PSI - Issue 28

8

Author name / Structural Integrity Procedia 00 (2019) 000–000

Yakubu Kasimu Galadima et al. / Procedia Structural Integrity 28 (2020) 1094–1105

1101

Table 1. Result of homogenization using both FEM and PD for the purpose of model validation

Effective Quantity

FEM

PD

1.6244x10 0.5257x10 0.000x10 0.5257x10 1.6244x10 0.000x10 0.000x10 0.000x10 0.4781x10 1.4543x10 11 11 11 11 11 11 11 11 11 11

1.7062x10 11 0.6417x10 11 0.0112x10 11 0.5808x10 11 1.7994x10 11 0.5968x10 11 0.0015x10 11 0.0040x10 11 1.8117x10 11 1.5084x10 11

1111 D 1122 D 1112 D 2211 D 2222 D 2212 D 1211 D 1222 D 1212 D

Effective elastic modulus ���

5.2. Effect of inclusion shape To study the effect of inclusion shape on the effective properties of composites, a composite with long parallel fibres of different shapes is considered. The material parameters of the matrix and fibre are as follows: 200GPa fiber E  , 1/ 3 fiber   , 100GPa matrix E  , 1 / 3 matrix   . The problem is solved for fibre volume fraction 0.4 f  and the RVE is subjected to a PBC. The deformed shape of the RVE for different inclusion shape is shown in Fig. 4 and the effective modulus and Poisson’s ratio for different inclusion shapes are presented in Table 2. A graph of perimeter of shape against the number of sides is shown in Fig. 5.

Table 2. Effective properties

Shape

Area

No of Sides Perimeter Poisson Ratio Effective modulus

Circle

0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4

1

2.242 2.883 2.530 2.411 2.354 2.322 2.303 2.280

0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34

1.33x10 11 1.37x10 11 1.34x10 11 1.35x10 11 1.35x10 11 1.33x10 11 1.32x10 11 1.24x10 11

Triangle

3 4 5 6 7 8 9

Square

Pentagon Hexagon Heptagon Octagon Decagon