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Machine learning applied to simulations of material mechanical behavior
Raisinger, Jan ; Novák, Lukáš (referee) ; Eliáš, Jan (advisor)
The thesis explores the possibility of using machine learning models to predict effective macroscopic material parameters of multiphase materials. The asymptotic expansion homogenization method is used together with the finite element method to create software in Python, which is used to calculate effective macroscale mechanical parameters of sets of heterogeneous arrangements. These sets are generated using several methods, e.g. as a realization of a discretized random field. The sets are used to train neural networks built using the Keras library. The accuracy of the networks and the quality of training data are assessed. The advantages and disadvantages of the networks compared to the FEM solver are demonstrated on their application in an optimization problem.
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Probabilistic discrete model of concrete fracturing
Kaděrová, Jana ; Lehký, David (referee) ; Konečný,, Petr (referee) ; Eliáš, Jan (advisor)
The thesis presents results of a numerical study on the performance of 3D discrete meso–scale lattice–particle model of concrete. The existing model was extended by introducing the spatial variability of chosen material parameter in form of random field. An experimental data from bending tests on notched and unnotched beams was exploited for the identification of model parameters as well as for the subsequent validation of its performance. With the basic and the extended randomized version of the model, numerical simulations were calculated so that the influence of the rate of fluctuation of the random field (governed by the correlation length) could be observed. The final part of the thesis describes the region in the beam active during the test in which the most of the fracture energy is released in terms of its size and shape. This region defines the strength of the whole member and as shown in the thesis, it does not have a constant size but it is influenced by the geometrical setup and the correlation length of the random field.
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Stochastic discrete modeling of progressive damage in concrete structures
Kučera, Michal ; Sadílek, Václav (referee) ; Vořechovský, Miroslav (advisor)
The work focuses on the statistical strength of structures made of quasi-brittle ma- terials, specifically concrete. Special attention is paid to the influence of the size of the structure on strength and on the entire process of material failure during loading. The mechanics of these processes are modeled using discrete models, and these models are also considered in a probabilistic variant with spatially variable material parameters. Spatial variability is then modeled using random fields. The work clarifies the effect of diffuse damage in the volume of the structure before reaching the maximum load on the further course of dissipative processes, especially on the shape of the fracture process zone and subsequently on its interaction with the random variability of material parame- ters in eccentrically drawn dogbone-shaped bodies. In addition to the tools of stochastic computer fracture mechanics, an analytical model based on averaging and subsequent analysis of the minimum of the random field is presented
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Analysis of occurrence of extremal values in time and space
Starý, Ladislav ; Volf, Petr (advisor) ; Dvořák, Jiří (referee)
This thesis describes and compares methods for statistical modeling of spatio- temporal data. Methods are extended by examples and numerical studies on real world data. Basic point of interest is statistical analysis of spatial data with unknown correlation structure and known position in space. Further analysis is focused on spatial data with temporal component - spatio-temporal data. Fi- nally, extremal values and their occurrences are discussed. The main aspiration of my thesis is to provide statistical tools for spatio-temporal data and analysis of extremal values of prediction. 1
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Probabilistic discrete model of concrete fracturing
Kaděrová, Jana ; Lehký, David (referee) ; Konečný,, Petr (referee) ; Eliáš, Jan (advisor)
The thesis presents results of a numerical study on the performance of 3D discrete meso–scale lattice–particle model of concrete. The existing model was extended by introducing the spatial variability of chosen material parameter in form of random field. An experimental data from bending tests on notched and unnotched beams was exploited for the identification of model parameters as well as for the subsequent validation of its performance. With the basic and the extended randomized version of the model, numerical simulations were calculated so that the influence of the rate of fluctuation of the random field (governed by the correlation length) could be observed. The final part of the thesis describes the region in the beam active during the test in which the most of the fracture energy is released in terms of its size and shape. This region defines the strength of the whole member and as shown in the thesis, it does not have a constant size but it is influenced by the geometrical setup and the correlation length of the random field.
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Analysis of occurrence of extremal values in time and space
Starý, Ladislav ; Volf, Petr (advisor) ; Dvořák, Jiří (referee)
This thesis describes and compares methods for statistical modeling of spatio- temporal data. Methods are extended by examples and numerical studies on real world data. Basic point of interest is statistical analysis of spatial data with unknown correlation structure and known position in space. Further analysis is focused on spatial data with temporal component - spatio-temporal data. Fi- nally, extremal values and their occurrences are discussed. The main aspiration of my thesis is to provide statistical tools for spatio-temporal data and analysis of extremal values of prediction. 1
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