Effects of cell irregularity on the elastic properties of 2D Voronoi honeycombs

doi:10.1016/S0022-5096(00)00046-6

Journal of the Mechanics and Physics of Solids

Volume 49, Issue 4, April 2001, Pages 857-870

https://doi.org/10.1016/S0022-5096(00)00046-6 Get rights and content

Abstract

Foams are more and more widely used in different areas. Most available mechanical models are usually based on idealised unit cell structures, and are not able to account for the natural variations in microstructure which are typical for most foam structures. The objective of this work has been to investigate how the cell irregularity affects the elastic properties of 2D random foams. We have constructed periodical random structures with different degrees of irregularity, and applied finite element analysis (FEA) to determine their effective elastic properties. The results indicate that, the more irregular the 2D random foams, the larger will be their effective Young's modulus and shear modulus, and the smaller will be their bulk modulus at a constant overall relative density. However, for varying degrees of irregularity, the foams remain isotropic and the Poisson's ratios are very close to 1. Both Young's modulus and Poisson's ratio of random Voronoi honeycombs having different degrees of regularity α, decrease gradually with increasing relative density ρ.

Introduction

Low-density foams are more and more widely used in engineering due to their promising mechanical, thermal, electrical and acoustical properties. The mechanical properties of foam materials have been studied extensively, and can be found in several comprehensive surveys (Weaire and Fortes, 1994; Gibson and Ashby, 1997; Evans et al., 1998). Theoretical models of two-dimensional cellular solids are usually based on a regular unit cell, which allows the derivation of structure-property relations (Gibson and Ashby, 1997; Zhu and Mills, 2000). A significant limitation of the unit-cell modelling approach is that it does not account for the natural variations in microstructure. Although several methods have been developed to consider the effects of microstructural variability on mechanical properties of foams, computer modelling of more realistic foam structures allows us to control the average microstructural features of the models and investigate how microstructural regularity affects the structure-property relations. In this paper, we have constructed 2D periodical random foams and performed finite element analysis to determine the effective elastic properties. The objective has been to investigate how cell irregularity affects the elastic properties of 2D random foams.

Section snippets

The construction of periodic honeycombs

Cellular solids are usually formed by the nucleation and growth of cells. If all cells nucleate randomly in space at the same time and grow at the same linear rate, the resulting structure is a Voronoi honeycomb (for 2D) or a Voronoi foam (for 3D).

The first step is to generate n nuclei in a square area A₀. A coordinate system is chosen, with the origin at the bottom left corner of the square, the x-axis in the horizontal direction and the y-axis vertical. Nucleation points are created in the

General methodology

ABAQUS software was used in the FEA analysis. Each cell wall is modelled, depending on its length, by 1–3 Timoshenko beam elements (ABAQUS element-type B22). With the assumption that all cell walls have the same thickness t, the relative density of the Voronoi honeycomb is specified by $ρ= t∑_{i=1}^{N} l_{i} L^{2},$ where l_i are the cell wall lengths and N is the total number of cell walls.

Young's modulus of the cell walls, E_s, was set to 1.0, and Poisson's ratio to 0.3. To determine Young's moduli and Poisson's

Discussion

Finite element models of periodic Voronoi honeycombs were developed to investigate the effects of cell regularity on the elastic properties. The analyses were limited to models having low relative density (ρ⩽0.25) and having struts of uniform thickness. Our results indicate that, both the effective Young's modulus and shear modulus increase, and the bulk modulus decreases with increasing irregularity for random Voronoi honeycombs having low relative density. However, for varying degrees of

Conclusions

Finite element models of random Voronoi honeycombs have been developed to study how cell irregularity affects the elastic properties. Periodic samples and periodic boundary conditions were used, and the analyses were limited to models having relative density less than 0.25. The results show that, the effective Young's modulus and shear modulus of a low-density periodic random Voronoi honeycomb could be 25 percent larger than those of a perfect honeycomb having the same relative density. The

Acknowledgments

The authors wish to thank Dr. Anthony Cunningham of Huntsman Corporation for his continued support of, and intellectual contributions to this work.

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Effects of cell irregularity on the elastic properties of 2D Voronoi honeycombs

Abstract

Introduction

Section snippets

The construction of periodic honeycombs

General methodology

Discussion

Conclusions

Acknowledgments

J. Mech. Phys. Solids

Progr. Mater. Sci.

Int. J. Mech. Sci.

Cellular Solids: Structure and Properties

The nonlinear elastic behaviour of polydisperse hexagonal foams and concentrated emulsions

J. Rheol.