Abstract
The Voronoi tessellation technique and the finite element (FE) method are utilized to investigate the microstructure-property relations of three-dimensional (3-D) cellular solids (foams) that have irregular cell shapes and non-uniform strut cross-sectional areas (SCSAs). Perturbations are introduced to a regular packing of seeds to generate a spatially periodic Voronoi diagram with different degrees of cell shape irregularity (amplitude a), and to the constant SCSA to generate a uniform distribution of SCSAs with different degrees of SCSA non-uniformity (amplitude b). Twenty FE models are constructed, based on the Voronoi diagrams for twenty foam samples (specimens) having the same pair of a and b, to obtain the mean values and standard deviations of the elastic properties. Spatially periodic boundary conditions are applied to each specimen. The simulation results indicate that for low-density imperfect foams, the elastic moduli increase as cell shapes become more irregular, but decrease as SCSAs get less uniform. When the relative density (R) increases, the elastic moduli of imperfect foams increase substantially, while the Poisson's ratios decrease moderately. The effect of the interaction between the two types of imperfections on foam elastic properties appears to be weak. In addition, it is found that the strut cross-sectional shape has a significant effect on the foam properties. Also, the elastic response of foams with the cell shape and SCSA imperfections appears to be isotropic regardless of changes in a, b and R and the strut cross-sectional shape. © 2005 Elsevier Ltd. All rights reserved.
| Original language | English |
|---|---|
| Pages (from-to) | 783-806 |
| Number of pages | 24 |
| Journal | Journal of the Mechanics and Physics of Solids |
| Volume | 54 |
| Issue number | 4 |
| Early online date | 15 Dec 2005 |
| DOIs | |
| Publication status | Published - Apr 2006 |
| Externally published | Yes |
Bibliographical note
The public access to the Qhull program initially made available by the Geometry Center at the University of Minnesota–Twin Cities is also greatly appreciated. In addition, the authors wish to thank Professor K. Bhattacharya and two anonymous reviewers for their helpful comments on an earlier version of the paper.Funding
The work reported here was partially funded by a grant from the AFOSR and by a contract from L & L Products. These supports are gratefully acknowledged.
Keywords
- Irregular cell shapes
- Non-uniform strut cross-sectional areas
- Open-cell foams
- Structure-property relations
- Voronoi tessellation