PSI - Issue 37

6

Anastopoulos G. Stylianos et al. / Procedia Structural Integrity 37 (2022) 485–491 Anastopoulos G Stylianos et al/ Structural Integrity Procedia 00 (2019) 000 – 000

490

80

4100

difference between calculated and targeted modulus of elasticity

target effective modulus calculated effective modulus of elasticity

4080

60

4060

40

4040

20

Difference [%]

4020

0

Effective modulus of elasticity [MPa]

0 20 40 60 80 100 120 140 160 180 200 4000

0 20 40 60 80 100 120 140 160 180 200 -20

(a) (b) Fig. 4 (a) Effective modulus of the optimization for 200 maximum iterations and maximum objective value 1 MPa; (b) difference between calculated and target effective modulus of the optimization case for 200 maximum iterations and maximum objective value 1 MPa. Iterations [-] Iterations [-]

80

4100

target effective modulus calculated effective modulus of elasticity

difference between calculated and targeted modulus of elasticity

60

4080

40

4060

4040

20

Difference [MPa]

4020

0

Effective modulus of elasticity [MPa]

4000

0 100 200 300 400 500 600 700 800 900 1000 -20

0 100 200 300 400 500 600 700 800 900 1000

(a)

(b)

Number of iterations [-]

Number of iterations [-]

Fig. 5 (a) Effective modulus of the optimization case for 1000 maximum iterations and maximum objective value 1e-4 MPa; (b) difference between calculated and target effective modulus of the optimization case for 1000 maximum iterations and maximum objective value 1e-4 MPa. 5. Discussion According to the presented methodology, the volume fraction required to attain a target effective modulus was successfully calculated with great accuracy. The success of the present procedure is demonstrated in Figs 6a and 6b. Every point of the diagrams represents an optimization case with a specific maximum number of iterations. As depicted in Fig. 6a the calculated effective modulus approximates the target effective modulus when the cycles of the optimization is close to 1000. In case convergence is achieved after the competition of 200 up to 1000 cycles, the accuracy of the calculated homogenized modulus is more than 99,9 % (Fig. 6a). Additionally, the CNTs volume fraction approaches the experimental volume fraction in case the optimization has 1000 maximum iterations (Fig. 6b). In conclusion, the present method is a reliable approach that may be applied to identify the optimal material synthesis of a high number of different types of composites, even of composites containing a high number of inclusions families with different shapes or components.