Engineering Transactions, 67, 2, pp. 271–288, 2019

Verification of Application of ANN Modelling in Study of Compressive Behaviour of Aluminium Sponges

Anna Małgorzata STRĘK
Cracow University of Technology

Cracow University of Technology

Arkadiusz KWIECIEŃ
Cracow University of Technology

Krzysztof WAŃCZYK
Foundry Research Institute, Center for Design and Prototyping

Institute of Ceramics and Building Materials, Refractory Materials Division in Gliwice

This article presents a preliminary neural network analysis of the compressive behaviour of aluminium open-cell sponges and answers the question of whether this phenomenon can be modelled using artificial intelligence. The research consisted of two phases: first – compression experiments, which in turn provided data for the second phase – the artificial neural network (ANN) analysis. A two-argument function was proposed and tested using the gathered experimental data with a two-layer feedforward network. The determination coefficient $R^2$ for linear correlation between targets and modelling outputs was chosen as the criterion for the assessment of the quality of modelling. The obtained values were $R^2 > 0.96$, which shows that neural networks hold the capacity to address the characterisation of the mechanical response of aluminium open-cell sponges in compression. Additionally, the mean absolute relative error (MARE) and the mean square error (MSE) were also determined.
Keywords: metal sponges; aluminium sponges; compression tests; artificial neural networks
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Degischer H., Kriszt B., Handbook of cellular metals: production, processing, applications, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, 2002.

García-Moreno F., Commercial applications of metal foams: their properties and production, Materials, 9(2): 85–111, 2016.

Sobczak J., Wojciechowski A., Boyko L., Drenchev L., Darłak P., Dudek P., Highly porous materials [in Polish: Materiały wysokoporowate], Instytut Odlewnictwa, Kraków, 2005.

Simancik F., Jerz J., Kovácik J., Minár P., Aluminium foam – a new light-weight structural material, Kovové Materiály (Metallic Materials), 35: 265–277, 1997.

Duocel r copper foam, ERG Materials and Aerospace Corp., Oakland, CA 94608, US, (accessed 15 Oct. 2018).

Dunand D.C., Processing of titanium foams, Advanced Engineering Materials, 6(6): 369–376, 2004.

Jakubowicz J., Adamek G., Dewidar M., Titanium foam made with saccharose as a space holder, Journal of Porous Materials, 20(5): 1137–1141, 2013.

Banhart J., Gold and gold alloy foams, Gold Bulletin, 41(3): 251–256, 2008.

Smith B.H., Szyniszewski S., Hajjar J.F., Schafer B.W., Arwade S.R., Steel foam for structures: A review of applications, manufacturing and material properties, Journal of Constructional Steel Research, 71: 1–10, 2012.

Duarte I., Oliveira M., Aluminium alloy foams: production and properties, [in:] K. Kondoh [Ed.], Powder Metallurgy, InTech, pp. 47–72, 2012.

Nieh T.G., Higashi K., Wadsworth J., Effect of cell morphology on the compressive properties of open-cell aluminum foams, Materials Science and Engineering: A, 283(1–2): 105–110, 2000.

Miedzinska D., Niezgoda T., Gieleta R., Numerical and experimental aluminum foam microstructure testing with the use of computed tomography, Computational Materials Science, 64: 90–95, 2012.

Zhou J., Shrotriya P., Soboyejo W.O., Mechanisms and mechanics of compressive deformation in open-cell Al foams, Mechanics of Materials, 36(8): 781–797, 2004.

Papadopoulos D.P., Omar H., Stergioudi F., Tsipas S.A., Lefakis H., Michailidis N., A novel method for producing Al-foams and evaluation of their compression behavior, Journal od Porous Materials, 17(6): 773–777, 2010.

Wicklein M., Thoma K., Numerical investigations of the elastic and plastic behaviour of an open-cell aluminium foam, Materials Science and Engineering: A, 397(1–2): 391–399, 2005.

Robertson I.M. et al., Towards an integrated materials characterization toolbox, Journal of Material Research, 26(1): 1341–1383, 2011.

Kurzynski M., Methods of artificial intelligence for engineers [in Polish: Metody sztucznej inteligencji dla inzynierów], PanstwowaWyzsza Szkoła Zawodowa im. Witelona w Legnicy, Stowarzyszenie „Wspólnota Akademicka”, Legnica, 2008.

Lefik M., Application of artificial neural networks in mechanics and engineering [in Polish: Zastosowanie sztucznych sieci neuronowych w mechanice i w inzynierii],Wydawnictwo Politechniki Łódzkiej, Łódz, 2005.

Jakubek M., Application of artificial neural networks in selected problems of experimental mechanics and structural engineering [in Polish: Zastosowanie sztucznych sieci neuronowych w wybranych zagadnieniach eksperymentalnej mechaniki materiałów i konstrukcji], PhD thesis, Politechnika Krakowska, Kraków, 2007.

Pietrzyk M., Kusiak J., Szeliga D., Rauch Ł., Sztangret Ł., Górecki G., Application of metamodels to identification of metallic materials models, Advances in Materials Science and Engineering, 2016, article ID: 2357534, 20 pages, 2016.

Strek A.M., Assessment of strength and functional properties of cellular materials [in Polish: Ocena własciwosci wytrzymałosciowych i funkcjonalnych materiałów komórkowych], PhD thesis, AGH, Kraków, 2017.

Kasza P., Lipowska B., Pecherski R.B., Strek A.M., Wanczyk K., Compression of open-cell aluminium, Engineering Transactions, 64(4): 629–634, 2016.

Strek A.M., Lipowska B., Wanczyk K., Selected aspects of manufacturing of aluminium sponge, Archives of Metallurgy and Materials, 64(3), 2019 (accepted, in print).

Banhart J., Manufacture, characterisation and application of cellular metals and metal foams, Progress in Materials Science, 46(6): 559–632, 2001.

Kränzlin N., Niederberger M., Controlled fabrication of porous metals from the nanometer to the macroscopic scale, Materials Horizons, 2: 359–377, 2015.

Kanaun S., Tkachenko O., Representative volume element and effective elastic properties of open cell foam materials with random microstructures, Journal of Mechanics of Materials and Structures, 2(8): 1607–1628, 2007.

ISO 13314:2011, Mechanical testing of metals – Ductility testing – Compression test for porous and cellular metals, International Organization for Testing, 2011.

Jang W.-Y., Kraynik A.M., Kyriakides S., On the microstructure of open-cell foams and its effect on elastic properties, International Journal of Solids and Structures, 45(7–8): 1845–1875, 2008.

Gibson I.J., Ashby M.F., The mechanics of three-dimensional cellular materials, Proceedings of the Royal Society A, 382(1782): 43–59, 1982.

Dudzik M., Mielnik R., Wróbel Z., Preliminary analysis of the effectiveness of the use of artificial neural networks for modelling time-voltage and time-current signals of the combination wave generator, [in:] SPEEDAM 2018 – Proceedings: International Symposium on Power Electronics, Electrical Drives, Automation and Motion, 8445277, pp. 1095–1100, 2018.

Dudzik M., Tomczyk K., Jagiełło A.S., Analysis of the error generated by the voltage output accelerometer using the optimal structure of an artificial neural network, [in:] Proceedings of the 19th International Conference on Research and Education in Mechatronics, REM 2018, 8421789, pp. 7–11, 2018.

Dudzik M., Mielnik R., Wróbel Z., Preliminary analysis of the effectiveness of the use of artificial neural networks for modeling time-voltage signal of the combination wave generator, 18th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering, ISEF 2017, 8090698, 2017.

McCaffrey J., How to standardize data for neural networks, Visual Studio Magazine 01/15/2014, (accessed 15 Sept 2018).

Demuth H., Beale M., Hagan M., Neural Network Toolbox 5 User’s Guide, The Math-Works Inc., 2007.

Mathworks documentation: mapminmax, (accessed 21 Feb 2019).

Matlab and automatic target normalization: mapminmax. Don’t trust your Matlab framework!, (accessed 21st Feb 2019).

Hagan M.T., Demuth H.B., Beale M.H., De Jesus O., Neural network design, 2nd Ed., eBook, 2014.

Levenberg K., A method for the solution of certain non-linear problems in least squares, Quarterly of Applied Mathematics, 2: 164–168, 1944.

Marquardt D.W., An algorithm for least-squares estimation of nonlinear parameters, SIAM Journal on Applied Mathematics, 11(2): 431–441, 1963.

Madsen K., Nielsen H.B., Tingleff O., Methods for non-linear least squares problems, Informatics and Mathematical Modelling Technical University of Denmark, 2nd Ed., April 2004, (accessed 15 Oct 2018).

Levenberg-Marquardt algorithm, article in Wikipedia, on-line: (accessed 15 Oct 2018).

Girard A., Excerpt from theoretical and instrumental optics review [in French: Excerpt from Revue d’optique théorique et instrumentale], Revue d’Optique, 37: 225–241, 397–424, 1958.

Wynne C.G., Lens designing by electronic digital computer: I, Proceedings of the Physical Society of London, 73(5): 777–787, 1959.

Morrison D.D., Methods for nonlinear least squares problems and convergence proofs, [in:] Proceedings of the Jet Propulsion Laboratory Seminar on Tracking Programs and Orbit Determination, Pasadena, California, pp. 1–9, 1960.

Dudzik M., Strek A.M., ANN architecture specifications for modelling of open-cell aluminium under compression, 2019 (in preparation).

DOI: 10.24423/EngTrans.991.20190615

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