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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.
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).
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).
In this work, a probabilistic framework for identification of traffic loads on concrete Bridge structures is presented using data from a FE structural model in combination with a finite volume approach for traffic load modelling. The identification approach uses Bayesian Inference to identify traffic loads from measured sensor data from travelling load experiments performed at BAM. The work focuses on the load identification part of the Framework utilizing global structural response measurements only. The obtained information on traffic loads can be forwarded to further analysis such as fatigue and structure state estimation or model updating.
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.
In this paper, a contact problem between two bodies, discretized by finite elements, is solved by adding an auxiliary NURBS layer between the bodies. The advantages of a smooth contact formulation in a NURBS approach are combined with simple mesh generation procedures for the bodies discretized with finite elements. Mesh tying conditions are used to couple the NURBS layer with the finite element discretization. The NURBS layer is the master side for contact and mesh tying. Mesh tying is enforced either using pointwise or mortar type approaches. Frictionless 2D and 3D contact problems are considered using small deformations. The contact problem is discretized with the mortar method and a penalty approach is used to enforce the contact constraints. A robust element-based quadrature is applied for mortar tying and contact discretizations, thus avoiding computationally expensive Segmentation.
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.
In this paper, the impact problem and the subsequent wave Propagation are considered. For the contact discretization an intermediate non-uniform rational B-spline (NURBS) layer is added between the contacting finite element bodies, which allows a smooth contact formulation and efficient element-based integration.
The impact event is ill-posed and requires a regularization to avoid propagating stress oscillations. A nonlinear mesh-dependent penalty regularization is used, where the stiffness of the penalty regularization increases upon mesh refinement. Explicit time integration methods are well suited for wave propagation problems, but are efficient only for diagonal mass matrices. Using a spectral element discretization in combination with a NURBS contact layer the bulk part of the mass matrix is diagonal.
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.