ELASTIC-MODULI OF 2-DIMENSIONAL COMPOSITES WITH SLIDING INCLUSIONS - A COMPARISON OF EFFECTIVE-MEDIUM THEORIES

We study the effective elastic moduli of two-dimensional (2D) composite materials containing sliding circular inclusions distributed randomly in the matrix. To simulate sliding we introduce a sliding parameter, which in two limiting cases gives perfect bonding and pure sliding boundary conditions. We evaluate elastic moduli using four effective medium theories; the self-consistent method, the differential scheme, the Mori-Tanaka method and the generalized self-consistent method. In this paper we focus on two aspects: one is the study of the effect of interface on the elastic constants of composites and the other is a comparison of the results from effective medium theories for the cases of both sliding and perfect bonding. In the discussion we use the recently-stated Cherkaev-Lurie-Milton theorem, which gives general relations between the effective elastic constants of 2D composites. We also compare the results from the effective medium theories with those from numerical simulations.