IP: 5.10.31.151 On: Fri, 23 Jun 2023 09:12:59 Copyright: American Scientific Publishers Delivered by Ingenta Materials Express Article Copyright © 2016 by American Scientific Publishers All rights reserved. Printed in the United States of America 2158-5849/2016/6/461/012 doi:10.1166/mex.2016.1341 www.aspbs.com/mex Effect of poisson’s ratio on functionally graded cellular structures Qing-Tian Deng 1, ∗ and Zhi-Chun Yang 2 1 School of Science, Chang’an University, Xi’an, 710064, China 2 School of Aeronautics, Northwestern Polytechnical University, Xi’an, 710072, China ABSTRACT Poisson’s ratio is one of the key parameters of material properties, and it could directly decide deformation and distribution of stress in materials and structures. In this paper, effects of Poisson’s ratio on static mechanical behaviours of functionally graded structure are investigated in three different kinds of elastic models. Configu- rations of unit cell and finite element (FE) models are utilized to analyze macro cellular structures under static compression loads. The properties of graphite sheet structure in micro-nano scaled structures are calculated. The unit cell varies from hexagonal to re-entrant configurations while Poisson’s ratio varies from positive to negative values gradually. The combined Fourier series-Galerkin method is introduced to solve beam struc- ture subjected to transverse loads. In the numerical results, it is found that Poisson’s ratio exhibits appreciable effects on bearing capacity, which indicates static properties can be improved by optimal design of cell shape material distribution and computational methodology. Keywords: Static Response, Functionally Graded Structure, Poisson’s Ratio, Cellular Structure. 1. INTRODUCTION Functionally graded materials (FGMs), are special com- posites whose composition varies continuously as a func- tion of a position along thickness of structure to achieve a required function. They have been widely applied in engi- neering fields including aircrafts, defense industries, space vehicles, and biomedical sectors. Functionally graded cel- lular structures (FGCSs) are one novel material, in which the variations of cell size and shape result in the function- ally variation of elastic properties of the cellular structure. Examples of FGCSs in nature are bamboo, banana peel and elk antler. 1 2 Previous studies on impact resistance and energy absorption of FGCSs have shown their poten- tial for creating impact resistant structures and cushion- ing materials. 3 4 Cui et al. 5 suggested that functionally graded foam exhibit superior energy absorption compared to uniform foam with equal mass. Ajdari et al. 6 studied ∗ Author to whom correspondence should be addressed. Email: [email protected] the crushing behavior and energy absorption of honeycomb made of FGM using the finite element (FE) simulation, which provides new insight into the behavior of engineered and biological cellular materials. Materials usually experience lateral contraction under axial tensile load, which possess a positive Poisson’s ratio (PPR). Negative Poisson’s ratios (NPR) are being considered as an unusual mechanical property, which are theoretically permissible and have been observed in some real materials. Functionally graded negative Poisson’s ratio (FGNPR) structures are one advanced material. Advanced material with NPR, such as honeycombs, foams and poly- mer materials, have been investigated by many researchers due to their special functions and various applications. Usually, structures with NPR can be obtained through a geometric modification of conventional hexagonal honey- comb, which leads to a re-entrant hexagon cell shape. For honeycombs, NPR property can be obtained due to the geometric layout of unit cell, in which cells undergo elongation both parallel and perpendicular to the direction Mater. Express, Vol. 6, No. 6, 2016 461
Effect of poisson’s ratio on functionally graded cellular structures
Jun 23, 2023
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