Approximation of Mechanical Fields around Short-Cylinder-Shaped Inclusions by Means of Artificial Neural Network

Abstract:

In this paper we present our approach to estimate mechanical fields (strains, stresses or displacements) inside isotropic infinite body with isotropic inclusions. Solution can be obtained easily for inclusions with ellipsoidal-like shapes by means of J. D. Eshelby's analytical solution given in 1957. Unfortunately for other distinct shapes of inclusions there is no analytic solution and finite element analysis is quite time consuming option. In our work, we focus on prediction of mechanical response for inclusions in form of short cylinders (e.g. steel fibers in steel-fiber-reinforced concrete) by means of artificial neural network. Which if trained on sufficiently large set of reference examples can predict desired mechanical fields and achieve considerable speed-up at the cost of approximate solution.

• Periodical: Applied Mechanics and Materials (Volume 825)
• Pages: 191-194
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.825.191
• Online since: February 2016
• Authors: Lukáš Zrůbek*, Anna Kučerová, Jan Novák
• Keywords: Artificial Neural Network, Finite Element Method, Mechanical Fields, Micromechanics, Short-Cylinder-Shaped Inclusions

References

[1] J. D. Eshelby: The determination of the elastic field of an ellipsoidal inclusion and related problems, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. (1957).

[2] K. Gurney: An introduction to neural networks, Boca Raton: CRC Press, (1997), xi, p.234, ISBN 978-1-85728-503-4.

[3] S. S. Haykin et al.: Neural networks and learning machines, 3rd ed. Upper Saddle River, N.J.: Pearson, (2009), p.934, ISBN 01-312-9376-1.

[4] T. Mareš, A. Kučerová: RegNeN 2012 [online], Faculty of Civil Engineering, Czech Technical University in Prague, (2012) [cited 2015-03-01] Available from: http: /klobouk. fsv. cvut. cz/~anicka/regnen/regnen. html.

[5] J. Novák: Generator of optimal LHS designs SPERM v. 2. 0, Centre for Integrated Design of Advanced Structures (CIDEAS), Czech Technical University in Prague, (2011).

[6] B. Patzák: OOFEM - an object-oriented simulation tool for advanced modelling of materials and structures, Acta Polytechnica, 52(6): 59-66, (2012).

DOI: 10.14311/1678

[7] T. Mareš, E. Janouchová, A. Kučerová: Different approaches to calibration of nonlinear mechanical models using artificial neural networks, (2015), submitted for publication, e-print: arXiv: 1502. 01380.

[8] L. Zrůbek, A. Kučerová, J. Novák: Artificial neural network in prediction of solution for Eshelby's inclusion problem, Proceedings of the 5th Conference Nano & Macro Mechanics, (2014), pp.219-226, ISBN 978-80-01-05569-4.