Abstract—In the study of honeycomb crushing under quasi- static loading, two parameters are important, the mean crushing stress and the wavelength of the folding mode. The previous theoretical models did not consider the true cylindrical curvature effects and the flow stress in the folding mode of honeycomb material. The present paper introduces a modification on Wierzbicki’s model based on considering two above mentioned parameters in estimating the mean crushing stress and the wavelength through implementation of the energy method. Comparison of the results obtained by the new model and Wierzbicki’s model with existing experimental data shows better prediction by the model presented in this paper. Keywords—Crush strength, Flow stress, Honeycomb, Quasi- static load. I. INTRODUCTION ONEYCOMB cellular structures, due to their light weight and high energy-absorbing capability, have been used extensively as energy absorbers or cushions to resist external loads. Previous studies on the crushing behavior of honeycomb structures included the early work reported by McFarland, who developed a semi-empirical model ,in which the failure modes was local buckling, to predict the crushing stress of hexagonal cell structures subjected to axial loading [1]. A subsequent paper by Wierzbicki gave an important analysis for the out-of-plane crushing resistance of hexagonal-cell structures, and presented results in a form convenient for design purposes. Comparisons of results from the analysis were made with experimental results. The analysis did not consider the effects of curvature and flow stress and material assumed to be rigid-perfect plastic [2].It has been discussed in [3] that considering the flow stress in the analysis of thin walled structures, leads to a better description of the material behavior. Subsequently mechanical properties of honeycomb structures in the lateral directions were investigated both analytically and experimentally by Gibson et al. [4], and Gibson and Ashby [5]. Various experimental and numerical studies on quasi- static and dynamic crush behaviors of honeycombs under out-of-plane compressive, multiaxial or combined loads have been reported [6-11]. For example Wu and Jiang [6] focused on the investigation of the crushing phenomena of M. Zarei Mahmoudabadi is with the Mechanical Engineering Department of Amirkabir University of Technology, Tehran, Iran (e-mail: m_zarei@aut.ac.ir). M. Sadighi is with the Mechanical Engineering Department of Amirkabir University of Technology, Tehran, Iran (corresponding author to provide phone: +98 21 6454 3448; fax: +98 21 6641 9736 ; e-mail: mojtaba@ aut.ac.ir). honeycomb structures under both quasi-static and dynamic loading conditions considering the effects of cell dimension, material strength and number of cells under loading. In [7] it is shown that the theoretical values in [6] must be corrected and their right values are computed. In this article, through implementation of energy method based on Wierzbicki’s model and considering curvature effects and flow stress, crushing strength and wavelength have been determined and evaluated by experimental results of [6]. II. FOLDING ELEMENT DEFINITION Because of the regular and symmetrical structure of the hexagonal honeycomb, it can be assembled from one folding element consisting of two angle elements joined together forming an angle of D 120 (Fig. 1). These two angle elements are bonded by means of an adhesive whose strength is smaller than that of the material itself, so during the crushing process, a part of the bond adjacent to the vertical edge is broken and the two angle elements are partially torn off. Fig. 1 Folding element of hexagonal honeycomb The global collapse mode of an angle element is shown in Fig. 2 that consists of (a) four plane trapezoidal elements moving as rigid bodies, (b) two sections of cylindrical surfaces that have an inextensional mode and only absorb the energy that is required for forming the two plastic hinges above and below them, (c) two sections of conical surfaces bonded by two propagating straight hinge lines, and (d) a section of a toroidal shell which undergoes an extension. The folding mode for the angle element shown in Fig. 2 is a one degree of freedom system whose geometry can be described either by the crushing distance δ , or the angle of rotation of the common walls in a folding element α , or the horizontal displacement of point D, defined as s (see Fig. 3). A Study on Metal Hexagonal Honeycomb Crushing Under Quasi-Static Loading M. Zarei Mahmoudabadi, and M. Sadighi H World Academy of Science, Engineering and Technology International Journal of Mechanical and Mechatronics Engineering Vol:3, No:5, 2009 575 International Scholarly and Scientific Research & Innovation 3(5) 2009 scholar.waset.org/1307-6892/9992 International Science Index, Mechanical and Mechatronics Engineering Vol:3, No:5, 2009 waset.org/Publication/9992