PSI - Issue 28

Stylianos Anastopoulos et al. / Procedia Structural Integrity 28 (2020) 2132–2141 S. Anastopoulos et al. / Structural Integrity Procedia 00 (2019) 000–000

2135

ii)

tensile perturbation in the y-direction gives

 

11



eff E E

  eff

(5)

0

22

22



0



 

11

33

(6)





eff

eff



 

 



0

0

12

23



22

22





0

0

( eff eff v v v  

23 eff

) / 2

(7)

21

And iii)

tensile perturbation in the z-direction gives

 

33

(8)



eff E E

  eff

0

33

33



0

 

 

11

22





(9)

eff

eff

 

 





0

0

31

13

33

33





0

0

( eff eff v v v  

eff

) / 2

(10)

31

32

For the numerical method, a Representative Volume Element was used in order to achieve homogenization. The RVE was subjected to three tensile (Fig. 4) and three shear loadings (Fig. 5) using the Epilysis © solver software. From these 6 loadings, strain – stress results were obtained. Those were in turn used to calculate the effective modulus of elasticity of the composite.

Fig. 4 RVE under the three different tensile loadings