@ARTICLE{Urbański_Aleksander_Multi-scale_2022,
 author={Urbański, Aleksander and Ligęza, Szymon and Drabczyk, Marcin},
 volume={vol. 68},
 number={No 4},
 journal={Archives of Civil Engineering},
 pages={179-197},
 howpublished={online},
 year={2022},
 publisher={WARSAW UNIVERSITY OF TECHNOLOGY FACULTY OF CIVIL ENGINEERING and COMMITTEE FOR CIVIL ENGINEERING POLISH ACADEMY OF SCIENCES},
 abstract={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.},
 type={Article},
 title={Multi-scale modelling of brick masonry using a numerical homogenisation technique and an artificial neural network},
 URL={http://journals.pan.pl/Content/125673/PDF-MASTER/art11_int.pdf},
 doi={10.24425/ace.2022.143033},
 keywords={artificial neural network, finite element method, homogenisation, masonry},
}