PSI - Issue 61

Ahmet Arda Akay et al. / Procedia Structural Integrity 61 (2024) 138–147 A.A. Akay et al. / Structural Integrity Procedia 00 (2024) 000–000

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(a) Single inclusion

(b) Multi inclusion

Fig. 6: Macroscopic stress-strain curves of two RVEs consisting single and multi inclusions, involving cohesive interface model with di ff erent iteration starting conditions, obtained for periodic displacement boundary condition (PBC)

Table 2: Investigated models

Cases Maximum Error Maximum Iteration M1 10 − 5 400 M2 10 − 7 800 M3 10 − 3 200 M4 10 − 9 1600

Fig. 7: Macroscopic stress-strain curve of RVE consisting multi inclu sions, involving cohesive interface model with di ff erent iteration stopping parameters obtained for periodic displacement boundary condition (PBC)

3.2.2. Comparison study based on di ff erent maximum iteration and maximum error criteria This study examines the situation where the interface starts from the condition in the previous loading step (BEM hist) in the interface equilibrium iterations. The e ff ect of the change of maximum error and a maximum number of iterations, presented in Equation (13), on the macroscopic behavior of the randomly distributed multi-inclusion RVE is compared. Each inclusion is divided into 30 elements and the outer edges of the RVE are discretized into 50 elements. Four di ff erent cases given in Table 2 are investigated. In Figure 7, the results obtained for all cases are presented. The red-colored curves are the results obtained with the MFTHE and Mori-Tanaka approaches presented in the literature. The black-colored curves are the results obtained with the boundary element method in this study. No major di ff erences are observed between our boundary element results. As expected, the case M3 displays a slightly di ff erent behavior than the other cases, in which the tolerances are low.

4. Conclusion

This study presents the boundary element formulation for elasticity problems and the implementation of bound ary conditions within the boundary element method for homogenization purposes. Following this accomplishment, we have delved into the critical domain of interface modeling, which holds a pivotal role in the mathematical repre sentation of all heterogeneous materials. The interface model introduced in this study is adopted from the research