Multi-scale modelling of brick masonry using a numerical homogenisation technique and an artificial neural network

• Autorzy: Urbański Aleksander , Ligęza Szymon , Drabczyk Marcin

Identyfikatory

DOI

10.24425/ace.2022.143033

Warianty tytułu

PL

Wielo-skalowe modelowanie muru z cegieł przy użyciu metody homogenizacji i sztucznych sieci neuronowych

• Języki publikacji: EN

Abstrakty

EN

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 Σn+1 with the old state Σn 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.

PL

W pracy przedstawiono sposób tworzenia makro-modelu konstytutywnego muru ceglanego. Przyjmuje się założenia płaskiego stanu naprężenia. Tworzony model nie jest modelem ortotropowym sprężysto-plastycznym, ale jest zbudowany jako sztuczna sieć neuronowa (SSN) dająca niejawną funkcję konstytutywną. Wiąże ona nowy stan naprężeń uogólnionych (sił membranowych) Σn+1 z poprzednim stanem Σn oraz przyrostem odkształceń uogólnionych ΔE. Forma tak utworzonego makro-modelu konstytutywnego jest zgodna z analizą przyrostową problemu statyki w przypadku nieliniowości materiałowych. Składniki muru (cegła i zaprawa) są opisane modelami sprężysto-plastycznymi Druckera-Pragera. Parametry materiałowe składników muru oraz geometria komórki powtarzalnej stanowią dane wejściowe, służące budowie makro-modelu muru.

Słowa kluczowe

EN

artificial neural network; finite element method; FEM; multiscale modeling; homogenisation; masonry

PL

homogenizacja; konstrukcja murowa; metoda elementów skończonych; MES; modelowanie wieloskalowe; sieć neuronowa sztuczna

• Wydawca: Komitet Inżynierii Lądowej i Wodnej PAN ; Politechnika Warszawska, Wydział Inżynierii Lądowej
• Czasopismo: Archives of Civil Engineering
• Rocznik: 2022
• Tom: Vol. 68, nr 4
• Strony: 179--197
• Opis fizyczny: Bibliogr. 24 poz., il., tab.

Twórcy

autor

Urbański Aleksander

• Cracow University of Technology, Faculty of Civil Engineering, Kraków, Poland

• https://orcid.org/0000-0002-5544-9134

autor

Ligęza Szymon

• AGH University of Science and Technology, Faculty of Drilling, Oil and Gas (doctoral student), Kraków, Poland

• https://orcid.org/0000-0001-6702-9260

autor

Drabczyk Marcin

• Idealogic Ltd., Kraków, Poland

• https://orcid.org/0000-0001-9245-1025

Bibliografia

• [1] S. Jemioło, L. Małyszko, FEM and constitutive modelling in analysis of masonry structures. Theoretical basis, vol. 1. Olsztyn: University of Warmia and Mazury, 2013 (in Polish).
• [2] P.B. Lourenço, “Computational strategies for masonry structures”, PhD thesis, Delft University of Technology, Netherlands, 1996.
• [3] P. Pegon, A. Anthoine, “Numerical strategies for solving continuum damage problems involving softening: Application to the homogenization of masonry”, in Advances in Non-Linear Finite Element Methods, B. Topping, et. al., Eds. Edinburgh, Scotland: CIVIL-COMP Ltd.,1994, pp. 143-157.
• [4] A. Cormeau, N.G. Shrive, “A 2D model for the prediction of failure modes in masonry subject to in-plane loads”, in Proceedings of 3th Computer Methods in Structural Masonry, Book&Journals International Ltd., 1995.
• [5] P. Bilko, L. Małyszko, “An Orthotropic Elastic-Plastic Constitutive Model for Masonry Walls”, Materials, 2020, vol. 13, art. ID 4064; DOI: 10.3390/ma13184064.
• [6] A. Zucchini, P.B. Lourenço, “A micro-mechanical model for the homogenisation of masonry”, International Journal of Solids and Structures, 2002, vol. 39, pp. 3233-3255; DOI: 10.1016/S0020-7683(02)00230-5.
• [7] S. Pietruszczak, X. Niu, “A mathematical description of macroscopic behaviour of brick masonry”, International Journal Solids Structures, 1992, vol. 29, pp. 531-546; DOI: 10.1016/0020-7683(92)90052-U.
• [8] A. Urbański, The unified, finite element formulation of homogenization of structural members with a periodic microstructure, Cracow University of Technology, 2005.
• [9] M. Kawa, “Failure criterion for brick masonry: A micro-mechanics approach”, Studia Geotechnica et Mechanica, 2014, vol. 36, no. 3, pp. 37-48; DOI: 10.2478/sgem-2014-0025.
• [10] A. Urbański, F. Pachla, K. Wartak-Dobosz, “An orthotropic elasto-plastic-damage model of masonry. Implementation as ZSoil user model”, in Numerics in geotechnics and structures 2015, T. Zimmermann, et al., Eds. Rossolis Editions & Zace Services Ltd, 2016, pp. 25-42.
• [11] Z. Waszczyszyn, “Neural Networks in the Analysis and Design of Structures”, CISM Courses and Lectures, no. 404. Wien -New York: Springer, 1999.
• [12] M. Lefik, “Artificial neural network for modelling an effective behavior of composite materials”, in Proceedings of the Fifth World Congress on Computational Mechanics (WCCM V), Vienna, Austria, July 7-12. Vienna University of Technology, 2002.
• [13] J. Ghaboussi, D.A. Pecknold, M. Zhang, R. HajAli, “Autoprogressive training of neural network constitutive models”, International Journal for Numerical Methods in Engineering, 1998, vol. 42, no. 1, pp. 105-126; DOI: 10.1002/(SICI)1097-0207(19980515)42:1<105::AID-NME356>3.0.CO;2-V.
• [14] Y.M.A. Hashash, S. Jung, J. Ghaboussi, “Numerical implementation of a neural network based material model in finite element analysis”, International Journal for Numerical Methods in Engineering, 2004, vol. 59, pp. 989-1005; DOI: 10.1002/nme.905.
• [15] P.A. Lucon, R.P. Donovan, “An artificial neural network approach to multiphase continua constitutive modeling”, Composites, 2007, vol. 38, no. 7-8, pp. 817-823; DOI: 10.1016/j.compositesb.2006.12.008.
• [16] G.A. Drosopoulos, G.E. Stavroulakis, “Data-driven computational homogenization using Neural Networks FE2-NN application on damaged masonry”, Journal on Computing and Cultural Heritage, 2021, vol. 14, no. 1, pp. 1-19; DOI: 10.1145/3423154.
• [17] I.B. Rocha, P. Kerfriden, F.P. van der Meer, “Micromechanics-based surrogate models for the response of composites: A critical comparison between a classical mesoscale constitutive model, hyper-reduction and neural networks”, European Journal of Mechanics and Solids, 2020, vol. 82; DOI: 10.1016/j.euromechsol.2020.103995.
• [18] B.A. Le, J. Yvonnet, Q.-C. He, “Computational homogenization of nonlinear elastic materials using neural networks”, International Journal for Numerical Methods in Engineering, 2015, vol. 104, no. 12, pp. 1061-1084; DOI: 10.1002/nme.4953.
• [19] H. Baluch, I. Nowosinska, “Application of Artificial Neural Networks in Planning Track Superstructure Repairs”, Archives of Civil Engineering, 2020, vol. 66, no. 4, pp. 45-060; DOI: 10.24425/ace.2020.135208.
• [20] J. Hertz, A. Krogh, R.G. Palmer, Introduction to the theory of neural computation. Redwood City, Calif: Addison-Wesley Pub, 1991.
• [21] C.M. Bishop, Pattern Recognition and Machine Learning. New York: Springer, 2006.
• [22] S. Raschka, Python Machine Learning. Gliwice, Poland: Helion, 2017 (in Polish).
• [23] M. Szeliga, Data Science and Machine Learning. Warsaw, Poland: PWN, 2017 (in Polish).
• [24] J. Bergstra, R. Bardenet, Y. Bengio, B. Kegl, “Algorithms for Hyper-Parameter Optimization”, in Advances in Neural Information Processing Systems 24. Curran Associates, Inc., 2011, pp. 2546-2554.