Numerical homogenization of nonlinear composites with a polarization-based FFT iterative scheme

This paper presents an extension of the polarization based iterative scheme in the context of nonlinear composites. The polarization based algorithm, used for computing the effective properties of composite materials, converges independently of the value of the contrast between the phases. However the application of this scheme in the initial form is restricted to the case of linear elasticity. In this paper we propose some modifications of this iterative scheme in order to deal with the most general case of nonlinear constituents. Two applications are proposed to show the capability of the method. The first concerns a composite made up of a power-law type nonlinear matrix with rigid inclusions while in the second illustration we deals with the determination of the macroscopic yield surface of porous plastic materials.