| Abstract: | This paper addresses the convergence characteristics of an iterative solution scheme of the Neumann‐type useful for obtaining homogenized mechanical material properties within an RVE. The analysis is based on the idea of “equivalent inclusions” and, within the context of stress/strain analysis, allows modeling of elastically highly heterogeneous bodies with the aid of discrete Fourier transforms. Within the iterative scheme the proof of convergence depends critically upon the choice of an appropriate, auxiliary stiffness matrix, which also determines the speed of convergence. Mathematically speaking it is based on Banach's fixpoint theorem and only results in necessary convergence conditions. However, for all cases of elastic heterogeneity that are of practical importance convergence can be demonstrated. |
