An accelerated Fast Fourier Transform algorithm for nonlinear composites

A fast numerical algorithm to compute the local and overall responses of nonlinear periodic composite materials is developed. This alternative formulation allows us to improve the convergence of the existing method of Moulinec and Suquet [1], [2]. In the present method a nonlinear elastic (or conducting) material is replaced by infinitely many locally linear thermoelastic materials with moduli that depend on the values of the local fields. This makes it possible to use the advantages of an algorithm developed by Eyre and Milton [3] which demonstrates faster convergence. The method is applied to compute the local fields as well as the effective response of nonlinear conducting and elastic periodic composites.