A computational scheme for linear and non-linear composites with arbitraryphase contrast

A numerical method making use of fast Fourier transforms has beets proposed in Moulinec and Suquet (1994, 1998) to investigate the effective propertie s of linear and non-linear composites. This method is based on an iterative scheme the rate of convergence of which is proportional to the contrast be tween the phases. Composites with high contrast (typically above 10(4)) or infinite contrast (those containing voids or rigid inclusions or highly non -linear materials) cannot be handled by the method. This paper presents two modified schemes. The first one is an accelerated scheme for composites wi th high contrast which extends to elasticity a scheme initially proposed in Eyre and Milton (1999). Its rate of convergence varies as the square root of the contrast. The second scheme, adequate for composites with infinite c ontrast, is based on an augmented Lagrangian method. The resulting saddle-p oint problem involves three steps. The first step consists of solving a lin ear elastic problem, using the fast Fourier transform method. In the second step, a non-linear problem is solved at each individual point in the volum e element. The third step consists of updating the Lagrange multiplier. App lications of this scheme to rigidly reinforced and to voided composites are shown. Copyright (C) 2001 John Wiley & Sons, Ltd.