In-plane elastic constants and strengths of circular cell honeycombs

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Abstract

The in-plane elastic modulus, Poisson’s ratio, brittle crushing strength and plastic yielding strength of honeycombs with hexagonally packed circular cells are analyzed theoretically. The resulting theoretical expressions are compared with the numerical results obtained from a series of finite element analyses for circular cell honeycombs with various relative densities, leading to a good correlation. It is also found that the in-plane mechanical properties of circular cell honeycombs are significantly affected by the ratio of cell-wall thickness to cell radius. Though the elastic constants along the two principal directions of circular cell honeycombs are the same, the brittle crushing strength and plastic yielding strength along the two principal directions are not identical. Furthermore, the in-plane mechanical properties of circular cell honeycombs are compared to those of regular hexagonal honeycombs with straight and uniform-thickness cell walls to evaluate their microstructural efficiency.

Introduction

The mechanical properties of cellular materials are described well by the cell-wall-bending model with uniform-thickness and straight cell walls proposed by Gibson and Ashby [1], and are found to be dependent on their relative density, cell morphology and the material properties of the solid from which they are made. Pre-existing microstructural imperfections, such as non-uniform cell-wall cross-section, non-straight profile of cell walls, missing cells and non-periodic microstructure resulting from manufacturing, are typically observed on real cellular materials, and their mechanical properties can be affected significantly [2], [3], [4]. Two-dimensional honeycombs with hexagonally packed circular cells were developed with enhanced mechanical properties. The mechanical properties of circular cell honeycombs under in-plane uniaxial stresses were analyzed theoretically, numerically and experimentally [5], [6], [7], [8], [9], [10], [11]. It was found that circular cell honeycombs are promising for use as load-bearing materials.

However, in previous studies [9], [10], [11] the contact surface between any two adjacent circular cells was oversimplified compared to that of real circular cell honeycombs. At the same time, the stored elastic strain energies of each circular cell caused by axial and shear forces were neglected in analyzing the in-plane mechanical properties of circular cell honeycombs. As a result, the existing theoretical expressions for describing the in-plane mechanical properties of circular cell honeycombs derived by Chung and Waas [9] are valid only when their relative density is small. In this paper, the in-plane mechanical properties of circular cell honeycombs are analyzed theoretically using a unit cell model with a more realistic cell geometry. The validity and accuracy of the resulting theoretical expressions are verified by conducting a series of finite element analyses.

Section snippets

Theoretical analysis

A model honeycomb with hexagonally packed circular cells is on the x1  x2 plane as schematically illustrated in Fig. 1. Within the model honeycomb with a unit thickness along the x3 direction, the cell radius and cell-wall thickness of each circular cell are R1 and t1, respectively, and any two adjacent circular cells are perfectly connected. The thickness of point contact between any two adjacent circular cells in Fig. 1, Fig. 2 t1, is different from that of overlapped surface contact, t1,

Finite element analysis

To check the accuracy and validity of the theoretical expressions derived from the unit cell model, a series of finite element analyses (FEAs) were conducted using a commercial finite element package ABAQUS. A repeating single-cell parallelogram, as illustrated in Fig. 5a, was utilized to numerically analyze the mechanical properties of circular cell honeycombs. In the finite element analyses, CPS8R (8-node bi-quadratic plane stress) plane stress elements were used. To simulate a circular cell

Elastic modulus

When t1/R1 approaches zero for a circular cell honeycomb with a much lower relative density, Eq. (13) is reduced to:EEs=1.396ρρs3

The above equation is similar to the following theoretical result provided by Chung and Waas [9] for hexagonally packed circular cell honeycombs with slightly different surface-contact areas between any two adjacent circular cells:EEs/(1-νs2)1.396ρ/ρs1-3/2π(ρ/ρs)3

It should be noted that Eq. (13) can be reduced to Eq. (19) if the contributions of axial and shear

Conclusions

The elastic constants, brittle crushing strength and plastic yielding strength of circular cell honeycombs are derived theoretically from unit cell models, and then verified numerically by conducting a series of finite element analyses. The differences between theoretical expressions and FEA numerical results are less than 2% even the relative density of circular cell honeycombs is increased up to 0.12. The theoretical expressions derived here can thus be utilized to calculate the elastic

Acknowledgment

The financial support of the National Science Council, Taiwan, ROC, under Contract Number: NSC 96-2628-E-006-228-MY3 is gratefully acknowledged.

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