Multi-scale modelling of brick masonry using a numerical homogenisation technique and an artificial neural network
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Cracow University of Technology, Faculty of Civil Engineering, ul. Warszawska 24, 31-155, Kraków, Poland
AGH University of Science and Technology, Faculty of Drilling, Oil and Gas (doctoral student), al. Mickiewicza 30, 30-059 Kraków, Poland
Idealogic Ltd., ul. Kapelanka 26, 30-347 Kraków, Poland
Submission date: 2022-02-23
Final revision date: 2022-04-29
Acceptance date: 2022-05-31
Publication date: 2022-12-30
Archives of Civil Engineering 2022;68(4):179-197
A new method of creating constitutive model of masonry is reported in this work. The model is not an explicit orthotropic elastic-plastic one, but with an artificial neural network (ANN) giving an implicit constitutive function. It relates the new state of generalised stresses Σ n+1 with the old state Σ n and with an increment of generalised strains ΔE (plane-stress conditions are assumed). The first step is to run a strain- controlled homogenisation, repeatedly, on a three-dimensional finite element model of a periodic cell, with elastic-plastic models (Drucker–Prager) of the components; thus a set of paths is created in (Σ, ΔE) space. From these paths, a set of patterns is formed to train the ANN. A description of how to prepare these data and a discussion on ANN training issues are presented. Finally, the procedure based on trained ANN is put into a finite-element code as a constitutive function. This enables the analysis of arbitrarily large masonry systems. The approach is verified by comparing the results of the developed model basing on ANN with a direct (single-scale) one, which showed acceptable accuracy.
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