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

2134

2.2. The Multi-Step Homogenization Method Adhering to the multi-step homogenization method, the composite is decomposed into "grains", with each grain containing one inclusion family and the matrix (Fig. 2). The inclusions in each family have the same material properties, aspect ratio, and orientation. In the first step homogenization is performed in each grain using the Mori Tanaka model; in the second step the Voigt formulation is used to compute the properties of the overall composite.

Fig. 2 Multi Step Homogenization Method representation (Abaqus documentation)

Fig. 2 Representative Volume Element

2.3. Modelling Composites Using Numerical method The representative volume element (RVE) is a sample of the material microstructure that the macroscopic body consists of as shown in Fig. 3. In order to be actually representative, the size of the RVE is of great importance. A definite perturbation is applied to calculate a definite material property. Two procedures may be followed, one for the isotropic case with two independent parameters ( E , v ) and one for the transverse isotropic case with five independent parameters ( E 11 , v 12 , E 22 , n 23 , G 12 ). For the isotropic case: i) tensile perturbation in the x-direction gives

 

11

(2)



eff E E

  eff

0

11

11



0

 



22

33





(3)

eff

eff



 

 



0

0

21

13



11

11





0

0

( eff eff v v v  

eff

) / 2

(4)

12

13