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The methods of computational damage mechanics are well-established for the description of degradation of materials under monotone loading. An extension to structural damage induced by cyclic loading is however significantly limited. This is due to enormous computational costs required to resolve each load cycle by conventional temporal incremental integration schemes while a typical fatigue loading history comprises between thousands and millions of cycles. Despite the permanent increase of computational resources and algorithmic performance, a successful approach is rather based on the development of novel multiscale in time integration schemes.
A Fourier transformation-based temporal integration (FTTI) is represented, which takes advantage of temporal scale separation incorporated into the cycle jump method. The response fields are approximated by a Fourier series whose coefficients undergo the evolution on a long-time scale. This is correlated with the evolution of the history variables, including damage, by means of the adaptive cycle jump method of various orders. The necessary extrapolation rates are obtained from the underlying solution of a short-time scale problem, which results from the oscillatory boundary condition and fulfills the global equilibrium of the Fourier coefficients. In this way, a remarkable speedup is achieved because the number of cycles to be fully integrated dramatically decreases.
The key idea behind the FTTI method is that the global in space equilibrium problem is linear since it is decoupled from the evolution equations. The latter are solved in the quadrature points under response fields prescribed throughout the whole load cycle. Consequently, integration of a single load cycle is much more efficient than the conventional single scale integration where the global equilibrium iteration and the local iteration of the evolution equations are coupled. This results in an additional speedup of the FTTI method.
The performance of the FTTI technique is demonstrated for two different constitutive behaviors: a viscoplastic model with a damage variable governed by the local equivalent viscoplastic strain; a quasi-brittle response where the damage variable is driven by a non-local equivalent strain. The latter is implicitly introduced as proposed by Peerlings. Both, the explicit and implicit extrapolation schemes are validated. The FTTI solutions agree very well with the reference cycle-by -cycle solutions, while significantly reducing the computational costs. The adaptive determination of the jump length can properly recognize the particular responses throughout the fatigue loading history (stationary fatigue, acceleration of fatigue damage when approaching failure) as well as stress redistribution phenomena.
The worldwide spread of windfarms brings new challenges, especially for concrete structures as a part of towers, connecting joints and foundations of wind turbines. High-cyclic loadings in such structures lead to a high relevance of the subject of fatigue. A proper assessment of the fatigue strength of concrete demands therefore a basis of reliable experimental data and the development of standardized testing methods. This article presents first results of an ongoing research program of BAM (Bundesanstalt für Materialforschung und -prüfung) which is a part of a joint project (WinConFat) funded by the German Federal Ministry for Economic Affairs and Energy. The subproject investigates the effects of size and slenderness of the specimens on the fatigue behaviour of high strength concrete at different stress levels. Not only the fatigue strength, but also the fatigue process itself is monitored by means of several measurement methods. Strain measurements are used to calculate the load dependent elastic modulus in the fatigue hysteresis as indicators for fatigue development. Furthermore, the application of non-destructive methods like acoustic emission analysis and ultrasonic measurement in laboratory tests gives a deeper insight into damage processes under cyclic loading. The results shall be used to improve design rules for concrete members under fatigue load and to develop or improve non-destructive techniques for in-service structural health monitoring.
Accurate models for the long term behavior of concrete structures are important to ensure a durable and reliable design.
A variety of interacting phenomena, such as the loss of prestress, the degradation due to chemical reactions or creep and shrinkage, influence the fatigue resistance. Therefore, a reliable numerical model to predict the performance of concrete over its lifetime is required.
The presented fatigue model is an extension of a static damage model to allow easy coupling in a multiphysics context. The evolution equation of the damage driving variable is enhanced to allow damage growth below the static limit. The model is defined in the time domain and does not include the number of cycles as a parameter.
Thus, it can capture both static and cyclic failure.
Additionally, this allows calibrating the majority of the model parameters static experiments. The model is integrated by resolving each loading cycle, requiring about ten time steps per cycle. The high computational costs are handled via a time scale separation.
The short time scale describes one cycle with marginal changes in the internal variables. These changes are integrated along the large time scale of material deterioration. Various high-order time integration schemes are compared.
Wöhler curves relate loading amplitudes to the number of cycles that the material endures. They are used to validate the model against experimental data.
Appropriate monitoring of transportation infrastructures (e.g. bridges) is of utmost importance to ensure safe operation conditions. Accurate and reliable assessment of such structures can be achieved through the integration of data from non-destructive testing, advanced modeling and model updating techniques. The Bayesian framework has been widely used for updating engineering and mechanical models, due to its probabilistic description of information, in which the posterior probability distribution reflects the knowledge, over the model parameters of interest, inferred from the data. For most real-life applications, the computation of the true posterior involves integrals that are analytically intractable, therefore the implementation of Bayesian inference requires in practice some approximation methods.
This paper investigates the application of Variational Bayesian Inference for structural model parameter identification and update, based on measurements from a real experimental setup. The Variational Bayesian method circumvents the issue of evaluating intractable integrals by using a factorized approximation of the true posterior (mean field approximation) and by choosing a family of conjugate distributions that facilitates the calculations. Inference in the Variational Bayesian framework is seen as solving an optimization problem with the aim of finding the parameters of the factorized posterior which would minimize its Kullback-Leibler divergence in relation to the exact posterior. The Variational Approach is an efficient alternative to sampling methods, such as Markov Chain Monte Carlo, since the latter’s accuracy depends on sampling from the posterior distribution a sufficient amount of times (and therefore requiring an equivalent number of computations of the forward problem, which can be quite expensve).
The durability of concrete structures and its performance over the lifetime is strongly influenced by many interacting phenomena such as e.g. mechanical degradation due to fatigue loading, loss of prestress, degradation due to chemical reactions or creep and shrinkage. Failure due to cyclic loading is generally not instantaneous, but characterized by a steady damage accumulation.
Many constitutive models for concrete are currently available, which are applicable for specific loading regimes, different time scales and different resolution scales. A key limitation is that the models often 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.
The objective of this paper is the presentation of numerical methods for the simulation of concrete under fatigue loading using a temporal multiscale method.
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. 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 time integration schemes.
Porous media flow is an important aspect of geomechanics and material behaviour of concrete under heating and drying. We will present a model for multiphase nonisothermal flow and its solution using the finite element method. In contrast to single phase models (e.g.), which have to consider vaporization or condensation as a temperate dependency on the thermal capacity, the phase changes will be explicitly considered. More complex models have been proposed (e.g.), which also capture the multiphase nature of the flow field. These models, however, also include the coupling to a mechanics field, with many of the constitutive relations of the flow field dependent on the specific damage formulation employed. The resulting complexity of the constitutive models leads to a high number of experiments and difficult calibration procedures to determine their parameters.
The simulation of the moisture distribution under fast and slow heating is presented. The constitutive relations employed here do not assume any particular damage-mechanical model and will therefore allow free choice when mechanical coupling is desired. The resulting pore pressure field is an important prerequisite for the modeling of concrete spalling. Suitable numerical methods to achieve optimal convergence will be discussed.
By using direct coupling between the parts of a multiphysics problem, the models for each part can be simplified, making calibration and sensitivity calculations easier. This is also important for more complicated problems, where the need for simpler material laws that handle coupled phenomena becomes more evident. In particular, this contribution is an essential step towards the modeling of concrete spalling.
Coupling of an isogeometric surface and bulk finite element discretization for contact problems
(2018)
The finite element (FE) framework is a standard tool for the simulation of mechanical problems providing advantages like automated meshing algorithms and effcient quadrature rules. However, for contact problems, the FE discretization is - due to the C0 continuity at element intersections - characterized by a non-smooth normal feld.
Conversely, isogeometric discretizations provide a smooth normal feld also at interelement borders and were recently applied to contact mechanical problems using the mortar method. The application of isogeometric analysis for complex volumetric problems has not reached the same level of automation as the FE-framework, i.e. due to the intricate mesh generation.
This work aims at combining the advantages of both discretization procedures by coupling an isogeometric contact surface with a bulk FE-discretization. The isogeometric contact interface is represented by a NURBS surface, which is tied to the FE mesh. For the discretization of the bulk parts, higher order spectral elements are used. The contact problem is discretized with the mortar method and a penalty approach is used to enforce the contact constraints. Two different types of coupling of the NURBS surface and the bulk part are considered: mortar and pointwise mesh tying. The mortar mesh tying approach shows accurate results, whereas the pointwise tying leads to large oscillations in the contact stresses. Element-based quadrature is applied for mortar tying, as well as for mortar contact discretizations. Using an isogeometric layer, the related quadrature error can be effciently reduced by a higher degree interpolation or increased integration order.
Modeling the interactions of creep, shrinkage and damage in a multiphysics simulation of concrete
(2018)
The time dependent, mechanical behavior of concrete is affected by multiple phenomena like creep, shrinkage and damage propagation. The interactions of these processes are supposed to have significant influence on the materials response to external loading. For example it can be observed that the compressive strength of concrete rises with lowering the moisture content [Dahms, 1968].
Most of the constitutive models for finite element methods are designed with just a single phenomena in mind. In multiphysics simulations it is quiet common to use a linear superposition, i.e. additive decomposition of the total strain into elastic shrinkage, creep or thermal strains.
In this paper, the interactions of creep, shrinkage and damage models are investigated, in particular for cases where the assumption of linear superposition is questionable. A gradient enhanced damage model proposed by [Peerlings et al., 1996] is employed. Creep is modeled as a Kelvin chain as described in [Jirásek and Bažant, 2001]. Shrinkage is simulated by using two different approaches. The first model simulates shrinkage as an additional moisture dependent strain component. In the second model, shrinkage is simulated as a moisture dependent pore pressure applied to the solid bulk.
The impact of model interactions will be discussed with a focus on simulating the influence of the moisture content on the macroscopic strength. The model is validated by comparison to experimental data.
Appropriate monitoring of transportation infrastructures (e.g. bridges) is of utmost importance to ensure safe operation conditions. Accurate and reliable assessment of such structures can be achieved through the integration of data from non-destructive testing, advanced modeling and model updating techniques. The Bayesian framework has been widely used for updating engineering and mechanical models, due to its probabilistic description of information, in which the posterior probability distribution reflects the knowledge, over the model parameters of interest, inferred from the data. For most real-life applications, the computation of the true posterior involves integrals that are analytically intractable, therefore the implementation of Bayesian inference requires in practice some approximation methods.
This paper investigates the application of Variational Bayesian Inference for structural model parameter identification and update, based on measurements from a real experimental setup. The Variational Bayesian method circumvents the issue of evaluating intractable integrals by using a factorized approximation of the true posterior (mean field approximation) and by choosing a family of conjugate distributions that facilitates the calculations. Inference in the Variational Bayesian framework is seen as solving an optimization problem with the aim of finding the parameters of the factorized posterior which would minimize its Kullback-Leibler divergence in relation to the exact posterior. The Variational Approach is an efficient alternative to sampling methods, such as Markov Chain Monte Carlo, since the latter’s accuracy depends on sampling from the posterior distribution a sufficient amount of times (and therefore requiring an equivalent number of computations of the forward problem, which can be quite expensive).