Table of Contents
ISRN Mechanical Engineering
Volume 2011, Article ID 570140, 10 pages
http://dx.doi.org/10.5402/2011/570140
Research Article

Equivalent Elastic Modulus of Asymmetrical Honeycomb

Department of Mechanical Engineering, Tokyo University of Science, Kagurazaka 1–3, Shinjuku-ku, Tokyo 162-8601, Japan

Received 19 March 2011; Accepted 9 April 2011

Academic Editors: J. Botsis, A. Tounsi, and X. Yang

Copyright © 2011 Dai-Heng Chen and Kenichi Masuda. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The equivalent elastic moduli of asymmetrical hexagonal honeycomb are studied by using a theoretical approach. The deformation of honeycomb consists of two types of deformations. The first is deformation inside the unit, which is caused by bending, stretching, and shearing of cell walls and rigid rotation of the unit; the second is relative displacement between units. The equivalent elastic modulus related to a direction parallel to one cell wall of the honeycomb is determined from the relative deformation between units. In addition, a method for calculating other elastic moduli by coordinate transformation is described, and the elastic moduli for various shapes of hexagon, which are obtained by systematically altering the regular hexagon, are investigated. It is found that the maximum compliance 𝐢 𝑦 𝑦 | m a x and the minimum compliance 𝐢 𝑦 𝑦 | m i n of elastic modulus 𝐢 𝑦 𝑦 in one rotation of the ( π‘₯ , 𝑦 ) coordinate system vary as the shape of the hexagon is changed. However, 𝐢 𝑦 𝑦 | m a x takes a minimum and 𝐢 𝑦 𝑦 | m i n takes a maximum when the honeycomb cell is a regular hexagon, for which the equivalent elastic moduli are unrelated to the selected coordinate system, and are constant with 𝐢 1 1 = 𝐢 2 2 .