PSI - Issue 28

Saiaf Bin Rayhan et al. / Procedia Structural Integrity 28 (2020) 1892–1900 Author name / Structural Integrity Procedia 00 (2019) 000–000

1895

4

direction at the face x  is obtained by normalizing with the face area. y  and y  are obtained similarly. Then the entries for 11 21 , D D and 31 D in the stiffness matrix are obtained. By repeating the steps for all other load cases, all the entries for the stiffness matrix are obtained. The stiffness matrix is inverted to obtain the compliance matrix as follows. x x L  is integrated.

(7)

  1 C D      

Finally, the engineering constants are computed from the following relationship.



yx   

1

                 

                   

0 0 0

zx

E E E

x

y

z









1

xy

zy

0 0 0

E E E

x

y

z



1 0 0 0

xz    

yz

E E E

(8)

  C

 

x

y

z

1

0 0 0

0 0 1

G

xy

0 0 0 0

0 1

G

yz

0 0 0 0 0

G

xz

3. Material Definition To calculate the stiffness of composite materials, elastic constants of fiber and matrix must be defined. It is generally assumed that fibers are orthotropic where the matrix is isotropic. To compare the stiffness results, the following material properties are adopted from the literature (Younes et al. (2012)), Table 1 and 2.

Table 1. Elastic moduli of fibers [7]

E 11 , GPa

E 22 , GPa

υ 12

υ 23

G 12 , GPa

G 23 , GPa

Fiber material

Carbon

232

15

0.279

0.49

24

5.034

Polyethylene

60.4

4.68

0.38

0.55

1.65

1.51

Table 2. Elastic moduli of matrix [7]

Matrix material

E, GPa

υ

Epoxy (With Carbon) Epoxy (With Polyethylene)

5.35 5.5

0.354 0.37

4. RVE geometry and boundary condition The first step of homogenization is the modeling of RVE. For unidirectional composite materials, three different RVE can be selected to calculate the stiffness of the material (Fig. 1). Then a blocked mesh is generated and a periodic boundary condition is employed by default (Ansys Inc. (2018)). In case the mesh is not periodic, non-periodic