PSI - Issue 28

Wenxuan Xia et al. / Procedia Structural Integrity 28 (2020) 820–828 Author name / Structural Integrity Procedia 00 (2019) 000–000

827

8

3.4. Cell with multiple microscopic voids A defected matrix cell with four microscopic voids positioned under a repetitive pattern as shown in the Fig. 3(b) is considered. Properties of such cell is given in Table 7.

Table 7. Material properties of the matrix cell with multiple voids. Material name Elastic modulus E ( Pa ) Poison Ratio v

Volume fraction

Matrix

2x10 9

0.3

0.8743363

Void

-

-

0.0314159 x 4

The 2D effective stiffness tensor is obtained as

9 1.9152877 10 5.7728186 10 9.1710183 10 5.7728186 10 1.9152877 10 5.9270207 10 Pa 9.1710183 10 5.9270207 10 6.6818474 10                             C The effective material properties are then evaluated as given in Table 8. Table 8. Effective material properties of the matrix cell with multiple voids. � ( Pa ) � ( Pa ) �� ( Pa ) Four voids 1.7412907x10 9 1.7412907x10 9 8 6 * 8 9 6 6 6 8

(18)

��

6.68184743x10 8

0.30033991

4. Conclusion Present study illustrates the feasibility of performing RVE homogenization on composite cells containing fibers and defect such as voids using ordinary state based peridynamics. The enforcement of periodic boundary condition in peridynamics homogenization is also being demonstrated. The homogenization result for fiber-reinforced composite using peridynamics RVE homogenization shows good agreement with finite element homogenization method.

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