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Coupled Systems Mechanics Volume 7, Number 1, February 2018 , pages 061-77 DOI: https://doi.org/10.12989/csm.2018.7.1.061 |
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High concentration ratio approximation of linear effective properties of materials with cubic inclusions |
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George Mejak
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| Abstract | ||
| This paper establish a high concentration ratio approximation of linear elastic properties of materials with periodic microstructure with cubic inclusions. The approximation is derived using first few terms of power series expansion of the solution of the equivalent eigenstrain problem with a homogeneous eigenstrain approximation. Viability of the approximation at high concentration ratios is proved by comparison with a numerical solution of the homogenization problem. To this end some theoretical result of symmetry properties of the homogenization problem are given. Using these results efficient numerical computation on a reduced computational domain is presented. | ||
| Key Words | ||
| periodic homogenization; material symmetries; equivalent eigenstrain method; effective elastic properties; asymptotic solution | ||
| Address | ||
| George Mejak: Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia | ||
