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The nonlinear behavior of concrete can be attributed to the propagation of microcracks within the heterogeneous internal material structure. In this thesis, a mesoscale model is developed which allows for the explicit simulation of these microcracks. Consequently, the actual physical phenomena causing the complex nonlinear macroscopic behavior of concrete can be represented using rather simple material formulations. On the mesoscale, the numerical model explicitly resolves the components of the internal material structure. For concrete, a three-phase model consisting of aggregates, mortar matrix and interfacial transition zone is proposed. Based on prescribed grading curves, an efficient algorithm for the generation of three-dimensional aggregate distributions using ellipsoids is presented. In the numerical model, tensile failure of the mortar matrix is described using a continuum damage approach. In order to reduce spurious mesh sensitivities, introduced by the softening behavior of the matrix material, nonlocal integral-type material formulations are applied. The propagation of cracks at the interface between aggregates and mortar matrix is represented in a discrete way using a cohesive crack approach. The iterative solution procedure is stabilized using a new path following constraint within the framework of load-displacement-constraint methods which allows for an efficient representation of snap-back phenomena. In several examples, the influence of the randomly generated heterogeneous material structure on the stochastic scatter of the results is analyzed. Furthermore, the ability of mesoscale models to represent size effects is investigated. Mesoscale simulations require the discretization of the internal material structure. Compared to simulations on the macroscale, the numerical effort and the memory demand increases dramatically. Due to the complexity of the numerical model, mesoscale simulations are, in general, limited to small specimens. In this thesis, an adaptive heterogeneous multiscale approach is presented which allows for the incorporation of mesoscale models within nonlinear simulations of concrete structures. In heterogeneous multiscale models, only critical regions, i.e. regions in which damage develops, are resolved on the mesoscale, whereas undamaged or sparsely damage regions are modeled on the macroscale. A crucial point in simulations with heterogeneous multiscale models is the coupling of sub-domains discretized on different length scales. The sub-domains differ not only in the size of the finite elements but also in the constitutive description. In this thesis, different methods for the coupling of non-matching discretizations - constraint equations, the mortar method and the arlequin method - are investigated and the application to heterogeneous multiscale models is presented. Another important point is the detection of critical regions. An adaptive solution procedure allowing the transfer of macroscale sub-domains to the mesoscale is proposed. In this context, several indicators which trigger the model adaptation are introduced. Finally, the application of the proposed adaptive heterogeneous multiscale approach in nonlinear simulations of concrete structures is presented.
From a macroscopic point of view, failure within concrete structures is characterized by the initiation and propagation of cracks. In the first part of the thesis, a methodology for macroscopic crack growth simulations for concrete structures using a cohesive discrete crack approach based on the extended finite element method is introduced. Particular attention is turned to the investigation of criteria for crack initiation and crack growth. A drawback of the macroscopic simulation is that the real physical phenomena leading to the nonlinear behavior are only modeled phenomenologically. For concrete, the nonlinear behavior is characterized by the initiation of microcracks which coalesce into macroscopic cracks. In order to obtain a higher resolution of this failure zones, a mesoscale model for concrete is developed that models particles, mortar matrix and the interfacial transition zone (ITZ) explicitly. The essential features are a representation of particles using a prescribed grading curve, a material formulation based on a cohesive approach for the ITZ and a combined model with damage and plasticity for the mortar matrix. Compared to numerical simulations, the response of real structures exhibits a stochastic scatter. This is e.g. due to the intrinsic heterogeneities of the structure. For mesoscale models, these intrinsic heterogeneities are simulated by using a random distribution of particles and by a simulation of spatially variable material parameters using random fields. There are two major problems related to numerical simulations on the mesoscale. First of all, the material parameters for the constitutive description of the materials are often difficult to measure directly. In order to estimate material parameters from macroscopic experiments, a parameter identification procedure based on Bayesian neural networks is developed which is universally applicable to any parameter identification problem in numerical simulations based on experimental results. This approach offers information about the most probable set of material parameters based on experimental data and information about the accuracy of the estimate. Consequently, this approach can be used a priori to determine a set of experiments to be carried out in order to fit the parameters of a numerical model to experimental data. The second problem is the computational effort required for mesoscale simulations of a full macroscopic structure. For this purpose, a coupling between mesoscale and macroscale model is developed. Representative mesoscale simulations are used to train a metamodel that is finally used as a constitutive model in a macroscopic simulation. Special focus is placed on the ability of appropriately simulating unloading.
Untersuchung des dynamischen Verhaltens von Eisenbahnbrücken bei wechselnden Umweltbedingungen
(2008)
Im Zuge des Ausbaus von Eisenbahnstrecken für den Hochgeschwindigkeitsverkehr muss sichergestellt werden, dass keine Resonanz zwischen den periodisch einwirkenden Radlasten und den Brückeneigenfrequenzen entsteht. Bei der Untersuchung einzelner Bauwerke wurden teilweise recht große Schwankungen des dynamischen Verhaltens im Verlauf der Jahreszeiten festgestellt. Um diese Beobachtungen zu präzisieren, wurden an zwei ausgewählten Walzträger-in-Beton-Brücken über den Zeitraum von 15 Monaten Beschleunigungsmessungen durchgeführt. Die gewonnenen Daten wurden mit der Stochastic Subspace Methode, die im ersten Teil der Arbeit näher erläutert wird, ausgewertet. Es konnte für alle Eigenmoden ein Absinken der Eigenfrequenz bei steigender Temperatur beobachtet werden. Um die Ursachen hierfür genauer zu untersuchen, wurde für eine der beiden Brücken ein Finite-Elemente-Modell mit dem Programm SLang erstellt. Mittels einer Sensitivitätsanalyse wurden die für das Schwingverhalten maßgebenden Systemeigenschaften identifiziert. Die anschließend durchgeführte Strukturoptimierung unter Nutzung des genetischen Algorithmus sowie des adaptiven Antwortflächenverfahrens konnte die Temperaturabhängigkeit einzelner Materialparameter aufzeigen, die zumindest eine Ursache für Schwankungen der Eigenfrequenzen darstellen.
In recent years increasingly consideration has been given to the lifetime extension of existing structures. This is based on the fact that a growing percentage of civil infrastructure as well as buildings is threatened by obsolescence and that due to simple monetary reasons this can no longer be countered by simply re-building everything anew. Hence maintenance interventions are required which allow partial or complete structural rehabilitation. However, maintenance interventions have to be economically reasonable, that is, maintenance expenditures have to be outweighed by expected future benefits. Is this not the case, then indeed the structure is obsolete - at least in its current functional, economic, technical, or social configuration - and innovative alternatives have to be evaluated. An optimization formulation for planning maintenance interventions based on cost-benefit criteria is proposed herein. The underlying formulation is as follows: (a) between maintenance interventions structural deterioration is described as a random process; (b) maintenance interventions can take place anytime throughout lifetime and comprise the rehabilitation of all deterioration states above a certain minimum level; and (c) maintenance interventions are optimized by taking into account all expected life-cycle costs (construction, failure, inspection and state-dependent repair costs) as well as state- or time-dependent benefit rates. The optimization is performed by an evolutionary algorithm. The proposed approach also allows to determine optimal lifetimes and acceptable failure rates. Numerical examples demonstrate the importance of defining benefit rates explicitly. It is shown, that the optimal solution to maintenance interventions requires to take action before reaching the acceptable failure rate or the zero expected net benefit rate level. Deferring decisions with respect to maintenance not only results, in general, in higher losses, but also results in overly hazardous structures.
The importance of modern simulation methods in the mechanical analysis of heterogeneous solids is presented in detail. Thereby the problem is noted that even for small bodies the required high-resolution analysis reaches the limits of today's computational power, in terms of memory demand as well as acceptable computational effort. A further problem is that frequently the accuracy of geometrical modelling of heterogeneous bodies is inadequate. The present work introduces a systematic combination and adaption of grid-based methods for achieving an essentially higher resolution in the numerical analysis of heterogeneous solids. Grid-based methods are as well primely suited for developing efficient and numerically stable algorithms for flexible geometrical modeling. A key aspect is the uniform data management for a grid, which can be utilized to reduce the effort and complexity of almost all concerned methods. A new finite element program, called Mulgrido, was just developed to realize this concept consistently and to test the proposed methods. Several disadvantages which generally result from grid discretizations are selectively corrected by modified methods. The present work is structured into a geometrical model, a mechanical model and a numerical model. The geometrical model includes digital image-based modeling and in particular several methods for the theory-based generation of inclusion-matrix models. Essential contributions refer to variable shape, size distribution, separation checks and placement procedures of inclusions. The mechanical model prepares the fundamentals of continuum mechanics, homogenization and damage modeling for the following numerical methods. The first topic of the numerical model introduces to a special version of B-spline finite elements. These finite elements are entirely variable in the order k of B-splines. For homogeneous bodies this means that the approximation quality can arbitrarily be scaled. In addition, the multiphase finite element concept in combination with transition zones along material interfaces yields a valuable solution for heterogeneous bodies. As the formulation is element-based, the storage of a global stiffness matrix is superseded such that the memory demand can essentially be reduced. This is possible in combination with iterative solver methods which represent the second topic of the numerical model. Here, the focus lies on multigrid methods where the number of required operations to solve a linear equation system only increases linearly with problem size. Moreover, for badly conditioned problems quite an essential improvement is achieved by preconditioning. The third part of the numerical model discusses certain aspects of damage simulation which are closely related to the proposed grid discretization. The strong efficiency of the linear analysis can be maintained for damage simulation. This is achieved by a damage-controlled sequentially linear iteration scheme. Finally a study on the effective material behavior of heterogeneous bodies is presented. Especially the influence of inclusion shapes is examined. By means of altogether more than one hundred thousand random geometrical arrangements, the effective material behavior is statistically analyzed and assessed.