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FenicsXConcrete
(2023)
Multiscale modeling of linear elastic heterogeneous structures via localized model order reduction
(2024)
In this paper, a methodology for fine scale modeling of large scale linear elastic structures is proposed, which combines the variational multiscale method, domain decomposition and model order reduction. The influence of the fine scale on the coarse scale is modelled by the use of an additive split of the displacement field, addressing applications without a clear scale separation. Local reduced spaces are constructed bysolving an oversampling problem with random boundary conditions. Herein, we inform the boundary conditions by a global reduced problem and compare our approach using physically meaningful correlated samples with existing approaches using uncorrelated samples. The local spaces are designed such that the local contribution of each subdomain can be coupled in a conforming way, which also preserves the sparsity pattern of standard finite element assembly procedures. Several numerical experiments show the accuracy and efficiency of the method, as well as its potential to reduce the size of the local spaces and the number of training samples compared to the uncorrelated sampling
With increasing focus on industrialized processing, investigating, understanding, and modelling the structural build-up of cementitious materials becomes more important. The structural build-up governs the key property of fresh printable materials -- buildability -- and it influences the mechanical properties after the deposition. The structural build-up rate can be adjusted by optimization of the mixture composition and the use of concrete admixtures. Additionally, it is known, that the environmental conditions, i.e. humidity and temperature have a significant impact on the kinetic of cement hydration and the resulting hardened properties, such as shrinkage, cracking resistance etc. In this study, small amplitude oscillatory shear (SAOS) tests are applied to examine the structural build-up rate of cement paste subject to different temperatures under controlled humidity. The results indicate significant influences of the ambient temperature on the intensity of the re-flocculation (Rthix) rate, while the structuration rate (Athix) is almost not affected. A bi-linear thixotropy model extended by temperature dependent parameters coupled with a linear viscoelastic material model is proposed to simulate the mechanical behaviour considering the structural build-up during the SAOS test.
With increasing focus on industrialized processing, investigating, understanding, and modelling the structural build-up of cementitious materials becomes more important. The structural build-up governs the key property of fresh printable materials -- buildability -- and it influences the mechanical properties after the deposition. The structural build-up rate can be adjusted by optimization of the mixture composition and the use of concrete admixtures. Additionally, it is known, that the environmental conditions, i.e. humidity and temperature have a significant impact on the kinetic of cement hydration and the resulting hardened properties, such as shrinkage, cracking resistance etc. In this study, small amplitude oscillatory shear (SAOS) tests are applied to examine the structural build-up rate of cement paste subject to different temperatures under controlled humidity. The results indicate significant influences of the ambient temperature on the intensity of the re-flocculation (Rthix) rate, while the structuration rate (Athix) is almost not affected. A bi-linear thixotropy model extended by temperature dependent parameters coupled with a linear viscoelastic material model is proposed to simulate the mechanical behaviour considering the structural build-up during the SAOS test
The key point of structural reliability analysis is the estimation of the failure probability (Pf), typically a rare event. This probability is defined as the integral over the failure domain which is given by a limit state function. Usually, this function is only implicit given by an underlying finite element simulation of the structure. It is generally not possible to solve the integral for Pf analytically. For that reason, simulation-based methods as well as methods based on surrogate modeling (or Response surface methods) has been developed. Nevertheless, these variance reducing methods still require a few thousand calculations of the underlying finite element model, making reliability Analysis computationally expensive for real applications.
The efficiency of structural model updating and the subsequent reliability analysis is increased by using the advantages of reduced order models. Coupling a reduced model of the structure of interest with a Bayesian model updating approach or an reliability analysis to estimate the failure probability reduce the computational cost of such complex analyses drastically.
The key point of structural reliability analysis is the estimation of the failure probability. This probability is defined as the integral over the failure domain which is given by a limit state function. Usually, this function is only implicit given by an underlying finite element simulation of the structure. It is generally not possible to solve the integral analytically. For that reason, numerical methods based on sampling and surrogates have been developed. Nevertheless, these sampling methods still require a few thousand calculations of the underlying finite element model, making reliability analysis computationally expensive for relevant applications.
Coupling a reduced order model (proper generalized decomposition) with an efficient variance reducing sampling algorithm can reduce the computational cost of reliability analysis drastically. In the proposed method, an importance sampling technique is coupled with a reduced structural model by means of PGD to estimate the failure probability. Instead of calculating the design point e.g. with optimization algorithms, the design point is adaptively estimated by using the idea of subset simulation. The failure probability is estimated in an iterative scheme based on adaptively computing the design point and refining the PGD model.
The main challenge using numerical models as digital twins in real applications is the calibration and validation of the model based on uncertain measurement data. Therefore, model updating approaches which are inverse optimization processes are applied. This requires a huge number of computations of the same numerical model with slightly different model parameters. For that reason, model updating becomes computationally very expensive for real applications.
Model reduction, e.g. the proper generalized decomposition method, is a popular concept to decrease the computational effort of complex numerical simulations. Therefore, a reduced model of the structure of interest is derived and will be used as surrogate model in a Variational Bayesian procedure to create a very efficient digital twin of the structure.
An efficient model updating approach by means of a PGD reduced model with random field material stiffness parameters is shown. The random field allows, to calibrate the model considering parameter changes over the spatial direction. These changes can be caused by local damages as well as by production. As an exemplary application a demonstrator bridge is used. Digital twins can reduce the costs for maintenance and inspections especially for the costly civil infrastructure with high requirements at their performance over the whole lifetime. Currently, the current state of the structure is determined by regular manual and visual inspections within constant intervals. However, the critical sections are often not directly accessible or impossible to be instrumented at all. In this case, model-based approaches where a digital twin is set up can improve the process. Based on this digital twin, a prognosis of the future performance of the structure, e.g. the failure probability, can be computed.
The influences of the reduction degree, the mesh discretization as well as the correlation length in the PGD Bayesian approach are studied by means of the digital twin of a simple pre-stressed concrete two field bridge.
Interlaboratory studies are common tools for collecting comparable data to implement standards for new materials or testing technologies. In the case of construction materials, these studies form the basis for recommendations and design codes. Depending on the study, the amount of data collected can be enormous, making manual handling and evaluation difficult. On the other hand, the importance of the FAIR (findable, accessible, interoperable, and reusable) principles for scientific data management, published by Wilkinson et al. in 2016, is constantly growing and changing the view on data usage.
The benefits of using data management tools such as data stores/repositories or electronic laboratory notebooks are many. Data is stored in a structured and accessible way (at least within a group) and data loss due to staff turnover is reduced. Tools usually support data publishing and analysis interfaces. In this way, data can be reused years later to generate new knowledge with future insights. On the other hand, there are many challenges in setting up a data repository, such as selecting suitable software tools, defining the data structure, enabling data access, and understanding by others and
ensuring maintenance, among others.
This talk discusses the advantages and challenges of setting up and applying a data repository using the interlaboratory study on the mechanical properties of printed concrete structures carried out in RILEM TC 304-ADC as example. First, the definition of a suitable data structure including all information is discussed. The tool-dependent upload process is then described. Here, the data
management system openBIS (open source software developed by ETH Zurich) is used. Since in most cases an open compute platform allowing access from different organisations is not possible or available due to data protection and maintenance issues, tool-independent export options are discussed and compared. Finally, the different query and analysis possibilities are demonstrated.
There is a rising attention of using numerical models for effcient structural monitoring and ensuring the structure's safety. Setting up virtual models as twin for real structures requires a model identification process calculating the unknown model parameters, which mostly are only indirectly measurable. This is a computationally very costly inverse optimization process, which often makes it unfeasible for real applications. Effcient surrogate models such as reduced order models can be used, to overcome this limitation. But the influence of the model accuracy on the identification process has then to be considered. The aim is to automatically control the influence of the model's accuracy on the identification. Here, a variational Bayesian inference approach[3] is coupled with a reduced forward model using the Proper Generalized Decomposition (PGD) method. The influence of the model accuracy on the inference result is studied and measured. Therefore, besides the commonly used Bayes factor the Kullback-Leibler divergences between the predicted posterior pdfs are proposed. In an adaptive inference procedure, the surrogate's accuracy is iteratively increased, and the convergence of the posterior pdf is analysed. The proposed adaptive identification process is applied to the identification of spatially distributed damage modeled by a random eld for a simple example with synthetic data as well as a small, reinforced bridge with real measurement data. It is shown that the proposed criteria can mirror the influence of the model accuracy and can be used to automatically select a suffciently accurate surrogate model.