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Constitutive material law approximation using Kriging, comparison to neural networks and evaluation of performance within numerical homogenization

Nikandros Stavros-Konstantinos

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Year 2023
Type of Item Diploma Work
Bibliographic Citation Stavros-Konstantinos Nikandros, "Constitutive material law approximation using Kriging, comparison to neural networks and evaluation of performance within numerical homogenization", Diploma Work, School of Electrical and Computer Engineering, Technical University of Crete, Chania, Greece, 2023
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The combination of Computational Mechanics with the broader field of Big Data has been increasingly explored in recent years. Its aim is to determine the mechanical response of large structures for which there is abundant experimental or numerical data but a gap in theoretical understanding. Such approaches utilize finite elements and detailed modeling for each structural element of the construction. This leads to large and complex models that are difficult to use for structural analysis. An algorithm of computational homogenization and multi-scale analysis, in combination with experimental material data from a known database, presents a solution to this problem. This approach involves a step where the constitutive law of the materials in the construction, i.e., the relationship of mechanical response, is calculated. This thesis examines the development of an approach to characterize material relationships, specifically the stress-strain curves, in nonlinear segments of a masonry wall. This research is part of an effort to incorporate experimental data into a computational homogenization and multi-scale analysis algorithm in engineering, specifically by replacing the classical computation of the constitutive law with the use of metamodels. The metamodels are numerical tools that calculate the constitutive law of materials using a database. The metamodels we employed are an artificial neural network and the geostatistical technique known as Kriging. The objective is to compare the use and results of these two metamodels within a computational homogenization algorithm to select the optimal metamodel in terms of complexity and performance. The results of this research show that the Kriging metamodel, with fewer training data than that of Neural Networks, achieves better approximations of the material constitutive law. This constitutes a step towards further optimizing the computational homogenization algorithm.

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