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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 102
PROCEEDINGS OF THE FOURTEENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING
Edited by:
Paper 102

Wang Tiling Aided Modelling of Closed Cell Foams

M. Doškár1, J. Novák1,2 and J. Nemecek1

1Department of Mechanics, Faculty of Civil Engineering
Czech Technical University in Prague, Czech Republic
2Institute of Structural Mechanics, Faculty of Civil Engineering
Brno University of Technology, Czech Republic

Full Bibliographic Reference for this paper
, "Wang Tiling Aided Modelling of Closed Cell Foams", in , (Editors), "Proceedings of the Fourteenth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 102, 2013. doi:10.4203/ccp.102.102
Keywords: closed-cell foam, Alporas®, homogenized properties, upper-lower bounds, Wang tilings, two-dimensional homogenization.

Summary
In this paper, a homogenization model of high porosity metallic foams based on a two-dimensional finite element analysis is presented. The assumed model is wired, which allows for correct volume fractions of metallic phase contrary to planar models obtained from scanned images. Two types of boundary conditions, static and kinematic uniform, along with a number of representative volume elements of different sizes are explored in order to arrive at upper and lower bounds for effective moduli. The geometries of computational models are synthesized by means of Wang tiles with morphologies spatially consistent with target medium. Although, we are aware of the fact that the rigorous three-dimensional model would be optimal for a reliable judgment of resulting material parameters, the main benefit of this work is seen in the effective way the geometries of computational models are created and kept in the computer memory. Moreover, the proposed two dimensional analysis reveals many difficulties we would have to deal with in three dimensions anyway.

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