Issue 49

A. Bendada et alii, Frattura ed Integrità Strutturale, 49 (2019) 655-665; DOI: 10.3221/IGF-ESIS.49.59

In-plane (x, y) parameters

Out-of-plane parameters

3          sin h t l 

h

 

   

2

z E :Young modulus in z direction

x E :Young modulus in x direction

t       

E

l



l    

E

S

3



cos

S

2 sin cos     h l l   



3

y E :Young modulus in y direction



t G h l       

cos

cos sin sin    

t E

        

yz G :Shear modulus in yz plane

S

S

h l l



sin

2



l





h

 

sin     

h

sin 2 1 cos l    

3

t         l

t  

xy G :Shear modulus in xy plane

xz G Shear modulus in xz plane

l



l

G

E

2        l h    l   

S

S

2 1 cos h 

 





h





l



h l

 

   

E E E E

2 sin sin cos   



y

s 

Poisson’s ratio xy 

Poisson’s ratio yz 

z

2 cos sin sin h l       

x

s 

Poisson’s ratio yx 

Poisson’s ratio xz 

 



z

Table 1 : Equivalent elastic properties of honeycomb core of Gibson.

Numerical approach In this study, an elaborated ANSYS program makes it possible to build the RVE model consisting of 40 cells of dimensions 166.27 x l mm  , 86.4 y l mm  , 8.8 z l mm  , as shown in Fig. 2, the material properties of the core are presented in Tab. 2. The numerical homogenization method consists of series of simulations carried out on the RVE.

3 / Kg m

Density (  )

2700

Poisson’s ratio Young modulus

0.34

69000 MPa

Figure 2 : Initial RVE model.

Table 2 : Material properties.

The RVE model is meshed using shell element. Three extension simulations in the directions x , y , z were applied on the RVE to estimate Young’s moduli x E , y E , z E and Poisson’s ratios xy  , yz  , xz  . Young’s moduli are determined using the tensile behavior relations ships of uniaxial linear elasticity with simple transformations:

i F E S

i 

i i   

(1)

i

657