On the convergence of the iterative self-consistent embedded cell model

• We study and prove the convergence of the iterative embedded-cell method.
• An Interface Affected Zone (IAZ) hypothesis is proposed.
• IAZ provides an insight into the nature of the convergence error.
• We provide a lower bound estimate for the amount of iterations till convergence.

The convergence behavior of the recently developed iterative self-consistent embedded cell method for the determination of the effective properties of composite materials has not been analyzed in detail up to now. In this contribution, we prove it to be unconditionally stable and to converge to the effective macroscopic value ± small error. This error is found to be inherent to the method and is attributed to the presence of the direct interface between the micro- and macro-world in the same model. Furthermore, we derive a lower bound of the amount of iterations till convergence and show it to be insensitive to the above error.