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Organisationseinheit der BAM
Numerical simulation of ultrasonic wave propagation using higher order methods in space and time
(2015)
The paper discusses the efficient simulation of ultrasonic wave propagation.
It is demonstrated that a combination of higher methods in space and time leads to a significant performance boost. Higher order spectral elements are used for the spatial
discretization. A comparison with standard finite elements shows the advantages when using explicit time integration schemes. For the temporal discretization, an efficient explicit fourth order Nyström method is presented. Its computational efficiency for wave propagation problems is compared to a second order Velocity Verlet integration.
Concrete is a complex material. Its properties evolve over time, especially at early age, and are dependent on environmental conditions, i.e. temperature and moisture conditions, as well as the composition of the material.
This leads to a variety of macroscopic phenomena such as hydration/solidification/hardening, creep and shrinkage, thermal strains, damage and inelastic deformations. Most of these phenomena are characterized by specific set of model assumptions and often an additive decomposition of strains into elastic, plastic, shrinkage and creep components is performed. Each of these phenomena are investigated separately and a number of respective independent models have been designed. The interactions are then accounted for by adding appropriate correction factors or additional models for the particular interaction. This paper discusses the importance of reconsider even in the experimental phase the model assumptions required to generalize the experimental data into models used in design codes. It is especially underlined that the complex macroscopic behaviour of concrete is strongly influenced by its multiscale and multiphyscis nature and two examples (shrinkage and fatigue) of interacting phenomena are discussed.
In der aktuellen Projektphase liegt der Fokus auf der Datenaufnahme, -bearbeitung und -speiche-rung mit dem Ziel, automatisierte Auswerteverfahren einsetzen zu können. Aktuell wurden primär punktuelle Messungen an ausgewählten Messtagen aufgenommen. Die Systeme sollen so weiter-entwickelt werden, dass sie sich auch für kontinuierliche Messungen im Rahmen von Monitoring-aufgaben eignen.
Ein wichtiger Fokus bei der Auswertung ist die Kombination mit numerischen Modellen, die mithilfe von Bayesian Update Verfahren und den aufgenommenen Messdaten kalibriert und im Verlauf der Monitoringaufgabe angepasst werden sollen. Insbesondere sollen auch zeitabhängige Modelle, die eine zeitliche Entwicklung von Struktureigenschaften beinhalten (Kriechen, Schwinden, Ermüdung, Korrosion) dazu verwendet werden, die zukünftige Performance der Struktur bewerten zu können. Basierend darauf werden dann Konzepte zur Planung von Inspektion und Wartung erstellt.
Growth of vehicle traffic density can be observed in many countries all over the world. This accretion is caused by world-wide population growth on the one hand, but also by increasing freight volumes and, thus, freight transports on the streets on the other hand.
This increased exposure becomes more and more of a problem for the civil infrastructure such as bridges. Many of these bridges are nowadays stressed to their limits by higher loads than they were originally designed for and/or operating times beyond the initially predicted life span. This raises questions about structural safety and lifetime prediction, of course, and therefore illustrates the need for accurate structural monitoring.
Since the lifetime of bridge structures is primarily influenced by their traffic loading, an accurate identification of load configurations over the whole length of a structure is most desirable.
In this paper, a method for vehicle load identification is proposed. It involves Bayesian Analysis and (quasi-)static importance functions in order to estimate vehicle positions, velocities and weights. The structure is modeled with finite elements in order to generate model predictions for different load configurations. The model predictions are compared to the actual measured data to identify the most probable loading configuration for that measurement. This involves the use of enhanced Monte Carlo simulations such as MCMC to reduce the computational effort. The measured data from different kinds of sensors can (and should) be combined for accuracy gain – in this case a combination of measured displacements and inclinations.
Since the measurements take place over some time during the passage of the vehicle, these estimations are carried out for several time instants for which the estimation is carried out. The advantage of using Bayesian Updating Method is the embodied learning effect leading to an improvement of the estimation when adding new information in a new calculation step.
Using the estimates for the loading conditions of a bridge structure as well as measurements of the structural responses, Bayesian analysis is again used in order to estimate localized structural parameters such as Young's modulus or Moments of Inertia in form of probability density functions yielding most probable values for the parameters.
Considering the difficulties for load identification close to the support poles of the bridge and therefore for the proposed structural parameter identification procedure, it is clear that this problem is ill posed. Bayesian regularization methods also have proven to be very effective when handling ill posed problems.
A coupled thermomechanical mesoscale model for concrete under heating is presented. When considering the heterogeneous structure under coupled loads, complex macroscopic material properties can be modelled using simple constitutive relations. For instance, damage evolution is directly driven by the incompatibility of thermal strains between matrix and aggregates. Without prescribing
fc = f(T), a decline in compressive strength with rising temperatures will be shown.
The heterogeneous mesostructure of concreted causes local stress concentrations. Stress dependent phenomena like damage and creep as well as their interactions are effected by those stress
concentrations. Therefore a material model’s macroscopic behavior will differ whether the mesoscale structure is considered or not. The differences between the mesoscale approach and an homogeneous approach will be presented. The results are discussed with focus on the true materials behavior.
Damage caused by stress concentrations in the complex mesoscopic geometry of concrete leads to continuous stress redistribution over the material’s life time. The presented fatigue damage model
captures this by resolving each load cycle in a cycle-by-cycle time integration. The model extends a static damage model to failure caused by the (time dependent) strain amplitudes and, thus, allows calibrating the majority of the material’s parameters in static experiments.
A finite element tearing and interconnecting (FETI) approach for phase-field models and Gradient enhanced damage models is presented. These diffusive crack models can solve fracture mechanics problems by integrating a set of partial differential equations and thus avoid the explicit treatment of discontinuities. However, they require a fine discretization in the vicinity of the crack. FETI methods distribute the computational cost among multiple processors and thus speed up the computation.
Die Brücken im Netz der Bundesverkehrswege sind überwiegend in einem ausreichenden bis guten Zustand. Allerdings steigt der Unterhalts- und Sanierungsaufwand aufgrund des inzwischen hohen Alters vieler Brücken sowie des ständig wachsenden Schwerlastverkehrs. Techniken zur Einschätzung der verbleibenden Lebensdauer von Brücken sowie zur dauerhaften Beobachtung des Tragverhaltens bzw. des Erfolges von Sanierungsmaßnahmen werden daher für den sicheren und wirtschaftlichen Betrieb dringend benötigt. Zur Evaluierung dafür geeigneter holistischer Ansätze wurde in der BAM das Projekt BLEIB - Bewertung, Lebensdauerprognose und Instandsetzung von Brückenbauwerken - ins Leben gerufen.
Ein zentrales Ergebnis des Projektes ist eine extern vorgespannte Stahlbetonbrücke als Zweifeldträger mit einer Gesamtlänge von 24 m, die für den Test verschiedenster Sensorsysteme, zur Validierung numerischer Modelle und zur Erprobung von Sanierungs- und Verstärkungsmaßnahmen entwickelt wurde. Für die Simulation unterschiedlicher Schädigungsgrade kann die Vorspannung der Brücke variiert werden. Die Brücke wird mit beweglichen Gewichten belastet und über einen Shaker zum Schwingen angeregt.
Das Brückenmodell wurde bewusst geschädigt, indem die Vorspannung der Struktur erstmalig schrittweise bis auf null reduziert wurde. Unter der Eigenlast verformte sich die Brücke, wodurch eine Rissbildung im Beton einsetzte. Die Zugspannung, die zuvor durch die Vorspannung aufgenommen wurde, übernahm Schritt für Schritt der Beton. Als die Zugspannungen die relativ geringe Zugfestigkeit des Betons überstiegen, begann dieser zu reißen und die schlaffe Bewehrung der Struktur nahm die Spannungen auf. Dieser Versuch wurde unter anderem von Schallemissionsmessungen begleitet. Der Rissbildungsprozess konnte damit, bei gleichzeitiger Aufzeichnung der Vorspannung, früh detektiert und die Risse geortet werden. Die Ergebnisse korrelieren gut mit den Ergebnissen der stereophotogrammetrischen Verformungsmessungen der Struktur.
Lifetime aspects including fatigue failure of concrete structures were traditionally only of minor importance. Because of the growing interest in maxing out the capacities of concrete, its fatigue failure under compression has become an issue. A variety of interacting phenomena such as e.g. loss of prestress, degradation due to chemical reactions or creep and shrinkage influence the fatigue resistance. Failure due to cyclic loads is generally not instantaneous, but characterized by a steady damage accumulation. Therefore, a reliable numerical model to predict the performance of concrete over its lifetime is required, which accurately captures order effects and full three-dimensional stress states.
Many constitutive models for concrete are currently available, which are applicable for specific loading regimes, different time scales and different resolution scales.
However, a key limitation of those models is that they generally do not address issues related to fatigue on a structural level. Very few models can be found in the literature that reproduce deterioration of concrete under repeated loading-unloading cycles. This is due to the computational effort necessary to explicitly resolve every cycle which exceeds the currently available computational resources. The limitation can only be overcome by the application of multiscale methods in time.
The objective of the paper is the development of numerical methods for the simulation of concrete under fatigue loading using temporal multiscale methods.
First, a continuum damage model for concrete is developed with a focus on fatigue under compressive stresses [1]. This includes the possibility to model stress redistributions and capture size effects. In contrast to cycle based approaches, where damage is accumulated based on the number of full stress cycles, a strain based approach is developed that can capture cyclic degradation under variable loading cycles including different amplitudes and loading frequencies. The model is designed to represent failure under static loading as a particular case of fatigue failure after a single loading cycle. As a consequence, most of the material parameters can be deduced from static tests. Only a limit set of additional constitutive parameters is required to accurately describe the evolution under fatigue loading. Another advantage of the proposed model is the possibility to directly incorporate other multi-physics effects such as creep and shrinkage or thermal loading on the constitutive level.
Second, a multiscale approach in time is presented to enable structural computations of fatigue failure with a reduced computational effort. The damage rate within the short time scale corresponding to a single cycle is computed based on a Fourier based approach [2]. This evolution equation is then solved on the long time scale using different implicit and explicit time integration schemes. Their performance and some limitations for specific loading regimes is discussed.
Finally, the developed methods will be validated and compared to experimental data.
[1] Vitaliy Kindrachuk, Marc Thiele, Jörg F. Unger. Constitutive modeling of creep-fatigue interaction for normal strength concrete under compression, International Journal of Fatigue, 78:81-94, 2015
[2] Vitaliy Kindrachuk, Jörg F. Unger. A Fourier transformation-based temporal integration scheme for viscoplastic solids subjected to fatigue deterioration, International Journal of Fatigue, 100:215-228, 2017