No description available.

Fatigue analysis is a critical stage in the design of any structural component. Typically fatigue is analysed during post-processing, but as the size of the analysed component increases, the amount of data stored for the analysis increases simultaneously. This increases the computational and memory requirements of the system, intensifying the work load on the engineer. A continuum mechanics approach namely ’Continuous time fatigue model’, for fatigue analysis is available in a prior study which reduces the computational requirements by simultaneously computing fatigue along with the stress. This model implements a moving endurance surface in the stress space along with the damage evolution equation to compute high-cycle fatigue. In this thesis the continuous time fatigue model is compared with conventional model (ie.Cycle counting) to study its feasibility. The thesis also aims to investigate the continuous time fatigue model and an evolved version of the model is developed for non-proportional load cases to identify its limitations and benefits.

No description available.

The development of advanced fiber reinforced cement-based materials to provide higher strength, ductility, and durability, as ultra-high performance fiber-reinforced concrete (UHPFRC), enables the design of precast beams with thin sections and reduced self-weight to meet the required flexural performance. However, such slender elements when subjected to transitory phases, and possibly also in permanent stages, are prone to instability failure. So, the present study aims to provide experimental data and analytical solution for UHPFRC beams during the lifting phase, and studies about the other stages. This type of test is rare and was not reported for UHPFRC beams. For testing, the beams were lifted by inclined cables and subjected to a transversal load applied at midspan to induce lateral instability. The displacements of the beams were monitored with total station equipment. Also, a new analytical solution was proposed to predict the failure load of lifted beams and closed-form analytical solutions to predict the rollover load of beams supported by bearing pads and subjected to different loading conditions. Furthermore, there are limited data that characterizes the constitutive behavior of this material. In this context, the present research also focused on providing such laboratory results for UHPFRC with different fiber contents. Besides, analytical models for damage evolution and stress-strain relationship are proposed and applied in numerical simulations. From the results, the UHPFRC beams failed by instability with a load capacity 3.7 times smaller than the flexural load capacity. Furthermore, the analytical solution for lifting predicted the peak load of the experiment with great accuracy. Also, the proposed equations for beams on bearing pads accurately predicted the experimental results available in the literature. The analytical and experimental rollover loads differed by 4.37% and 13.6% for the two studied cases. From material, the stiffness degradation occurred rapidly in UHPFRC under tensile loading while occurred gradually in compression. Also, fiber content influenced toughness and degradation evolution significantly over the loading cycles. Proposed equations were utilized in the Plastic-Damage model of Abaqus that predicted accurately damage growth and cyclic envelopes during all the phases of the tension, compression, and bending tests. The calibrated numerical model also predicted the experimental results with the UHPFRC beams. / O desenvolvimento de materiais avançados à base de cimento reforçado com fibra para fornecer maior resistência, ductilidade e durabilidade, como o concreto de ultra-alto desempenho reforçado com fibras (UHPFRC), permite o projeto de vigas pré-moldadas com seções esbeltas e peso próprio reduzido que atendem desempenho estrutural requerido. No entanto, esses elementos delgados quando submetidos a fases transitórias e também em serviço são propensos a falhar por instabilidade. Então, o presente estudo tem por objetivo apresentar resultados experimentais e soluções analíticas para vigas de UHPFRC durante a fase de içamento e estudos sobre as outras fases. Este tipo de teste é raro e não foi reportado para vigas de UHPFRC. Para o teste, as vigas foram levantadas por cabos inclinados e submetidas a uma carga concentrada transversal aplicada no meio do vão para induzir a instabilidade lateral. Os deslocamentos das vigas foram monitorados com estação total. Além disso, uma nova solução analítica foi proposta para prever a carga de instabilidade das vigas içadas e soluções analíticas para prever a carga de tombamento de vigas suportadas por aparelho de apoio e submetidas a diferentes condições de carregamento. Além disso, existem poucos resultados experimentais que caracterizam o comportamento constitutivo deste material. Neste contexto, a presente pesquisa também se concentrou em fornecer tais resultados experimentais para UHPFRC com diferentes teores de fibras. Além disso, modelos analíticos para evolução de dano e relação tensão-deformação são propostos e aplicados em simulações numéricas. A partir dos resultados, as vigas em içamento falharam por instabilidade com uma capacidade de carga 3,7 vezes menor que a capacidade à flexão. Além disso, a solução analítica para içamento previu carga máxima do experimento com grande precisão. As equações propostas para vigas sobre aparelhos de apoio previram com precisão os resultados experimentais disponíveis na literatura. As cargas de tombamento analíticas e experimental diferiram em 4,37% e 13,6% para os dois casos estudados. Dos resultados do material, a degradação da rigidez ocorreu de maneira rápida no UHPFRC submetido à tração enquanto ocorreu gradualmente na compressão. O teor de fibras influenciou significativamente a tenacidade e a degradação nos ciclos de carregamento. As equações propostas foram utilizadas em um modelo de Dano acoplado à plasticidade que previu com precisão a evolução do dano e as envoltórias cíclicas durante todas as fases dos testes de tração, compressão e flexão. O modelo numérico calibrado também previu os resultados experimentais das vigas de UHPFRC.

The development of advanced fiber reinforced cement-based materials to provide higher strength, ductility, and durability, as ultra-high performance fiber-reinforced concrete (UHPFRC), enables the design of precast beams with thin sections and reduced self-weight to meet the required flexural performance. However, such slender elements when subjected to transitory phases, and possibly also in permanent stages, are prone to instability failure. So, the present study aims to provide experimental data and analytical solution for UHPFRC beams during the lifting phase, and studies about the other stages. This type of test is rare and was not reported for UHPFRC beams. For testing, the beams were lifted by inclined cables and subjected to a transversal load applied at midspan to induce lateral instability. The displacements of the beams were monitored with total station equipment. Also, a new analytical solution was proposed to predict the failure load of lifted beams and closed-form analytical solutions to predict the rollover load of beams supported by bearing pads and subjected to different loading conditions. Furthermore, there are limited data that characterizes the constitutive behavior of this material. In this context, the present research also focused on providing such laboratory results for UHPFRC with different fiber contents. Besides, analytical models for damage evolution and stress-strain relationship are proposed and applied in numerical simulations. From the results, the UHPFRC beams failed by instability with a load capacity 3.7 times smaller than the flexural load capacity. Furthermore, the analytical solution for lifting predicted the peak load of the experiment with great accuracy. Also, the proposed equations for beams on bearing pads accurately predicted the experimental results available in the literature. The analytical and experimental rollover loads differed by 4.37% and 13.6% for the two studied cases. From material, the stiffness degradation occurred rapidly in UHPFRC under tensile loading while occurred gradually in compression. Also, fiber content influenced toughness and degradation evolution significantly over the loading cycles. Proposed equations were utilized in the Plastic-Damage model of Abaqus that predicted accurately damage growth and cyclic envelopes during all the phases of the tension, compression, and bending tests. The calibrated numerical model also predicted the experimental results with the UHPFRC beams. / O desenvolvimento de materiais avançados à base de cimento reforçado com fibra para fornecer maior resistência, ductilidade e durabilidade, como o concreto de ultra-alto desempenho reforçado com fibras (UHPFRC), permite o projeto de vigas pré-moldadas com seções esbeltas e peso próprio reduzido que atendem desempenho estrutural requerido. No entanto, esses elementos delgados quando submetidos a fases transitórias e também em serviço são propensos a falhar por instabilidade. Então, o presente estudo tem por objetivo apresentar resultados experimentais e soluções analíticas para vigas de UHPFRC durante a fase de içamento e estudos sobre as outras fases. Este tipo de teste é raro e não foi reportado para vigas de UHPFRC. Para o teste, as vigas foram levantadas por cabos inclinados e submetidas a uma carga concentrada transversal aplicada no meio do vão para induzir a instabilidade lateral. Os deslocamentos das vigas foram monitorados com estação total. Além disso, uma nova solução analítica foi proposta para prever a carga de instabilidade das vigas içadas e soluções analíticas para prever a carga de tombamento de vigas suportadas por aparelho de apoio e submetidas a diferentes condições de carregamento. Além disso, existem poucos resultados experimentais que caracterizam o comportamento constitutivo deste material. Neste contexto, a presente pesquisa também se concentrou em fornecer tais resultados experimentais para UHPFRC com diferentes teores de fibras. Além disso, modelos analíticos para evolução de dano e relação tensão-deformação são propostos e aplicados em simulações numéricas. A partir dos resultados, as vigas em içamento falharam por instabilidade com uma capacidade de carga 3,7 vezes menor que a capacidade à flexão. Além disso, a solução analítica para içamento previu carga máxima do experimento com grande precisão. As equações propostas para vigas sobre aparelhos de apoio previram com precisão os resultados experimentais disponíveis na literatura. As cargas de tombamento analíticas e experimental diferiram em 4,37% e 13,6% para os dois casos estudados. Dos resultados do material, a degradação da rigidez ocorreu de maneira rápida no UHPFRC submetido à tração enquanto ocorreu gradualmente na compressão. O teor de fibras influenciou significativamente a tenacidade e a degradação nos ciclos de carregamento. As equações propostas foram utilizadas em um modelo de Dano acoplado à plasticidade que previu com precisão a evolução do dano e as envoltórias cíclicas durante todas as fases dos testes de tração, compressão e flexão. O modelo numérico calibrado também previu os resultados experimentais das vigas de UHPFRC.

Fatigue in concrete is a complex phenomenon involving formation of microcracks, their coalescence into major crack and simultaneous formation of the fracture process zone ahead of the crack tip. Complex phenomena are best dealt through an energy approach and hence it is reasonable to use the theory of thermodynamics. Fracture mechanics and damage mechanics are two theories that are based on physically sound principles and are used to describe failure processes in materials. The former deals with the study of macroscopic cracks, whereas the latter defines the state of microcracking. In this study, the concepts from these theories are utilized to improve our understanding and modeling of fatigue process in concrete. In this thesis, a closed form expression for the thermodynamic function entropy is proposed and examined for its size independency and its use as a material property to characterize failure of concrete under fatigue. In the thermodynamic formalism, dissipative phenomena are described by a dissipation potential or its dual, from which evolution laws for internal variables could be defined. In this work, closed form expressions for dual of dissipation potential are derived using concepts of dimensional analysis and self-similarity within the framework of fracture mechanics and damage mechanics. Consequently, a fatigue crack propagation law and a fatigue damage evolution law are proposed respectively. A method is proposed in this study to correlate fracture mechanics and damage mechanics theories by equating the potentials obtained in each theory. Through this equivalence, a crack could be transformed into an equivalent damage zone and vice versa. Also, damage state corresponding to a given crack in a member can be quantified in terms of a damage index. An analytical way of computing size independent S-N curves is proposed, using a nonlocal damage theory by including aggregate size and specimen size in the formulation. It is realized from this study that fracture mechanics and damage mechanics theories should be used in a unified manner in order to accurately model the process of fatigue in concrete. Furthermore, based on the models developed in this study, several damage indicators for fatigue of concrete are proposed. The advantages and limitations of each of these indices are presented such that, the relevant damage index could be used, based on available parameters. Additionally, deterministic sensitivity studies are carried out to determine the most important parameters influencing fatigue life of a concrete member.

No description available.

Diese Dissertation beschäftigt sich mit der rigorosen Herleitung effektiver Modelle zur Beschreibung von Schädigungsprozessen. Diese effektiven Modelle werden für verschiedene raten-unabhängige Schädigungsmodelle linear elastischer Materialien hergeleitet. Den Ausgangspunkt stellt dabei ein unidirektionales Mikrostrukturevolutionsmodell dar, dessen Fundament eine Familie geordneter zulässiger Mikrostrukturen bildet. Jede Mikrostruktur dieser Familie besitzt die gleiche intrinsische Längenskala. Zur Herleitung eines effektiven Modells wird das asymptotische Verhalten dieser Längenskala mittels Techniken der Zwei-Skalen-Konvergenz untersucht. Um das Grenzmodell zu identifizieren, bedarf es einer Mikrostrukturregularisierung, die als diskreter Gradient für stückweise konstante Funktionen aufgefasst werden kann. Die Mikrostruktur des effektiven Modells ist punktweise durch ein Einheitszellenproblem gegeben, welches die Mikro- von der Makroskala trennt. Ausgehend vom Homogenisierungsresultat für die unidirektionale Mikrostrukturevolution werden effektive Modelle für Zwei-Phasen-Schädungsprozesse hergeleitet. Die aus zwei Phasen bestehende Mikrostruktur der mikroskopischen Modelle ermöglicht z.B. die Modellierung von Schädigung durch das Wachstum von Inklusionen aus geschädigtem Material verschiedener Form und Größe. Außerdem kann Schädigung durch das Wachstum mikroskopischer Hohlräume und Mikrorissen betrachtet werden. Die Größe der Defekte skaliert mit der intrinsischen Längenskala und die unidirektionale Mikrostrukturevolution verhindert, dass bei fixierter Längenskala die Defekte für fortlaufende Zeit schrumpfen. Das Material des Grenzmodells ist dann in jedem Punkt als Mischung von ungeschädigtem und geschädigtem Material durch das Einheitszellenproblem gegeben. Dabei liefert das Einheitszellenproblem nicht nur das Mischungsverhältnis sondern auch die genaue geometrische Mischungsverteilung, die dem effektiven Material des jeweiligen Materialpunktes zugrunde liegt. / This dissertation at hand deals with the rigorous derivation of such effective models used to describe damage processes. For different rate-independent damage processes in linear elastic material these effective models are derived as the asymptotic limit of microscopic models. The starting point is represented by a unidirectional microstructure evolution model which is based on a family of ordered admissible microstructures. Each microstructure of that family possesses the same intrinsic length scale. To derive an effective model, the asymptotic behavior of this intrinsic length scale is investigated with the help of techniques of the two-scale convergence. For this purpose, a microstructure-regularizing term, which can be understood as a discrete gradient for piecewise constant functions, is needed to identify the limit model. The microstructure of the effective model is given pointwisely by a so-called unit cell problem which separates the microscopic scale from the macroscopic scale. Based on these homogenization results for unidirectional microstructure evolution models, effective models for brutal damage processes are provided. There, the microstructure consists of only two phases, namely undamaged material which comprises defects of damaged material with various sizes and shapes. In this way damage progression can be modeled by the growth of inclusions of weak material, the growth of voids, or the growth of microscopic cracks. The size of the defects is scaled by the intrinsic length scale and the unidirectional microstructure evolution prevents that, for a fixed length scale, the defects shrink for progressing time. According to the unit cell problem, the material of the limit model is then given as a mixture of damaged and undamaged material. In a specific material point of the limit model, that unit cell problem does not only define the mixture ratio but also the exact geometrical mixture distribution.

Der Vortrag beschreibt wie sich mittels der unterschiedlichen Berechnungsverfahren zur Lösung dynamischer Strukturpobleme der Einschlag eines idealisierten Bruchstücks in eine Schutzwand berechnen lässt. Dies wird mittels zweier kommerzieller FEM-Programme beschrieben: a.) Creo Simulate nutzt zur Lösung die Methode der modalen Superposition, d.h., es können nur lineare dynamische Systeme mit rein modaler Dämpfung berechnet werden. Kontakt zwischen zwei Bauteilen lässt sich damit nicht erfassen. Die unbekannte Kraft-Zeit-Funktion des Einschlagvorganges muss also geeignet abgeschätzt und als äußere Last auf die Schutzwand aufgebracht werden. Je dynamischer der Einschlagvorgang, desto eher wird der Gültigkeitsbereich des zugrunde liegenden linearen Modells verlassen. b.) Abaqus/Explicit nutzt ein direktes Zeitintegrationsverfahren zur schrittweisen Lösung der zugrunde liegenden Differentialgleichung, die keine tangentiale Steifigkeitsmatrix benötigt. Damit können sowohl Materialnichtlinearitäten als auch Kontakt geeignet erfasst und damit die Kraft-Zeit-Funktion des Einschlages ermittelt werden. Auch bei extrem hochdynamischen Vorgängen liefert diese Methode ein gutes Ergebnis. Es müssen dafür jedoch weit mehr Werkstoffdaten bekannt sein, um das nichtlineare elasto-plastische Materialverhalten mit Schädigungseffekten korrekt zu beschreiben. Die Schwierigkeiten der Werkstoffdatenbestimmung werden in den Grundlagen erläutert. / The presentation describes how to analyze the impact of an idealized fragment into a stell protective panel with different dynamic analysis methods. Two different commercial Finite Element codes are used for this: a.) Creo Simulate: This code uses the method of modal superposition for analyzing the dynamic response of linear dynamic systems. Therefore, only modal damping and no contact can be used. The unknown force-vs.-time curve of the impact event cannot be computed, but must be assumed and applied as external force to the steel protective panel. As more dynamic the impact, as sooner the range of validity of the underlying linear model is left. b.) Abaqus/Explicit: This code uses a direct integration method for an incremental (step by step) solution of the underlying differential equation, which does not need a tangential stiffness matrix. In this way, matieral nonlinearities as well as contact can be obtained as one result of the FEM analysis. Even for extremely high-dynamic impacts, good results can be obtained. But, the nonlinear elasto-plastic material behavior with damage initiation and damage evolution must be characterized with a lot of effort. The principal difficulties of the material characterization are described.

Der Vortrag beschreibt wie sich mittels der unterschiedlichen Berechnungsverfahren zur Lösung dynamischer Strukturpobleme der Einschlag eines idealisierten Bruchstücks in eine Schutzwand berechnen lässt. Dies wird mittels zweier kommerzieller FEM-Programme beschrieben: a.) Creo Simulate nutzt zur Lösung die Methode der modalen Superposition, d.h., es können nur lineare dynamische Systeme mit rein modaler Dämpfung berechnet werden. Kontakt zwischen zwei Bauteilen lässt sich damit nicht erfassen. Die unbekannte Kraft-Zeit-Funktion des Einschlagvorganges muss also geeignet abgeschätzt und als äußere Last auf die Schutzwand aufgebracht werden. Je dynamischer der Einschlagvorgang, desto eher wird der Gültigkeitsbereich des zugrunde liegenden linearen Modells verlassen. b.) Abaqus/Explicit nutzt ein direktes Zeitintegrationsverfahren zur schrittweisen Lösung der zugrunde liegenden Differentialgleichung, die keine tangentiale Steifigkeitsmatrix benötigt. Damit können sowohl Materialnichtlinearitäten als auch Kontakt geeignet erfasst und damit die Kraft-Zeit-Funktion des Einschlages ermittelt werden. Auch bei extrem hochdynamischen Vorgängen liefert diese Methode ein gutes Ergebnis. Es müssen dafür jedoch weit mehr Werkstoffdaten bekannt sein, um das nichtlineare elasto-plastische Materialverhalten mit Schädigungseffekten korrekt zu beschreiben. Die Schwierigkeiten der Werkstoffdatenbestimmung werden in den Grundlagen erläutert. / The presentation describes how to analyze the impact of an idealized fragment into a stell protective panel with different dynamic analysis methods. Two different commercial Finite Element codes are used for this: a.) Creo Simulate: This code uses the method of modal superposition for analyzing the dynamic response of linear dynamic systems. Therefore, only modal damping and no contact can be used. The unknown force-vs.-time curve of the impact event cannot be computed, but must be assumed and applied as external force to the steel protective panel. As more dynamic the impact, as sooner the range of validity of the underlying linear model is left. b.) Abaqus/Explicit: This code uses a direct integration method for an incremental (step by step) solution of the underlying differential equation, which does not need a tangential stiffness matrix. In this way, matieral nonlinearities as well as contact can be obtained as one result of the FEM analysis. Even for extremely high-dynamic impacts, good results can be obtained. But, the nonlinear elasto-plastic material behavior with damage initiation and damage evolution must be characterized with a lot of effort. The principal difficulties of the material characterization are described.