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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
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. 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. 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.
FAIR (findable, accessible, interoperable and reusable) data usage is one of the main principals that many of the research and funding organizations include in their strategic plans, which means that following the main principals of FAIR data is required in many research projects. The definition of data being FAIR is very general, and when implementing that for a specific application or project or even setting a standardized procedure within a working group, a company or a research community, many challenges arise. In this contribution, an overview about our experience with different methods, tools and procedures is outlined.
We begin with a motivation on potential use cases for the applications of FAIR data with increasing complexity starting from a reproducible research paper over collaborative projects with multiple participants such as Round-Robin tests up to data-based models within standardization codes, applications in machine learning or parameter estimation of physics-based simulation models.
In a second part, different options for structuring the data are discussed. On the one hand, this includes a discussion on how to define actual data structures and in particular metadata schema, and on the other hand, two different systems for storing the data are discussed. The first one is the openBIS system, which is an open-source Lab notebook and PostgreSQL based data management system. A second option are a semantic representations using RDF based ontologies for the domain of interest.
In a third section, requirements for workflow tools to automate data processing are discussed and their integration into reproducible data analysis is presented with an outlook on required information to be stored as metadata in the database.
Finally, the presented procedures are exemplarily demonstrated for the calibration of a temperature dependent constitutive model for additively manufactured mortar. Metadata schemata for a rheological measurement setup are derived and implemented in an openBIS database. After a short review of a potential numerical model predicting the structural build-up behaviour, the automatic workflow to use the stored data for model parameter estimation is demonstrated.
A key limitation of the most constitutive models that reproduce a Degradation of quasi-brittle materials is that they generally do not address issues related to fatigue. One reason is the huge computational costs to resolve each load cycle on the structural level. The goal of this paper is the development of a temporal Integration scheme, which significantly increases the computational efficiency of the finite element method in comparison to conventional temporal integrations.
The essential constituent of the fatigue model is an implicit gradient-enhanced formulation of the damage rate. The evolution of the field variables is computed as amultiscale Fourier series in time.On a microchronological scale attributed to single cycles, the initial boundary value problem is approximated by linear BVPs with respect to the Fourier coefficients. Using the adaptive cycle jump concept, the obtained damage rates are transferred to a coarsermacrochronological scale associated with the duration of material deterioration. The performance of the developedmethod is hence improved due to an efficient numerical treatment of the microchronological problem in combination with the cycle jump technique on the macrochronological scale. Validation examples demonstrate the convergence of the obtained solutions to the reference simulations while significantly reducing the computational costs.
Using continuum damage mechanics (CDM) for lifetime prediction requires numerical integration of evolving damage until the onset of failure. The primary challenge for the simulation of structural fatigue failure is caused by the enormous computational costs due to cycle-by-cycle temporal integration throughout the whole loading history, which is in the order of 103–107 cycles. As a consequence, most approaches circumvent this problem and use empirical methods such as Wöhler curves. They are well suited for approximating the lifetime, but they are not capable to capture a realistic degradation of the material including redistribution of stresses. The main objective of the paper is to provide a technique for finite element (FE) simulations of structures under fatigue loading while reducing computational costs.
A Fourier transformation-based temporal integration (FTTI) scheme is proposed, which adapts the conventional FE method for modeling the viscoplastic deterioration in a structure subjected to cyclic loading. The response fields are represented by a Fourier series which assumes a temporal scale separation: a microchronological (short time) scale arises from the oscillatory loading and a macrochronological (long time) scale is due to the slow material relaxation resulting from yielding and damage evolution. The original dynamic boundary value problem (BVP) is approximated by the stationary BVP on the microchronological scale. Alternation of the displacement field on the macrochronological scale is correlated with evolution of the history variables by means of a high order adaptive cycle jump method. Performance and significant acceleration of the FE simulations is demonstrated at different loading scenarios for a constitutive damage model where the progressive damage accumulation is driven by viscoplastic yielding.
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 regularized model for impact in explicit dynamics applied to the split Hopkinson pressure bar
(2016)
In the numerical simulation of Impact phenomena, artificial oscillations can occur due to an instantaneous change of velocity in the contact area. In this paper, a nonlinear penalty regularization is used to avoid these oscillations. Aparticular focus is the investigation of higher order methods in space and time to increase the computational efficiency. The spatial discretization is realized by higher order spectral element methods that are characterized by a diagonal mass matrix. The time integration scheme is based on half-explicit Runge–Kutta scheme of fourth order. For the conditionally stable scheme, the critical time step is influenced by the penalty regularization. A framework is presented to adjust the penalty stiffness and the time step for a specific mesh to avoid oscillations. The methods presented in this paper are applied to 1D-simulations of a split Hopkinson pressure bar, which is commonly used for the investigation of materials under dynamic loading.
In this paper, a new methodology based on the Hill–Mandel lemma in an FE² sense is proposed that is able to deal with localized deformations. This is achieved by decomposing the displacement field of the fine scale model into a homogeneous part, fluctuations, and a
cracking part based on additional degrees of freedom (X¹)—the crack opening in normal and tangential directions. Based on this decomposition, the Hill–Mandel lemma is extended to relate coarse and fine scale energies using the assumption of separation of scales such
that the fine scale model is not required to have the same size as the corresponding
macroscopic integration point. In addition, a procedure is introduced to mimic periodic
boundary conditions in the linear elastic range by adding additional shape functions for the boundary nodes that represent the difference between periodic boundary conditions and pure displacement boundary conditions due to the same macroscopic strain. In order to decrease the computational effort, an adaptive strategy is proposed allowing different
macroscopic integration points to be resolved in different levels on the fine scale.
The problem of polydisperse sphere packings is applied to concrete mesoscale geometries in finite sized specimens. Realistic sphere diameter distributions are derived from concrete grading curves. An event-driven molecular dynamics simulation using growing particles is introduced. Compared to the widely used random sequential addition algorithm, it reaches denser aggregate packings and saves computation time at high volume fractions.
A minimal distance between particles strongly influences the maximum aggregate content. It is essential to obtain undistorted elements when meshing the geometry for finite element simulations. The algorithm maximizes this value and produces meshable concrete mesostructures with more than 70% aggregate content.
Combination of model reduction and adaptive subset simulation for structural reliability problems
(2019)
A safe and robust design is a key criterion when building a structure or a component. Ensuring this criterion can either be performed by fullfilling prescribed safety margins, or by using a full probabilistic approach with a computation of the failure probability. The latter approach is particularly well suited for complex Problems with an interaction of different physical penomena that can be described in a numerical model. The bottleneck in this approach is the computational effort. Sampling methods such as Markov chain Monte Carlo methods are often used to evaluate the system reliability. Due to small failure probabilities (e.g. 10^6) and complex physical models with already and extensive computational effort for a single set of parameters, these methods a prohibitively expensive. The focus of this contribution is to demonstrate the advantages of combining model reduction techniques within the concept a variance reducing adaptive sampling procedures. In the developed method, a modification of the adaptive subset simulation based on Papaioannou et al. 2015 is used and coupled with a limit state function based on Proper Generalized Decomposition (PGD) (Chinesta et al. 2011). In the subset simulation the failure probability is expressed as a product of larger conditional failure probabilities. The intermediate failure events are chosen as a decreasing sequence. Instead of solving each conditional probability with a Markov chain approach, an importance sampling approach is used. It is be shown that the accuracy of the estimation depends mainly on the number of samples in the last sub-problem. For model reduction, the PGD approach is used to solve the structural problem a priori for a given Parameter space (physical space plus all random parameters). The PGD approach results in an approximation of the problem output within a prescribed range of all input Parameters (load factor, material properties, ..). The approximation of the solution by a separated form allows an evaluation of the limit state function within the sampling algorithm with almost no cost. This coupled PGD – adaptive subset Simulation approach is used to estimate the failure probability of examples with different complexity. The convergence, the error propagation as well as the reduction in computational time is discussed.