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Keywords: homogenization, cellular, material, bounds, topology, optimization..

Summary

The homogenization theory is often used to compute the elastic properties of periodic composite materials based on the shape and periodicity of a unit-cell. The unit-cell is thus representative of the smallest periodic heterogeneity of the composite medium. The resulting properties are to be interpreted as describing a homogeneous medium equivalent to the periodic porous medium of the actual composite. However, this theory hypothesizes that the feature size of the unit-cell, is much smaller than the resulting composite global dimension (dimensionless unitcell), as well as the application of periodic boundary conditions to the unit-cell domain. As a result of these hypotheses it is critical to investigate the problem of how good homogenization predictions are when compared to the actual properties of a composite generated by the finite spatial repetition of a unit-cell characterized by dimensional quantities. Related research work involving two-dimensional bimaterial unit-cells with material symmetry has been already reported. As it follows, one addresses again this research topic although considering here the case of three-dimensional porous unit-cells with no a priori material symmetry (anisotropic case). The unit-cell designs here are obtained maximizing the stiffness objective function subjected to constraints on permeability. The outcome of the present work indicates that, for practical purposes, it is sufficient in these examples to have a low scale factor to replace the non-homogeneous composite by the equivalent homogeneous material with the moduli given by homogenization theory. These observations are also consistent with previous works although they had been focused on bidimensional microstructures with material symmetry.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 106 PROCEEDINGS OF THE TWELFTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: Paper 247 Scale-Size Effects Analysis on Predicting the Mechanical Properties of Periodic Composite Materials P.G. Coelho¹, J.M. Guedes² and H.C. Rodrigues² ¹Department of Mechanical and Industrial Engineering, Faculty of Sciences and Technology, Universidade Nova de Lisboa, Portugal ²Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Portugal doi:10.4203/ccp.106.247 purchase the full-text of this paper Full Bibliographic Reference for this paper P.G. Coelho, J.M. Guedes, H.C. Rodrigues, "Scale-Size Effects Analysis on Predicting the Mechanical Properties of Periodic Composite Materials", in , (Editors), "Proceedings of the Twelfth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 247, 2014. doi:10.4203/ccp.106.247 Keywords: homogenization, cellular, material, bounds, topology, optimization.. Summary The homogenization theory is often used to compute the elastic properties of periodic composite materials based on the shape and periodicity of a unit-cell. The unit-cell is thus representative of the smallest periodic heterogeneity of the composite medium. The resulting properties are to be interpreted as describing a homogeneous medium equivalent to the periodic porous medium of the actual composite. However, this theory hypothesizes that the feature size of the unit-cell, is much smaller than the resulting composite global dimension (dimensionless unitcell), as well as the application of periodic boundary conditions to the unit-cell domain. As a result of these hypotheses it is critical to investigate the problem of how good homogenization predictions are when compared to the actual properties of a composite generated by the finite spatial repetition of a unit-cell characterized by dimensional quantities. Related research work involving two-dimensional bimaterial unit-cells with material symmetry has been already reported. As it follows, one addresses again this research topic although considering here the case of three-dimensional porous unit-cells with no a priori material symmetry (anisotropic case). The unit-cell designs here are obtained maximizing the stiffness objective function subjected to constraints on permeability. The outcome of the present work indicates that, for practical purposes, it is sufficient in these examples to have a low scale factor to replace the non-homogeneous composite by the equivalent homogeneous material with the moduli given by homogenization theory. These observations are also consistent with previous works although they had been focused on bidimensional microstructures with material symmetry. purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £65 +P&P)
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