are often inefficient or inaccurate. Therefor, we use an up-to-date approach, based on a finite element method with embedded discontinuity. We derive new finite element formulations with a quite complex kinematics of the basic elements, as well as rather complex description of discontinuous displacement fields. We derived several finite element formulations for analysis of different structural components. First we present a finite element for limit load analysis of reinforced concrete plates. Stress-resultant elastoplastic and elastoviscoplastic plate finite element formulation along with a unified computational procedure that covers both formulations are presented next. Further, a nonlinear shell finite element, based on a two-surface yield function, that includes both isotropic and kinematic material hardening is presented. The last two finite elements derived in this work are intended to model the localized failure in planar beams and 2D solids. The embedded discontinuity in rotations was built into elastoplastic Euler-Bernoulli beam finite element, and a procedure, based on a precomputed analysis of a part of a structure, by using a refined numerical model, is proposed to obtain the beam constitutive model parameters. Finally, we derive an elastoplastic quadrilateral two-dimensional finite element formulation with embedded strong discontinuity, whose kinematics can model linear jumps in both normal and tangential displacements along the discontinuity line. Numerical simulations show, that the derived finite elements, along with the accompanied numerical algorithms, are an efficient and a rather robust tool for limit load and failure analysis of structures. Among other examples, we present a simulation of crack growth in brittle material and a simulation of shear band failure in ductile material. All the computer codes of the finite element formulations presented in this work have been generated through the symbolic programming of the finite element computer code and the expression optimization in AceGen computer program. The performance of these elements has been presented in numerous numerical examples, all performed by the AceFem computer program

Objectifs de la thèse : l’analyse à rupture de structure de type solides et membranes et la modélisation de la rupture quasi-fragile par la méthode des éléments finis à forte discontinuité en cas de solide 2D. Dans ce travail, la méthode de continuation avec une équation de contrainte quadratique est présentée sous sa forme linéarisée. En présence de ruptures locales, la méthode de continuation standard peut échouer. Afin d’améliorer la performance de cette méthode, nous proposons de nouvelles versions plus sophistiquées qui prennent en compte les ruptures locales des matériaux. D’une part, une version est basée sur une équation supplémentaire adaptative imposant une limitation. Cette version est considérée relativement satisfaisante pour les matériaux adoucissants. D’autres versions sont basées sur le contrôle de la dissipation incrémentale pour les matériaux inélastiques. Plusieurs formulations d’éléments finis à forte discontinuité sont présentées en détails pour l’analyse de rupture quasi-fragile. Les approximations discrètes du champ de déplacement sont basées sur des éléments quadrilatéraux isoparamétriques ou des éléments quadrilatéraux enrichis par la méthode des modes incompatibles. Afin de décrire la formation d’une fissure ainsi que son ouverture, la cinématique de l’élément est enrichie par quatre modes de séparation et des paramètres cinématiques. On a également proposé un nouvel algorithme de repérage de fissure pour l’évaluation de la propagation de la fissure à travers le maillage. Plusieurs exemples numériques sont réalisés afin de montrer la performance de l’élément quadrilatéral à forte discontinuité ainsi que l’algorithme de repérage de fissure proposé
The thesis studies: the methods for failure analysis of solids and structures, and the embedded strong discontinuity finite elements for modelling material failures in quasi brittle 2d solids. As for the failure analysis, the consistently linearized path-following method with quadratic constraint equation is first presented and studied in detail. The derived path-following method can be applied in the nonlinear finite element analysis of solids and structures in order to compute a highly nonlinear solution path. However, when analysing the nonlinear problems with the localized material failures (i.e. materialsoftening), standard path-following methods can fail. For this reason we derived new versions of the pathfollowing method, with other constraint functions, more suited for problems that take into account localized material failures. One version is based on adaptive one-degree-of-freedom constraint equation, which proved to be relatively successful in analysing problems with the material softening that are modelled by the embedded-discontinuity finite elements. The other versions are based on controlling incremental plastic dissipation or plastic work in an inelastic structure. The dissipation due to crack opening and propagation, computed by e.g. embedded discontinuity finite elements, is taken into account. The advantages and disadvantages of the presented path-following methods with different constraint equations are discussed and illustrated on a set of numerical examples. As for the modelling material failures in quasi brittle 2d solids (e.g. concrete), several embedded strong discontinuity finite element formulations are derived and studied. The considered formulations are based either on: (a) classical displacement-based isoparametric quadrilateral finite element or (b) on quadrilateral finite element enhanced with incompatible displacements. In order to describe a crack formation and opening, the element kinematics is enhanced by four basic separation modes and related kinematic parameters. The interpolation functions that describe enhanced kinematics have a jump in displacements along the crack. Two possibilities were studied for deriving the operators in the local equilibrium equations that are responsible for relating the bulk stresses with the tractions in the crack. For the crack embedment, the major-principle-stress criterion was used, which is suitable for the quasi brittle materials. The normal and tangential cohesion tractions in the crack are described by two uncoupled, nonassociative damage-softening constitutive relations. A new crack tracing algorithm is proposed for computation of crack propagation through the mesh. It allows for crack formation in several elements in a single solution increment. Results of a set of numerical examples are provided in order to assess the performance of derived embedded strong discontinuity quadrilateral finite element formulations, the crack tracing algorithm, and the solution methods
Doktorska disertacija obravnava: (i) metode za porušno analizo trdnih teles in konstrukcij, ter (ii) končne elemente z vgrajeno močno nezveznostjo za modeliranje materialne porušitve v kvazi krhkih 2d trdnih telesih. Za porušno analizo smo najprej preučili konsistentno linearizirano metodo sledenja ravnotežne poti skvadratno vezno enačbo (metoda krožnega loka). Metoda omogoča izračun analize nelinearnih modelov, ki imajo izrazito nelinearno ravnotežno pot. Kljub temu standardne metode sledenja poti lahko odpovedo,kadar analiziramo nelinearne probleme z lokalizirano materialno porušitvijo (mehčanje materiala). Zatosmo izpeljali nove različice metode sledenja poti z drugimi veznimi enačbami, ki so bolj primerne zaprobleme z lokalizirano porušitvijo materiala. Ena različica temelji na adaptivni vezni enačbi, pri katerivodimo izbrano prostostno stopnjo. Izkazalo se je, da je metoda relativno uspešna pri analizi problemov zmaterialnim mehčanjem, ki so modelirani s končnimi elementi z vgrajeno nezveznostjo. Druge različicetemeljijo na kontroli plastične disipacije ali plastičnega dela v neelastičnem trdnem telesu ali konstrukciji.Upoštevana je tudi disipacija zaradi širjenja razpok v elementih z vgrajeno nezveznostjo. Prednosti inslabosti predstavljenih metod sledenja ravnotežnih poti z različnimi veznimi enačbami so predstavljeni naštevilnih numeričnih primerih. Za modeliranje porušitve materiala v kvazi krhkih 2d trdnih telesih (npr. betonskih) smo izpeljali različne formulacije končnih elementov z vgrajeno močno nezveznostjo v pomikih. Obravnavane formulacije temeljijo bodisi (a) na klasičnem izoparametričnem štirikotnem končnem elementu bodisi (b) na štirikotnem končnem elementu, ki je izboljšan z nekompatibilnimi oblikami za pomike. Nastanek in širjenje razpoke opišemo tako, da kinematiko v elementu dopolnimo s štirimi osnovnimi oblikami širjenja razpoke in pripadajočimi kinematičnimi parametri. Interpolacijske funkcije, ki opisujejo izboljšano kinematiko, zajemajo skoke v pomikih vzdolž razpoke. Obravnavali smo dva načina izpeljave operatorjev, ki nastopajo v lokalni ravnotežni enačbi in povezujejo napetosti v končnem elementu z napetostmi na vgrajeni nezveznosti. Kriterij za vstavitev nezveznosti (razpoke) temelji na kriteriju največje glavne napetosti in je primeren za krhke materiale. Normalne in tangentne kohezijske napetosti v razpoki opišemo z dvema nepovezanima, poškodbenima konstitutivnima zakonoma za mehčanje. Predlagamo novi algoritem za sledenje razpoki za izračun širjenja razpoke v mreži končnih elementov. Algoritem omogoča formacijo razpok v več končnih elementih v enem obtežnem koraku. Izračunali smo številne numerične primere, da bi ocenili delovanje izpeljanih formulacij štirikotnih končnih elementov z vgrajeno nezveznostjo in algoritma za sledenje razpoki kot tudi delovanje metod sledenja ravnotežnih poti

The Sandia GeoModel is a continuum elastoplastic constitutive model which captures many features of the mechanical response for geological materials over a wide range of porosities and strain rates. Among the specific features incorporated into the formulation are a smooth compression cap, isotropic/kinematic hardening, nonlinear pressure dependence, strength differential effect, and rate sensitivity. This study attempts to provide enhancements regarding computational tractability, domain of applicability, and robustness of the model. A new functional form is presented for the yield and plastic potential functions. The model is also furnished with a smooth, elliptical tension cap to account for the tensile failure. This reformulation renders a more accurate, robust and efficient model as it eliminates spurious solutions attributed to the original form. In addition, this constitutive model is adopted in bifurcation analysis to track the inception of new localization and crack path propagation. For the post-localization regime, a cohesive-law fracture model, able to address mixed-model failure condition, is implemented to characterize the constitutive softening behavior on the surface of discontinuity. To capture propagating fracture, the Assumed Enhanced Strain (AES) method is invoked. Particular mathematical treatments are incorporated into the simulation concerning numerical efficiency and robustness issues. Finally, the aforementioned modified cap plasticity model is employed to investigate the nonlinear dynamic response of the earthen substructure of the rail. Studying the effects of high-speed trains on the track substructure.

Boiler tubes used in power plants and manufacturing industries are susceptible to numerous failures due to the harsh environment in which they operate, usually involving high temperature, pressure and erosive-corrosive environment. Among the wide range of failures associated with the tubes, localized external erosion is prevalent. In spite of efforts made over the years to solve this problem, localized erosion of boiler tubes continues to be a leading cause of tube leakages and unscheduled boiler outages in power plants and other utilities. There is, therefore, a need to approach this problem systematically and engage in rigorous studies that will allow improved management of this persistent problem. In this thesis, comprehensive studies were first carried out on modelled variants of localized external eroded boiler tubes with conceptualized flaw geometries, such as could be seen in real situations. The outcome of these investigations provided insights into the factors that influence the failure of these tubes while in use. The stress concentration, plasticity and flaw geometry all play critical roles in influencing the failure of tubes. Also, the failure pressures of the modelled tubes were analyzed in relation with several other failure criteria, to determine which failure criteria will be most suitable for the failure assessment of the localized tubes. Based on the result of the analysis, plastic strain in the range 5%-7% is recommended as a compromise between the extreme benchmark failure criterion of 20%, and the overly conservative 2%. The insights gained from the studies carried out on conceptualized variants of localized thinned tubes were extended to real localized external eroded tubes obtained from the industry and used to develop an improved and efficient failure assessment methodology framework for heat resistant seamless tubes while in service. This was done by treating the tubes as an inverse problem and using an optimization technique to obtain the flaw geometric properties of the tubes so as to effectively replicate them on the conceptualized geometries. Using two Material Properties Council (MPC) models generated based on the properties of the tubes as a function of their operating temperatures, comprehensive nonlinear finite element analyses (NLFEA) were conducted on the 160 finite element models. These tubes were assessed based on the maximum equivalent plastic strain and Von Mises stress produced at the deepest point of the flaw area within each of the tubes when subjected to their respective operating pressures at which they failed. The failure assessment outcome revealed that most of the heat resistant tubes while in service will remain intact and not fail if their remaining tube thicknesses were within (0.7 𝑡𝑚𝑖𝑛 to 𝑡𝑚𝑖𝑛), where 𝑡𝑚𝑖𝑛 is the minimum remaining thickness of the tube based on allowable stress. In addition, a 5% plastic strain ( 𝑃5%) and equivalent Von Mises stress criteria of 0.8 𝜎𝑢𝑡𝑠 were deduced as failure criteria to guard against the failure of these tubes while in service, and also avoid their early replacement. The developed methodology framework was checked and compared with the API-ASME FFS standard and found to be in good agreement with it, also more efficient and with reduced conservatism. Finally, sensitive studies were conducted based on the developed methodology to examine how the combination of the flaw geometry and material factors could possibly influence the failure of the tubes while in use. The study outcome shows that there were no appreciable changes in the normalized Von-Mises stress ratios and the plastic strain response for the normalized remaining thickness of the tubes. The proposed 𝑃5% and 0.8 𝜎𝑢𝑡𝑠 limits accurately predicted the failure for all the tubes and were reasonably safe limit for the tubes. Insights gained from the strain hardenability of the tubes studied will also provide guidance with taking proactive measures for the maintenance of the tubes. In summary, all the insights gained from this research and the developed failure assessment methodology framework will be helpful in categorizing the severity of localized external erosion on tubes while in use, and also support maintenance decisions on these critical assets. Keywords: Boiler tubes, localized external erosion, plastic deformation, stress concentration, flaw geometry, failure criteria, plastic strain, conceptualized finite element models, nonlinear finite-element analysis, equivalent Von Mises stress, API-ASME FFS Standard.
Thesis (PhD)--University of Pretoria, 2020.
Mechanical and Aeronautical Engineering
PhD
Unrestricted

When a patient is diagnosed with various spinal injuries, deformities, or advanced degeneration, it is commonly suggested that he/she undergoes surgery for spinal fusion. Most current procedures in spinal fusion restrict mobility in one or multiple levels of the spine so that, over time, new bone will grow between the levels creating a single motionless unit of bone. The bilateral pedicle screw system (BPSS) has long been considered to be the "gold standard" in spinal fusion. However, for patients with osteoporosis, adequate fixation within the bone-screw interface has continuously been difficult to achieve or has come with high risk of other forms of catastrophic damage. Reflecting this, a new pedicle screw design was developed and evaluated against current standard pedicle screws commonly used in spinal surgery. All screw designs were also tested with a common cement augmentation technique surrounding the circumference of the screw. All tests measured pullout strength, stiffness, energy to failure, toughness, and the amount of destruction to the surrounding synthetic bone. While the newly designed pedicle screw failed to produce significantly stronger pullout forces in comparison to the standard screws, it did show evidence of a longer lasting residual axial resistance and a safer mode of failure than the standard screw, hinting that the design may benefit individuals who experience screw pullout and are awaiting reinstrumentation.

.Ce travail de thèse s'intéresse à la caractérisation de la déformation diffuse et localisée dans les grès isotropes et anisotropes sous contrainte de chargement monotone. En particulier, la cinématique de la localisation émergente et continue est étudiée dans une approche à la fois expérimentale, analytique et numérique, explorant l'effet de différentes sollicitations triaxial vrai dans le plan octaédrique.Plusieurs séries d'essais expérimentaux ont été réalisées en laboratoire, au sein d'une cellule de chargement en triaxial vrai (TTA), permettant la mesure de champs cinématiques à haute résolution spatiale et temporelle à la surface de l'échantillon. D'importants développements apportés au court de ce travail de thèse ont permis l'implémentation de modes de chargement par contrôle des invariants du tenseur de contrainte, tout en mesurant les déformations en temps réel par combinaison de jauges de déformation et mesures par corrélation d'images numériques (DIC). Utilisant cet appareil expérimental, deux campagnes d'essais ont été réalisées, mettant l'emphase sur la caractérisation du comportement mécanique d'un grès des Vosges isotrope largement étudié, ainsi que d'un grès des Vosges anisotrope nouvellement étudié. Ce dernier grès ayant été sélectionné pour sa composition matérielle en plans de litage orienté et organisé en couches de différentes porosités. Les séries d'essais mécaniques sur ces grès fournissent un apport important à la compréhension du caractère émergent et évolutif de la localisation, à différents stades du chargement déviatoire. Le caractère unique ce ces essais permet ainsi une analyse comparative approfondie entre la réponse macroscopique en contrainte-déformation et l'analyse des champs cinématiques par la DIC, et par tomographie à rayons X post-mortem. De plus, explorant des chemins de contrainte encore peu étudiés, l'analyse des essais expérimentaux sur le rôle indépendant de la contrainte moyenne, de l'angle de Lode et de l’orientation des plans de litage apporte une contribution novatrice à l'étude du comportement mécanique des roches poreuses. En particulier, la résistance à la rupture du grès, la manifestation de la localisation , ainsi que la transition du comportement ductile sont étudiées sous différentes conditions de chargement.En ce qui a trait au développement analytique, une analyse en bifurcation est proposée pour un modèle original à trois invariants, validé dans le cas des essais expérimentaux obtenus pour le grès isotrope. La pertinence de ce modèle théorique est démontrée pour la prédiction de l'orientation des bandes de cisaillement et de l'angle de dilatance à la rupture.Parallèlement, un modèle double-échelle basé sur l'homogénéisation numérique est présenté. Dans cette approche combinée, un modèle macroscopique en 2D des éléments finis (FEM) est couplé à un modèle microscopique en 3D des éléments discrets (DEM), sur la base d'un volume élémentaire représentative (VER) et dans la cadre d'un système hiérarchique (FEMxDEM) comportant une régularisation par second gradient. Ce modèle est étendu dans la portée des présents travaux pour l'étude des matériaux granulaire cimentés, par le développement d'une loi frictionnelle-cohésive endommageable au niveau de la DEM. Dans une vaste étude numérique de simulations en conditions de chargement triaxial vrai, ce modèle hiérarchique est utilisé afin d'explorer l'effet de différents arrangements granulaire (DEM), ainsi que différentes distributions hétérogènes à l'échelle macroscopique (FEM). En ce sens, deux types d'anisotropies résultant de l'hétérogénéité, définie à chacune des échelles, sont davantage étudiés. La réponse mécanique et la déformation localisée, émergeant du modèle constitutif à l'échelle du VER, démontrent une bonne concordance des comportements mécaniques complexes par rapport aux résultats de l'étude expérimentale
The objective of this doctoral thesis consists in the characterization of diffuse and localized deformations during monotonic loading of both isotropic and anisotropic porous sandstones. In particular, the kinematics of emerging and persistent strain localization structures are investigated in a combination of complementary experimental, analytical and numerical approaches, exploring the effect of different true triaxial loading paths in the octahedral plane.A series of experimental loading tests have been performed in a laboratory environment comprising a high pressure true triaxial apparatus (TTA), which is designed to provide access to full-field measurements of one of the sample surfaces at high spacial and temporal resolutions. Important developments contributed in this work enabled to extend the capabilities for this apparatus to perform invariant controlled loading paths, while acquiring direct strain measurements from a combination of strain gauges and digital image correlation (DIC). Using this apparatus, two experimental campaigns have been realized, focusing on the mechanical characterization of both a well-studied isotropic Vosges sandstone and a newly studied anisotropic Vosges sandstone. The later sandstone has been selected for the organization of its granular fabric in thin bedding plane layers of variable porosity. The results from these series of mechanical loading experiments contribute an original insight into the emergence and development of localized deformation during different stages of loading. A combined analysis is performed on the evolution of the macroscopic stress-strain responses, full-field measurements of incremental strains through DIC, as well as post-mortem x-ray tomography. Additionally, in this investigation exploring rarely considered loading paths, the independent role of the mean stress, the Lode angle and the orientation of the bedding planes is systematically studied according to their respective influence on the material strength, the manifestation of localized structures and the transition towards a ductile behavior of the material.In terms of analytical development, a bifurcation analysis is proposed for a novel three invariant model, validated with experimental results obtained for the isotropic sandstone. This theoretical model, proved to be successful in predicting both the deformation band inclination and the dilatancy angle of the material at failure.In parallel, a double scale model based on numerical homogenization is presented. In this approach, a macro 2D finite element model (FEM) is coupled to a micro 3D discrete element model (DEM) at the particle scale of a representative elementary volume (REV) in the frame of a hierarchical scheme (FEMxDEM), with second gradient regularization. This model is extended in the scope of this work to the study of cemented granular materials, with the development of a frictional-cohesive damageable contact law, implemented at the DEM level. In an extensive series of true triaxial loading simulations, the hierarchical numerical model is used to explore both the influence of different micro-structural arrangements (DEM) and heterogeneities at the sample scale (FEM). In this respect, two types of anisotropies resulting from heterogeneities defined at each scales are further investigated. The mechanical response and localized deformation, emerging from the micro-scale constitutive model, is shown to display significant correspondence with experimental observations in the studied Vosges sandstones.This combination of advanced experimental, analytical and numerical studies contributes a unique insight into important and open questions regarding the mechanical response and deformation processes of cemented granular materials

Dans le cadre de cette thèse, une approche de calcul de couplage multi-échelle et multi-physique en 2D et en 3D est présentée. La modélisation multi-échelle d’une structure consiste de l’échelle macro qui représente la réponse homogénéisée de la structure entière, tandis que l’échelle micro peut capturer les détails du comportement à la petite échelle du matériau, où des mécanismes inélastiques, tels que la plasticité ou l’endommagement, peuvent être pris en compte. L’intérieur de chaque macro-élément est rempli par le maillage à l’échelle micro qui s’y adapte entièrement. Les deux échelles sont couplées à travers le champ de déplacements imposé à l’interface. Le calcul par éléments finis est effectué, en utilisant une procédure de solution operator-split sur les deux échelles. En 2D, une discontinuité dans le champ de déplacements est introduite à l’échelle macro dans un élément fini Q4, pour pouvoir capturer l’adoucissement comportement d’un matériau piézoélectrique. Un degré de liberté supplémentaire qui représente le voltage est ajouté aux noeuds des macro-éléments de tétraèdre et d’hexaèdre en 3D. La poutre de Timoshenko comportant un modèle de commutation de polarisation est utilisée à l’échelle micro. Également, une formulation multi-échelle de Hellinger-Reissner a été développée et implémentée pour un simple patch test en électrostatique. La procédure proposée est mise en œuvre dans le logiciel de calcul par éléments finis FEAP - Finite Element Analysis Program. Pour simuler le comportement aux deux échelles, FEAP est modifié, et deux versions différentes du code sont obtenues - macroFEAP et microFEAP. Le couplage de ces codes est réalisé avec Component Template Library - CTL qui rend possible l’échange d’informations entre les deux échelles. Les capacités de cette approche multi-échelle en 2D et en 3D sont démontrées dans un environnement purement mécanique, mais aussi multi-physique. La formulation théorique et l’application algorithmique sont présentées, et les avantages de la méthode multi-échelle pour la modélisation des matériaux hétérogènes sont illustrés avec plusieurs exemples numériques
In this thesis, a multi-scale and multi-physics coupling computation procedure for a 2D and 3D setting is presented. When modeling the behavior of a structure by a multi-scale method, the macro-scale is used to describe the homogenized response of the structure, and the micro-scale to describe the details of the behavior on the smaller scale of the material where some inelastic mechanisms, like damage or plasticity, can be taken into account. The micro-scale mesh is defined for each macro-scale element in a way to fit entirely inside it. The two scales are coupled by imposing a constraint on the displacement field over their interface. The computation is performed using the operator split solution procedure on both scales, using the standard finite element method. In a 2D setting, an embedded discontinuity is implemented in the Q4 macroscale element to capture the softening behavior happening on the micro-scale. For the micro-scale element, a constant strain triangle (CST) is used. In a 3D setting, a macro-scale tetrahedral and hexahedral elements are developed, while on the micro-scale Timoshenko beam finite elements are used. This multi-scale methodology is extended with a multi-physics functionality, to simulate the behavior of a piezoelectric material. An additional degree of freedom (voltage) is added on the nodes of the 3D macro-scale tetrahedral and hexahedral elements. For the micro-scale element, a Timoshenko beam element with added polarization switching model is used. Also, a multi-scale Hellinger- Reissner formulation for electrostatics has been developed and implemented for a simple electrostatic patch test. For implementing the proposed procedure, Finite Element Analysis Program (FEAP) is used. To simulate the behavior on both macro and micro-scale, FEAP is modified and two different version of FEAP code are implemented – macroFEAP and microFEAP. For coupling, the two codes are exchanging information between them, and Component Template Library (CTL) is used. The capabilities of the proposed multi-scale approach in a 2D and 3D pure mechanics settings, but also multi-physics environment have been shown. The theoretical formulation and algorithmic implementation are described, and the advantages of the multi-scale approach for modeling heterogeneous materials are shown on several numerical examples

The formation and development of localisation bands and/or cracks have been experimentally identified as the key failure mechanism governing responses of quasi-brittle geomaterials like concrete, sandstones and soft rocks. In fact, key features of the material behaviour, including Lode-angle dependence, size effect and brittle-ductile transition can be considered as consequences stemming from the localised failure mechanism in several loading conditions. For geomaterials with fibre reinforcement (i.e., fibre reinforced concrete), even though adding short fibres into the material significantly changes its mechanical characteristics and performances, the development of cracks and localisation bands remains the central mechanism driving the material responses. In this case, the bridging effect caused by fibres across cracks, together with the material cohesive-frictional resistance, refrains cracks from further developing and forces the material to form more cracks throughout the structure to dissipate the given energy. This prolongs the coalescence of diffuse micro/meso-cracks to form a macro-crack and considerably improve the material strength and ductility. Classical continuum models, in principle, can capture the overall responses of the material with stress-strain relationships formulated from experimental observations at the macroscopic level. However, the material behaviour in these models is homogenous throughout the whole element domain, leading to an incorrect dependence of dissipated energy and specimen responses on the discretisation resolution. This is because they fail to capture the difference of deformation and behaviour between the localisation zone and its surrounding bulk material. As a result, with the presence of crack/localisation band, the definition of averaged quantities such as overall stress and strain is not adequate to describe the volume element and using them for analysing post-localisation behaviour of quasi-brittle geomaterials is inappropriate, if not totally incorrect. Consequently, classical approaches that ignore the strong heterogeneity induced by the localisation of deformation suffer from mesh convergence issues in Boundary Value Problems (BVPs) analysis. In this research, the localised failure mechanism is employed as the basis to develop a continuum-based constitutive model for quasi-brittle geomaterials with and without fibre reinforcement. The cracks/localisation bands are explicitly included as an intrinsic part of the model with its own behaviour in conjunction with the responses of the surrounding bulk material. This allows an additional constitutive relationship, together with its internal variables, to be defined inside the localisation band to describe its microstructural changes under the course of loading. The material inelastic behaviour and important features such as brittle-ductile transition, Lode-angle dependence, size effect and hydrostatic pressure dependence can thus be correctly captured in association with observable failure patterns at constitutive level. The model, constructed in this manner, is also capable of featuring multiple localisation bands/cracks inside the constitutive equations to account for any change of loading path and avoid unphysical stress-locking naturally. In addition, for modelling quasi-brittle geomaterials with fibre reinforcement, the incorporation of cracks within the constitutive model enables the inclusion of separate models describing the fibre bridging effect and material cohesive-frictional resistance. As a result, the interactions between these two components and their contributions to the stress transfer across a crack are naturally captured for different types of fibres and their volume contents. The transition from hardening to softening, corresponding to the change from diffuse cracking phase to localised failure can also be reflected as a consequence. Furthermore, owing to the explicit inclusion of cracks in the model, the resulting constitutive behaviour automatically scales with the discretisation resolution and the results are thus mesh-independent when solving BVPs, without requiring any additional regularisation. Model validations against experimental data show that the proposed model is simple yet effective in capturing the localised failure of quasi-brittle geomaterials with and without fibre reinforcement at both constitutive and structural levels. The model is proven to be reliable and computationally inexpensive, with a few model parameters which can be identified and calibrated in a consistent and physically meaningful manner. The proposed model can thus be applied straightforwardly for the analysis and design of solids/structures made of rocks or concrete, with or without fibre reinforcements.
Thesis (Ph.D.) -- University of Adelaide, School of Civil, Environmental and Mining Engineering, 2019