Effects of cell irregularity on the high strain compression of

1359-6454/02/$22.00 2002 Published by Elsevier Science Ltd on behalf of Acta Materialia Inc. PII: S 1 3 5 9 - 6 4 5 4 ( 0 1 ) 0 0 4 0 2 - 5
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H.X. Zhu, A.H. Windle / Acta Materialia 50 (2002) 1041–1052
Mechanical models are usually based on models of cell structure. Unit cell models have proved to be useful in understanding some of the key aspects of the mechanical behaviour of foams [1–10] and, as long as the mechanical properties of the solid are known, this method can give the full response of the foam or the honeycomb subjected to a stress or a strain. Based on the regular Kelvin cell structure, Zhu et al. [4] derived all the three independent elastic constants as functions of the Young’s modulus of the solid material, the relative density of the foam and the shape of the cell edge cross-section, and found that such structure is nearly isotropic. They [4,5] also found that, if a Kelvin foam is compressed in the
Keywords: Foams; High strain compression; Computer simulation; Microstructure
1. Introduction Low-density open-cell foams are widely used in engineering applications such as lightweight structural sandwich panels or components designed for absorbing impact energy. Research works on the mechanical properties and deformation mechanisms of foams have received wide attention [1].
* Corresponding author. E-mail address: ahwl@ (A.H. Windle). 1 Present address: Polymer and Colloids Group, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UK.
Abstract The high strain compression of low-density open-cell polymer foams has been modelled by finite element analysis. We used a Voronoi method to generate periodic structures with different degrees of randomness of the cell size and shape, then to investigate the influence of this randomness on the response of Voronoi open-cell foams to high strain compression. It is found that, although the reduced compressive stress–strain relationship and the Poisson’s ratio vary in different directions for individual samples, the models are, on average, isotropic. A highly irregular foam has a larger tangential modulus at very low strains and a lower effective stress at high compressive strains than a more regular foam. The geometrical properties were investigated and used to predict the compressive stress–strain relationships for random open-cell foams with different degrees of cell regularity. For irregular low density foams, strut bending and twisting (the “springs-in-parallel” model) dominate the mechanical response at low strains and strut buckling (the “springs-in-series” model) becomes the main deformation mechanism at large compressive strains. 2002 Published by Elsevier Science Ltd on behalf of Acta Materialia Inc.
[111] direction, strut twisting plays almost the same important role as strut bending does in the foam deformation. However, most cellular materials usually have random cells. Thus, despite their proven utility, unit cell models do not accurately represent the microstructure of most real foams. To better represent the microstructure, random Voronoi technique and finite element analysis have been used in modelling the mechanical properties of foams [11–15]. Shulmeister et al. [12] have modelled foam structure by random Voronoi cells using finite element analysis. They started from regular bcc and fcc lattice nuclei distributions, subsequently gave the nuclei positions an increasing random offset and constructed the random structure using the Voronoi procedure. However, all the struts at the boundary are normal to the boundary face giving a much stiffer structure. Their simulated compressive stress–strain relationship [12] for random open-cell foams is about 6 times larger than the theoretical results [5] for a regular Kelvin foam. Also, as their model is not periodic, they could not have been able to apply periodic boundary conditions in the FEA analysis. As is well known, boundary conditions can greatly influence the mechanical response of a structure, and even mixed boundary conditions tend to underestimate the mechanical properties of foams [13–15]. In our previous work [14], we found that the periodic Voronoi foams are averagely isotropic, and the cell regularity has a strong effect on the elastic properties of Voronoi foams. The aim of this work is to determine the influence of disorder in foam cell size and shape on the high strain compression of open-cell foams. We have constructed 3D periodic random structures with different degrees of irregularity, and applied finite element analysis to derive the compressive stress–strain relationships. The geometrical properties of random foams have also been investigated and used to predict the reduced compressive stress–strain relationships for foams with varying degrees of regularities. 2. The definition of the regularity 2.1. The construction of periodic random Voronoi foams Cellular solids are usually formed by nucleation and growth of cells. If all cells nucleate randomly