Issue 49

A. Bendada et alii, Frattura ed Integrità Strutturale, 49 (2019) 655-665; DOI: 10.3221/IGF-ESIS.49.59 656 identification of the core and the skins material behaviours, and secondly an adequate kinematic model to obtain a reasonable computational cost. For reasons of characterizing the honeycomb core, the cellular core is replaced by a quasi- homogeneous medium, and the sandwich theory can be adopted to analyze the sandwich structure [1], In 1958 Kelsey first provided a set of equations for xz G and yz G based on energy methods applied on the honeycomb cell walls[2]. Gibson and Ashby extended this analytical approach to drive all the nine orthotropic parameters [3]. Other improvement of theorical model proposed by Masters and Evans for predicting the in-plane elastic stiffness of honeycomb cores based on deformation of honeycomb cells [4]. Xu et al presented another investing approach [5]. Chen and Davalos improved an analytical model to calculate the modulus and interface constraints for extension problems [6]. A new analytical method to analyze the out-of-plane stiffness of honeycomb cores based on the modified laminate theory proposed by Meraghni et al [7]. Hu and al presented a complete review of the various Kinematics and theories concerning the sandwich composite modeling [8] Experimental methods on testing the elastic properties of honeycomb core have been developed. Young’s moduli in the thickness direction were determined by compression tests [9]. Cunningham et al proposed a new measurement technique for estimating the shear strain in a totally enclosed core [10]. Saito et al considered an aluminium honeycomb sandwich panel as an orthotropic Timoshenko beam for identifying the corresponding parameters by solving the least squares problems by a non-linear optimization method [11]. Finite element model of e Representative Volume Element (RVE) of more complicated honeycomb sandwich cores [12] can be constructed to predict the elastic equivalent properties [13, 14]. In the past decades, many researchers have studied the vibration of sandwich structures. Kerwin proposed a new theoretical model which is developed for the damping in sandwich structure [15]. By varying the thickness and materials of the skins, it’s possible to obtain a desired performance, particularly high strength and stiffness- to-mass ratio [16-18]. The objective of present paper is to carry out a comparative study on numerical and experimental techniques capable of predicting the mechanical parameters of honeycomb core. For initial prediction; the analytical Gibson and Ashby formulations are used for determining the constants parameters that will be compared with numerical homogenization results. Once the honeycomb core is homogenized, the whole sandwich panel constituted of three elastic layers: isotropic/orthotropic/isotropic was created using the finite element code ANSYS and numerical modal analysis was performed. In order to validate the accuracy of the numerical approach, experimental modal analysis was carried out. According to the important error between numerical-experimental results, the inaccurate initial elastic constants need to be improved. In reality, the aluminum honeycomb core contains the double cell wall which is not taken into account in the initial RVE. So, the in-plane parameter xy G and out-of plane parameters z E , yz G were selected to be estimated again by a new RVE which takes into consideration the double thickness wall. Comparison between the measured and the new computed eigenvalues and the corresponding eigenmodes shows the good agreement and minimized error which confirms the improved properties and the 3D model of panel that will be used for the next numerical analysis to predict the influence of the delamination on the structure rigidity. H OMOGENIZATION PROCEDURE The classical Gibson method he analytical expressions (Tab. 1) used for the elastic properties prediction of honeycomb core which is assimilated to an orthotropic material, are based on the important research of [3] where S E and S  present the Young modulus and Poisson’s ratio of the cell material. The unit cell of the honeycomb core is a regular hexagon (Fig.1) of dimensions: 0.08 t mm  , 11.085 h mm  , 0 30   , density of 3 29 /m Kg and W-oriented configuration. Figure 1 : Unit regular hexagon cell of honeycomb with simple wall. T