Simplification of the (n+1)-phase model and its extension to non linear behavior

Abstract The proposed paper is a procedure aimed to predict the overall behavior of non linear n-layered inclusion-reinforced materials from the behavior of their constituents. For that purpose, the homogenization technic relies on the concept of Morphologically Representative Pattern (M.R.P). The M.R.P used in this paper is a n-phase composite sphere. The modified method based on the second-order moment of the strain field presented by P. Ponte Castaneda and P. Suquet has been used here. The three main points of this paper are, on the one hand, a revisit of the (n+1)-phase model and, on the other hand, the derivation of the second-order moment of the strain field in the particular case of the Generalized Self Consistent Scheme named (n+1)-phase model and its use to predict the behavior of composite materials made of inclusions embedded in a non linear matrix.